Talk:Centrifugal force/Archive 10

all these forks
While I admit that I haven't looked at them in extreme detail, all these disambiguated "centrifugal force" articles, as far as I can tell, are discussing the same thing, just from different perspectives (or perhaps different philosophical viewpoints). That's not good; it's bordering on the policy/guideline against POV forks. Of course if there's enough to say about a philosophical perspective on a concept, then that perspective can get its own article with a link/summary in the main article, but there should be only one main article, which should summarize all current viewpoints. These badly need a merge into a single centrifugal force article.

I'm getting the impression that you may be having problems with a particular editor with a strong POV, though I haven't looked in enough detail to be sure which editor or which POV. If that's the case then WP ways need to be explained to him; he shouldn't be allowed to perpetuate the current mess, which is not a good situation for anyone. --Trovatore (talk) 22:50, 10 September 2008 (UTC)


 * Uh huh. How about you look at it in extreme detail, and get back to us if and when you actually have an informed point of view?- (User) WolfKeeper (Talk) 23:05, 10 September 2008 (UTC)


 * You also might like to read WP:NOTADICT which explains why two or more things that happened to be termed Centrifugal force do not automagically get to go in the same article. The relevant part is: 'Topics with the same or similar titles for different things are found in different articles'.- (User) WolfKeeper (Talk) 23:09, 10 September 2008 (UTC)


 * If -- and I am not persuaded that this is the case -- the different articles are actually discussing different things, rather than different ways of looking at the same thing, then why is it that centrifugal force redirects here, rather than being a disambiguation page? If this article is in fact the primary among the four (which I would think it would be) then it should just be named centrifugal force, with a hatnote for the dab page. If, on the other hand, the four articles discuss truly different things and none of them is clearly primary, then centrifugal force itself should be dab page. --Trovatore (talk) 23:23, 10 September 2008 (UTC)
 * Your proposal about disambiguation makes sense.
 * However, combining pages doesn't look like a good idea. History shows that centrifugal force is a magnet for confused debate, partly because there are conflicting terminologies for it, and half the world believes only one or the other of the two. Partly also because everyone has an intuitive notion of centrifugal force that gives it a reality not easily supplanted by abstract arguments about "frames of reference". The present set-up is a device to limit this unending debate that historically has recycled every few months as different new-comers to the page raise the same old issues.
 * The page divisions mean that debate focuses upon more specific issues, and that some of the arguments that arise again and again can be dealt with in a succinct manner by reference to specific examples within the limited context of the page where debate flares.
 * It may evolve that this separation of topics has not ended the problem, but so far so good.
 * It isn't inconceivable that some such sacrifices are necessary concessions to the reality of an encyclopedia that is modifiable by anyone. No-one wants to ride herd on the education of the English-speaking world via Wikipedia Talk pages.Brews ohare (talk) 14:53, 11 September 2008 (UTC)
 * Just for the record, I don't consider this to be in any way a sacrifice, the Wikipedia's rules actually do push you towards this layout.- (User) WolfKeeper (Talk) 15:06, 11 September 2008 (UTC)
 * I'd add to these remarks that the different pages do discuss different aspects of "centrifugal force". For example Centrifugal force (rotating reference frame) discusses examples based upon observations of a general nature in frames rotating about fixed axes, while Centrifugal force (planar motion) describes centrifugal force as it arises in the specific observation of a particle traveling a planar trajectory from the viewpoint of various observers that are using different types of coordinate systems. There is some common text of a general nature, for the sake of easy reading, but it is pretty minimal. Brews ohare (talk) 15:35, 11 September 2008 (UTC)

I have some sympathy for the idea that a single article could probably encompass all of the more-or-less related concepts that go under the name of "centrifugal force". Admittedly, there are some genuinely distinct concepts that go by that name... such as the reactive force versus the inertial force. But these two concepts are not entirely un-related (even though they are distinct).

As an aside, I recently found an scholarly paper written in 1898 in which the author ranted about the mis-use of the term "centrifugal force", and he had compiled about a dozen references, tabulating how many defined it "correctly" (in his opinion), and how many defined it "incorrectly". (His idea of "correct" was the reactive force definition.) I just mention this to point out that people have had issues with this for a long time, and it isn't just in Wikipedia talk pages that this has been an on-going topic of discussion/debate.

Recognizing that the reactive force really is a distinct definition of the term, I think most editors found it acceptable (though perhaps not all considered it desirable) to segregate that into a separate article. But then the really tricky part begins, because even within the "fictitous/inertial force" definition, there are different approaches that can be taken, different views of the subject, ultimately arising from different conceptions of the very foundations of science (intuitive, informal, and specialized versus abstract, rigorous, and general). The literature is mixed with regard to how these different views are presented, and naturally the intuitive/informal/specialized approach is to be found in the majority of texts, simply because the majority of texts are written at an introductory level and tend to rely on the intuitive informal and specialized approach to things, because it's simpler.

To be honest, I think the main reason we've been unable to consolidate the entire subject of centrifugal force (within mechanics), or even just the inertial/fictitious force part of the subject, into a single article is that some editors feel very strongly (just as did the guy back in 1898) that there is only ONE "correct" usage and interpretation of the term, and they don't want to sully their article with any hint or suggestion that there might be any other permissible usages within mechanics. Unfortunately the literature contains a variety of treatments of the subject, usually in sources that are not really focused on this as their main subject, and we have to try to derive a reasonable overall article from these somewhat disparate sources. I think it could be done (probably in less space than the current article), but only if the editors decided that the subject is large and contains many distinct but aspects, and it isn't necessary (or appropriate) to denigrate all but one particular aspect.Fugal (talk) 07:27, 12 September 2008 (UTC)
 * The different pages present different aspects of the term "centrifugal force", not different interpretations or points of view. Specifically, centrifugal force (rotating reference frame) is restricted to discussion of centrifugal force as it appears in reference frames rotating about a fixed axis, while centrifugal force (planar motion) treats centrifugal force as it occurs in the observation of a particle in planar motion (a restricted example) as seen from several different non-inertial frames. It also might be noted that centrifugal force (planar motion) presents two terminologies, not "one correct usage". Discussion of that page probably should appear on its discussion page, not here. Brews ohare (talk) 12:25, 12 September 2008 (UTC)

By the way, the forked article about "planar" motion is, I believe, very mis-named, because there is no need for any restriction to planar motion. There have been some mis-understandings expressed on these discussion pages about things like whether there is even such a thing as three-dimensional polar coordinates, and this kind of view seems to underly the mis-naming of that fork. Also there has been a persistent resistance to the introduction of the fully general formalism that emcompasses all aspects of fully general motion (as opposed to rotation about a fixed axis, which is really more of a text book exercise, as compared with most real applications that involve general motion), with fully general systems of reference. Within that context, the entire subject of centrifugal force is very simple, unified, and coherent, but without making use of that formalism (which requires a level of abstraction that is unfamiliar to some), it splits into seemingly disjoint subjects, hence all the forking. It occurs to me that perhaps what's needed is an article specifically on the subject of the many meanings and interpretations of the term "centrifugal force" in dynamics. This could be the main article on centrifugal force, with branches to sub-articles where individuals could expound at greater length on their own preferred views of the subject.Fugal (talk) 07:27, 12 September 2008 (UTC)


 * The article centrifugal force (planar motion) does treat planar motion, and the math on that page is restricted to that case. Of course, more general, non-planar trajectories along 3-dimensional curves could also be treated by extending the formalism to include things like torsion. But it is not a misnaming of the page to say what it actually describes.: Discussion of that page probably should appear on its discussion page, not here.
 * A more general treatment, e.g. based upon concepts of differential geometry and general relativity would be an interesting page in itself, but, as Fugal has pointed out, it would be consulted mainly by specialists because that kind of background is not general, restricted to mathematicians and physicists with specialized training.
 * By broadening the discussion to treat fictitious forces in general, rather than the very particular centrifugal force, a very general treatment for the case of particle motion in both inertial and non-inertial frames employing Cartesian coordinates is provided at fictitious force. It does not, however, treat general relativity and curvilinear coordinate systems. Brews ohare (talk) 12:39, 12 September 2008 (UTC)


 * We shouldn't confuse the introduction of general curvilinear coordinates with general relativity. I think there's common agreement among all the editors that this article (or these articles) are restricted to classical (i.e., pre-relativistic) dynamics. Within that context, general curvilinear coordinates are the most comprehensive, and when the discussion is framed in those terms, the entire subject becomes unified, and one sees that what had seemed to be distinct concepts are really just different ways of looking at exactly the same thing. This is why the disagreement over dictionary versus encyclopedia is so ambiguous, because what seems to be different definitions from one point of view are really just different points of view from another point of view.Fugal (talk) 13:40, 12 September 2008 (UTC)


 * Unification of viewpoint seems to me a bit more complicated than using curvilinear coordinates. Math connected to general formulas and their simplification to apply to specific coordinate systems is unrelated to the physics, which is concerned with relating the results of observers in disparate states of motion (inertial cf. non-inertial) regardless of what coordinate system they choose to employ. I'd agree that "just the same thing" can be described in various coordinate systems. However, the fictitious forces and the classification of the various contributions as "centrifugal", "Coriolis", or "Euler" depends strongly upon the observer's state of motion (e.g. are they rotating? and about what axis, oriented how?) and not upon their selection of coordinates (Cartesian, arc-length, etc.) to describe what they see. Perhaps a detailed statement of just what could be unified and just how that could be done might be provided? Brews ohare (talk) 18:11, 12 September 2008 (UTC)

It's already been provided (several times, by at least two different editors), so I'm unsure if provided it again will be productive. The other editor commented that you didn't seem to be really trying to understand, and I'd have to endorse that impression. However, I'll think about possibly posting a detailed summary statement of the unified view, maybe later today if I get around to it. But before you would be in a position to understand it, I think you need to clarify some misunderstandings that you've expressed in your latest message.

You refer to "the results of observers in disparate states of motion", but observers don't have results. Measurements have results. This may seem like an unimportant quibble, but it isn't. It’s vitally important to be clear and precise. What you most likely mean is something like "the results of measurements performed by observers in disparate states of motion". But as soon as you state this explicitly, it is apparent that what you’re describing is nothing other than a coordinate system (or perhaps an equivalence class of coordinate systems, i.e., a system of reference, or a reference frame). In order to quantify the measured (i.e., observed) positions and motions of a particle, there must be a system of measure, which extends over the region of interest, and this is tantamount to a system of coordinates.

The Wikipedia article on Reference Frames, which I gather was written mostly by you, contains the your characteristic focus on “observers”, as if there is some kind of anthropomorphic quality of an “observational frame of reference” distinct from a plain old “frame of reference” (system or systems of coordinates). The source that you cited for this point of view is a quaint little introductory book entitled “How and Why in Basic Mechanics” by A. Kumar and Shrish Barve. That book does indeed refer to observers, but please (please!) make note of the following words from that very book, which it presents in the form of a dialogue between a professor and a clueless newbie:


 * I used words like 'relative to some observer'. The word 'observer', however, can be very misleading. It gives an impression that we are talking of a person looking at the phenomena, making appropriate measurements and possibly comparing them with those of another person. I suggest you banish this picture from your mind.


 * I am surprised. What is wrong with it?


 * Physics deals with numbers—measurements cairied out by impersonal Instruments. The person behind the instruments is irrelevant for physics; that is what one means by objectivity in science. So it is best to deseribe phenomena without invoking the notion of an observer...


 * We replace the image of an 'observer' by an impersonal abstract object; we simply imagine a frame of long rigid rods extending out from a point (origin) in space in three independent directions… [Please note that this amounts to the stipulation of rectilinear Cartesian coordinates, so all subsequent statements are restricted to this sub-class of coordinate systems. You may recall that I previously advised you to check your sources for stipulations of this kind.]  Thus. for example, the frame of reference of a train is an abstract aitifact which has the same motion as thal of thc train. Therefore, instead of saying, for example, that the trajectory of a stone dropped out of a running train is a straight line for a train observer and a parabola for a ground observer, it is better to say that the trajectory is a straight line in the train's frame of reference and a parabola in the ground's frame of reference.

I realize this is somewhat repetitive, because I've explained this very same thing to you before, but your response was to disregard it because I'm "amazing ignorant". So my hope is that showing you that even your own source, which you've cited as the source for your belief in the paramount important of the concept of an "observer", actually goes to great lengths to disavow that of view, and to corroborate what I told you.

Now, having said all this to explain why these concepts can only be formulated in terms of coordinate systems, it's obviously true that we could choose to work only with quantities (such as absolute acceleration) that are invariant, regardless of the system of reference, but on this basis there are no fictitious forces. The introduction of fictitious forces entails a decision to forego absolute coordinate-independent acceleration, and to work with a coordinate-dependent acceleration. Hence the very subject that we're dealing with requires us to treat coordinate-dependent quantities.

The main point is that your alleged bifurcation between "mathematical descriptions" and "physical descriptions" does not exist. It won't be possible to make much progress with this article (or with any of the other articles that you've edited) until you relinquish the idea of such a bifurcation. From the standpoint of Wikipedia, your bifurcation is novel narrative, and is unsupporeted even by your own cited references (as shown above). I challenge you to cite a single reputable reference that distinguishes between mathematical descriptions and physical descriptions. If you're unable to find such a reference, I think you should stop making that point of view the basis for your editing of Wikipedia articles.Fugal (talk) 17:52, 13 September 2008 (UTC)

Response to Fugal
You refer to "the results of observers in disparate states of motion", but observers don't have results. Measurements have results. This may seem like an unimportant quibble, but it isn't. It’s vitally important to be clear and precise.Fugal (talk) 17:52, 13 September 2008 (UTC)
 * "Observer" is a technical term, but it does not imply any particular coordinate system or any specific measurement apparatus. It is not "anthropomorphic" and is a term in good standing in the literature. The quote you provide suggests the term "observer" be avoided only because of certain misconceptions related to the carry-over of popular meaning to a context where a technical meaning exists. The authors use the term "observer" themselves in answers to the student on the same page. I can produce quotes employing "observer" in a technical sense that already are present in various Wiki articles (see Frame of reference) in case you missed them. A googlebook of phrase "inertial observer" provides 647 books with this term. Brews ohare (talk) 00:21, 14 September 2008 (UTC)

Now, having said all this to explain why these concepts can only be formulated in terms of coordinate systems, it's obviously true that we could choose to work only with quantities (such as absolute acceleration) that are invariant, regardless of the system of reference, but on this basis there are no fictitious forces. The introduction of fictitious forces entails a decision to forgo absolute coordinate-independent acceleration, and to work with a coordinate-dependent acceleration. Hence the very subject that we're dealing with requires us to treat coordinate-dependent quantities.Fugal (talk) 17:52, 13 September 2008 (UTC)
 * Well, we are totally at odds here. The adoption of a non-inertial frame automatically introduces fictitious forces, regardless of any subsequent adoption of a particular coordinate system. Moreover, the definition of "absolute acceleration" probably will involve the definition of an inertial frame of reference, although this term is sometimes applied as follows: if a point P in frame ʕ is fixed relative the frame, the absolute acceleration of point Q in frame ʕ is its acceleration relative to P. What is your meaning?
 * I'd note that physical quantities like vectors and tensors are commonly considered to refer to entities that exist independent of coordinate systems, although coordinate systems can be introduced to make their manipulation more mechanical. The velocity vector of a particle, as an example, is coordinate-system independent, but it is not independent of the velocity of the frame of reference: it is "observer's state-of-motion" dependent in a manner that is independent of the observer's choice of coordinate system; for example, independent of the observer's choice for orientation of their coordinate system.
 * Perhaps you would wish to enter a detailed debate on this point? Brews ohare (talk) 00:32, 14 September 2008 (UTC)

The main point is that your alleged bifurcation between "mathematical descriptions" and "physical descriptions" does not exist.Fugal (talk) 17:52, 13 September 2008 (UTC)
 * This point needs further discussion, I'd guess. For example, the "physical description" provided by the phrase "the kid is sliding down the water slide" could be expressed mathematically in terms of the position s along the slide at time t or as the coordinates of the kid (x, y, z) at time t, or, instead of time, in terms of the distance the moon has orbited during the slide, or how far a certain beam of light traveled. That would be several mathematical descriptions of the same physical event. What is only "alleged" in this bifurcation? The mathematical description is many-to-one in relation to the physics. Brews ohare (talk) 19:40, 13 September 2008 (UTC)

Response to Fugal (cont'd)
You say the quote I provided from your source (e.g., “it is best to deseribe phenomena without invoking the notion of an observer... I suggest you banish this picture from your mind”) doesn’t dismiss the term “observer”. You go on to say that the quote disapproves of certain misconceptions related to the term, and that is certainly true. Unfortunately, it is precisely those misconceptions to which you have fallen prey, and which you are promoting in your edits here. For example, you say "The adoption of a non-inertial frame automatically introduces fictitious forces, regardless of any subsequent adoption of a particular coordinate system." That’s a partially true statement, but to the limited extent that it’s true, it supports my position rather than yours. A frame is an equivalence class of coordinate systems,Fugal (talk) 02:18, 14 September 2008 (UTC)
 * The statement that a frame is "an equivalence class of coordinate systems" is interesting. Question 1: What are the rules for membership in this class? Question 2: Any references for this? Question 3: Is it more natural or easier to talk of "an equivalence class of coordinate systems" than to say that an observer has a choice of coordinate systems; actually any of the standard mathematical choices (curvilinear, polar, Cartesian, …); and whichever is chosen, it must adopt the observer's state of motion inasmuch as it travels with the observer? Thus, the "equivalence class" is simply all possible mathematical coordinate systems that travel with the observer, no? Brews ohare (talk) 04:48, 14 September 2008 (UTC)

and by selecting a particular frame we are partially specifying a system of measure which, combined with the pretense that the second derivative of spatial position with respect to time represents the true absolute acceleration in Newton’s law, does indeed entail the treatment of the remaining components of the true acceleration as fictitious forces.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * I believe you are reverting to the "coordinate definition" of fictitious force here:that is, the approach that drags all contributions to the acceleration except the second derivative to the force-side of the equation; the physical or "state-of-motion" definition (appropriate to the discussion of fictitious force in the setting of inertial vs. non-inertial frames) does not do this, and does not imply all terms other than the second time derivative are fictitious. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

But this contradicts your position for two reasons:

First, this is already a blatently “mathematical” development, because we are choosing to pretend that the absolute acceleration of an object equals a particular mathematical function of our chosen coordinates (remember, the choice of a frame specifies the absolute shape of the time axis), despite the fact that we know full well that this function of our coordinates does not equal the absolute acceleration. It amounts to pretending that a family of curved lines are straight, even though we know they are really curved. This occurs because the inertial basis vectors at a given location in space change with time. Fugal (talk) 02:18, 14 September 2008 (UTC)
 * This all may be true of the "coordinate system" approach, but I regard that, as apparently you do also, as simply a device of mathematical convenience. The approach basic to the centrifugal force article is the "state-of-motion" approach that states that inertial forces appear only in non-inertial frames. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

Second, we have so far only partially specified a system of measure, by narrowing the choices down to the members of a certain equivalence class of mutually stationary coordinate systems. Within this class there are a variety of spatial coordinate systems, for some of which the inertial basis vectors at a given instant of time change with spatial position. The selection of these systems of measure entails additional fictitious forces in exactly the same sense that the specification of the temporal variation in the inertial basis vectors does.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * Here I'd disagree. The distinction between fictitious forces in the "state-of-motion" sense and in the "coordinate-system" sense is lost, and the two usages are being smeared together. To repeat, "state-of-motion" fictitious forces are always zero in an inertial frame, while "coordinate-system" fictitious forces may or may not be, and in general curvilinear coordinate systems are non-zero in inertial frames. Brews ohare (talk) 06:06, 14 September 2008 (UTC)

Again, this is because we choose to pretend that the absolute acceleration of an object equals a particular mathematical function of our chosen coordinates, despite the fact that we know full well that this function of our coordinates does not equal the absolute acceleration. Just as before, it amounts to pretending that a family of curved lines are straight, even though we know they are really curved.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * Here we return to the "coordinate-system" definition of fictitious forces. Brews ohare (talk) 05:58, 14 September 2008 (UTC)

Some of the spatial systems of measure within a given frame consist of rectilinear Cartesian coordinates, in which the basis vectors at a given instant of time do not change with spatial position. As has been shown by explicit quotations, the text books and papers that neglect the spatial variation in basis vectors do so by stipulating that they exclude from consideration any spatial coordinate systems whose basis vectors change with position. They usually do this tacitly, by saying that a spatial system of measure consists of three rectilinear Cartesian axes. (I’ve given you the quotations in which two of your own sources make this stipulation.) On this restricted and asymmetric basis, it is of course correct to say that fictitious forces are uniquely determined by the choice of a reference frame. But the point is that this is a restricted and asymmetric basis, because spatial coordinate axes need not be absolutely straight, just as temporal axes need not be absolutely straight.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * Again, the restriction to Cartesian coordinates does simplify things, inasmuch as all the phony terms in the fictitious force due to the spatial and temporal variation of the unit vectors go away. However, I have no issue with your gripes over what I consider a mere mathematical gimmick in the "coordinate-system" terminology.

References have been cited which present the unrestricted and symmetrical treatment, in which we do not stipulate in advance that curved temporal axes are allowed but curvilinear spatial axes are excluded. This gives a unified and symmetrical treatment of the entire subject in general, which I can outline for you (again) if you wish.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * I regret prevailing upon you, but yes, I'd like that outline. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

You say “That would be several mathematical descriptions of the same physical event. What is only "alleged" in this bifurcation? The mathematical description is many-to-one in relation to the physics.” The bifurcation you've alleged is between different choices from among the many possible mathematical descriptions of events. There is nothing absolute about fictitious forces. They are a purely artificial concept that arises when we choose a particular system of coordinates (or a class of systems) and then decide that if our chosen coordinate axes are curved we are going to pretend they are straight, which we do by pretending that a particular mathematical function of our coordinates represents the true acceleration of an object (even though we know it doesn’t).Fugal (talk) 02:18, 14 September 2008 (UTC)
 * As I have tried to explain above, I do not subscribe to the system you denigrate, and so will not try to support it. Brews ohare (talk) 04:48, 14 September 2008 (UTC)

You allege a bifurcation between two different sets of mathematical descriptions, those that are familiar to you, and those that aren’t. You call the former descriptions “physical” and the latter “mathematical”. My point is that this bifurcation represents nothing but your personal prejudices and the limitations of your understanding, rather than any real bifurcation of the conceptual subject, and moreover that this bifurcation leads to the "forking" in the subject, which several editors consider undesirable.Fugal (talk) 02:18, 14 September 2008 (UTC)
 * I do not understand these remarks. I suspect they stem from supposing I am arguing for the "coordinate-system" mathematically convenient approach, which I do not support. I would agree we do not understand each other, but laying all the blame upon my limitations is ungraceful, to say the least.
 * The distinction between "physical descriptions" and "mathematical descriptions" is not as you describe it. The physical description in my first example is "sliding" (familiar to me and to you) and the mathematical descriptions consist of describing the succession of space-time points using various different choices of variables. The physical description in my second example is the observed vector velocity of a particle, a physically distinct entity that depends upon the state-of-motion of the observer, but not upon the observer's coordinate system. These examples provide  very simple, clear distinctions, attributable to neither prejudice nor ignorance, I'd say.
 * The real issue probably comes down to the distinction between the two usages for fictitious force, what I have termed "state-of-motion" and "coordinate-system" fictitious forces. You have argued before that there is no such distinction, and maybe that is where matters rest? Is that the issue? Is that the only issue? Are we back to the discussion at Fugal's positions? Brews ohare (talk) 06:26, 14 September 2008 (UTC)

To make it handy, here is the earlier summary:

Fugal's positions

 * Fugal:My position is that [the mathematical terminology for certain terms in the acceleration of a body as viewed in curvilinear coordinates] is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature.


 * Brews-ohare:My view is that it is not a viewpoint, but a different use of terminology. That these terms constitute a different usage is shown (in part) by the fact that these terms are an artifact of the coordinate system, and therefore appear in every state of motion, every frame of reference, in both inertial and non-inertial frames. That is not true of centrifugal force as defined in this article. As a different subject, a reference to this alternative usage is all that is needed. I believe Wolfkeeper has the same view. Brews ohare (talk) 14:41, 12 August 2008 (UTC)
 * Fugal: The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force.
 * Brews_ohare: Here is only one citation (of many from googlebooks) that contradicts this remark: Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 15:55, 12 August 2008 (UTC)
 * Fugal:Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer.
 * Brews_ohare: My point exactly: however, centrifugal force (as used in this article) does depend on the state of motion of the observer. In Newtonian mechanics, a state of acceleration (a state of motion) identifies a non-inertial frame of reference. A citation: "If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics . Brews ohare (talk) 15:37, 12 August 2008 (UTC)
 * Fugal:Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations".
 * Brews_ohare:In fact there are two meanings for fictitious force: one depends on the state of motion of the observer (see above) and one is a mathematical act of poetic license, applying picturesque language to certain terms that arise in the acceleration when calculated in curvilinear coordinates, without regard for the observer's state of motion. Are we going 'round and 'round here?!? Here are two quotes relating "state of motion" and "coordinate system":

and from J. D. Norton: Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", while the mathematical version of "fictitious force" has exactly the opposite dependencies, indicates that two different ideas are referred to by the same terminology. The present article is about one of these two ideas, not both of them. Brews ohare (talk) 06:30, 14 September 2008 (UTC)


 * The core of the entire problem here is your novel narrative related to "state of motion" as opposed to "coordinate system". Note that your reference says a frame specifies a state of motion at every point; it does not say that a state of motion at a single point specifies a frame. The reason it doesn't say this is because it's not true, but unfortunately this is the proposition on which you've based your entire view of this subject.


 * Look, as Tim Rias and I have both explained to you - repeatedly, at great length, and in several different ways - a state of motion does not suffice to unambiguously establish a system of measure over a region of space and time. Your intuitive notion that a "state of motion" (e.g., of an "observer") possesses an unambiguous extension to surrounding regions is simply incorrect. None of the references you repeatedly quote gives any support to this misunderstanding of yours. When I read any of your cited references, I think "yes, exactly right", and when I read any of Tim Rias's comments I think "yes, exactly right", and when I read any of the rest of the vast literature on this subject I think "yes, exactly right", but when I read any of your comments my reaction is "No, completely and utterly wrong". Why do you suppose this is?


 * I'm really not sure how any progress can be made here. You appear (to me) to be either unable or unwilling to let go of the mistaken idea that a state of motion possesses an unambiguous "physical" mapping from one place to another (an idea that you associate with an "observer", as if the word "observer" somehow magically enables two plus two to equal five). This imaginary unambiguous mapping is what you call physical, and all other mappings are what you call mathematical. As I said before, this false dichotomy simply represents the limitations of your understanding. I've explained what is wrong with your beliefs in great detail, (as have others), and have tried expressing it in various ways, hoping that one of these ways would turn on the light bulb for you, but nothing seems to help. How do you suggest we proceed?Fugal (talk) 07:33, 14 September 2008 (UTC)

Proposed procedure for resolution

 * 1) Move the discussion to Talk:Centrifugal force (planar motion).
 * 2) Further details on a proposal for resolution of differences are there. Brews ohare (talk) 17:02, 14 September 2008 (UTC)

That page has been split off from this "rotating reference frame" page so as not to be fixated on the rotating reference frame simplifications, but unfortunately you have based your discussion on that page explicitly on the text in the section entitled (wait for it...) "Rotating Reference Frames" in Stommel and Moore. You ignore the section where that reference addresses centrifugal force in the more general context.Fugal (talk) 17:25, 14 September 2008 (UTC)
 * What have I ignored by these authors that is pertinent? Brews ohare (talk) 17:37, 14 September 2008 (UTC)


 * The part where they discuss centrifugal force in stationary systems of reference.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * Any specific items? Any page numbers? Brews ohare (talk) 21:03, 14 September 2008 (UTC)


 * Yes indeed. The items and page numbers that were presented months ago when the reference was first introduced, and the quotes explicitly contradicting your views were presented.Fugal (talk) 17:25, 14 September 2008 (UTC)


 * Your reply contains no data. It is a vague reference to the past, where my recollection is that you quoted Stommel and Moore out of context, and were corrected. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

And you (yet again) insist on inserting your own original research about a distinction between "coordinate-system fictitious forces" and "state of motion fictitious forces", which is not contained in any of the references you cite in support of it. As has been pointed out previously by others, the very fact that you find it necessary to coin these neoligisms is prima facie evidence that you are constructing novel narratives. Fugal (talk) 17:25, 14 September 2008 (UTC)
 * I am simply distinguishing between different usages. That different usages are used in the literature is supported by direct quotations. Brews ohare (talk) 17:37, 14 September 2008 (UTC)
 * The explanation for what you call "different usages" has been given to you repeatedly, by multiple editors. It is simply different contexts, e.g., once someone has stipulated that they are restricting their spatial coordinate systems to the class of rectilinear Cartesian coordinates, the statements limited to curved time axes then are correct, but they are conditional statements, within the specified context. So your novel narrative and neologisms, both of which violate Wikipedia policy, are not appropriate.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * It is not a question of context: formulas for exactly the same situation produce different results for fictitious forces. These formulas are derived in the subsection proposed for critique, and are clearly different. You refuse to engage. Brews ohare (talk) 21:03, 14 September 2008 (UTC)


 * Once again, your conception of what consistites "the same" or "different" "situations" is fallacious. Fictitious forces are not absolute entities, they are dependent on the chosen system of reference (as well as on the arbitrary decision to conflate the identities of certain mathematical functions of those terms of reference). I do not refuse to engage, and I have engaged, but I do decline to be repetitive, and in particular to continue presenting explanations to issues concerning the foundations of physics over and over again to someone who has demonstrated an unshakeable determination to avoid understanding. Look, Wikipedia is not intended to be a venue where original researchers can come to extort discussions from experts on their pet ideas.Fugal (talk) 23:31, 14 September 2008 (UTC)
 * We're not talking foundations of physics here. We're talking about failure to critique planar motion observed from a rotating frame, which embodies at a very simple and concrete level the issues at stake in a context where rant could be avoided and real ideas discussed. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

Also, the naming of that forked article (planar motion) is itself part of your novel narrative, because the whole point of the other page was to write about the LESS restricted view of the subject, whereas by giving it the bizzare name "planar motion" you are implying that the page presents a MORE restricted view. And so on. All this has been explained to you over and over (and over) again, and not just by me.Fugal (talk) 17:25, 14 September 2008 (UTC)
 * Since I wrote the other page entirely, its purpose is obviously what I have made it. Brews ohare (talk) 17:37, 14 September 2008 (UTC)


 * Please see the Wikipedia policy on "ownership". You do not own any article, nor are you the sole arbiter as to the purpose or content of any article. Multiple editors here have suggested that you seem to be violating the Wikipedia policy in your attitude of "ownership", as exemplified by the statement above.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * Fugal, that you would distort my remarks in this way is unconscionable. What I said was that your notion about what was the original purpose of this page is erroneous because I originated the page and selected the subject. That does not preclude anyone editing the page. What is the matter with you? Brews ohare (talk) 21:03, 14 September 2008 (UTC)


 * It isn't a distortion. Once again, you mis-understand. I was referring to your re-direct of my question, when I asked if you had any suggestions for how we should proceed, after both I and another editor had explained to you, over and over and over, the general unified view of this subject. You re-directed the discussion of THAT topic to your "planar motion" page, despite the fact that THAT topic has nothing to do with "planar motion".Fugal (talk) 23:31, 14 September 2008 (UTC)
 * And how does the subject of "redirection" relate to the misconception you raised about "the whole point of the other page was to write about the LESS restricted view of the subject". Can't you stay on topic? Brews ohare (talk) 13:00, 15 September 2008 (UTC)
 * From your perspective, the "matter with me" is that I decline to engage with an "original researcher" on the subject of his own original research. Such individuals should post their ideas on Usenet discussion groups. I realize it's tempting for an original researcher to come to Wikipedia and try to engage experts and professionals in discussions of their novel ideas, but that isn't the purpose of Wikipedia.Fugal (talk) 23:31, 14 September 2008 (UTC)
 * Well, as an "expert and professional" I suppose that "discussion of novel ideas" is one of your forté's. But we are just talking about two uses of the same terminology, something more prosaic. Brews ohare (talk) 13:00, 15 September 2008 (UTC)

My proposal for making progress is for you to focus your efforts on this rotating reference frame page, and for the "planar motion" page to be renamed something like "Centrifugal force (general)", and for that page to be edited by people who understand the general concept of centrifugal force, which includes as a subset - but is not limited to - the "rotating reference frame" aspects. At some point, the redundancy will become clear, and I'd expect the "rotating reference frame" page to be removed, but in the mean time it may serve a useful purpose, allowing the editing of the "general" page to proceed on a reasonable basis.Fugal (talk) 17:25, 14 September 2008 (UTC)
 * Well, these "other people" can write "Centrifugal force (general)" if they can be rounded up. There is no need to re-write or re-name the existing page on planar motion, as that is a particular topic with its own discussion.Brews ohare (talk) 17:37, 14 September 2008 (UTC)
 * There is, in my judgement, no need or justification for a separate fork to a page on "planar motion", because it is contained as a subset of the full spatial motion discussion. On the other hand, the content of the page which you named "planar motion" really isn't planar motion, as anyone who cares to take a look can see for themselves. (Note that you yourself just moments ago recommended re-directing all discussion of the more general view of centrifugal force to that page, so you are obviously aware that the content of that page is not "planar motion".)Fugal (talk) 19:33, 14 September 2008 (UTC)
 * There is presently no "full spatial motion discussion". There is no reason at present to change the specific and limited discussion pages on "rotation about a fixed axis" and "planar motion" to become such a general page: a general page can stand on its own whenever it comes along.
 * You say "the page which you named "planar motion" really isn't planar motion". That statement is hogwash: look at the math. It all applies to planar motion of a particle, and will not work for a more general 3D motion. What is the matter with you?Brews ohare (talk) 21:03, 14 September 2008 (UTC)
 * Anyone who is interested can view that article for themselves, and decide for themselves if the subject is "planar motion".Fugal (talk) 23:31, 14 September 2008 (UTC)
 * And how did you decide this article is not about planar motion? Brews ohare (talk) 13:00, 15 September 2008 (UTC)


 * Again, you distort matters by saying I "recommended re-directing all discussion of the more general view of centrifugal force". What I did do was recommend that a discussion of a particular subsection of the page Centrifugal force (planar motion) be moved to that talk page. What is the matter with you? Brews ohare (talk) 21:03, 14 September 2008 (UTC)


 * Again, that isn't the re-direct I'm referring to. I'm talking about your latest re-direct of the discussion pertaining to the general unified approach to the overall subject, which of course has nothing to do specifically with "planar motion".
 * This event is a creation of your imagination. It never happened. Brews ohare (talk) 13:11, 15 September 2008 (UTC)


 * I interpret your vague general remarks, as opposed to specific textual and mathematical criticism of the proposed section, as a desire to pontificate rather than contribute. Brews ohare (talk) 17:51, 14 September 2008 (UTC)


 * The specific textual and mathematical criticism has been presented on this discussion page many many (many) times.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * Fugal: That simply is untrue – no-one has reviewed the subsection proposed or made any concrete proposal. Brews ohare (talk) 19:46, 14 September 2008 (UTC)


 * You're mistaken. The novel narrative, neoligisms, and original research aspects have all been specifically and repeatedly pointed out. Also, a correct, concise, and complete version was added to the article, and you deleted it.Fugal (talk) 23:31, 14 September 2008 (UTC)
 * Reasons for deletion provided at were never responded to. Brews ohare (talk) 13:00, 15 September 2008 (UTC)
 * Your reason for deleting it is that you did not understand it and you found that I would not engage with you in a discussion of your original research, misrepresentations, and neoligisms.Fugal (talk) 23:31, 14 September 2008 (UTC)
 * I think you mean you have ranted a lot in vague context about "novel narrative, neologisms, and original research", but you disdain to critique in any more specific way. That applies to the reasons for deletion above, to and, in particular, to the subsection planar motion observed from a rotating frame. Brews ohare (talk) 14:11, 15 September 2008 (UTC)


 * Wikipedia discussion pages are specifically NOT intended to be a venue for the discussion of the subject of an article. They are supposed to be where editors discuss the suitability of various edits in terms of the criteria established by Wikipedia policy. This consists of determining things like whether something is original research, novel narrative, neoligisms, and whether it accurately represents the views presented in reputable sources (verifiability). It does NOT consist of proving something to be "true" or "false". It's unfortunate that the policy had to be adopted, but it was prompted as the only practical way of dealing with individuals who are fixated on a certain topic and are absolutely convinced that their novel narrative on the topic is correct, and they can PROVE it. No amount of discussion or "engagement" with such individual will do any good. Hence the following official Wikipedia Policy:


 * begin quote-
 * Wikipedia's founder, Jimbo Wales, has described original research as follows: The phrase "original research" originated primarily as a practical means to deal with physics cranks, of which of course there are a number on the Web. The basic concept is as follows: It can be quite difficult for us to make any valid judgment as to whether a particular thing is true or not. It isn't appropriate for us to try to determine whether someone's novel theory of physics is valid; we aren't really equipped to do that. But what we can do is check whether or not it actually has been published in reputable journals or by reputable publishers. So it's quite convenient to avoid judging the credibility of things by simply sticking to things that have been judged credible by people much better equipped to decide." (WikiEN-l, December 3, 2004).


 * The phrase "original research" in this context refers to untested theories; data, statements, concepts and ideas that have not been published in a reputable publication; or any new interpretation, analysis, or synthesis of published data, statements, concepts or ideas that, in the words of Wikipedia's founder Jimbo Wales, would amount to a "novel narrative or interpretation" ... regardless of whether it's true or not; and regardless of whether you can prove it or not.
 * end quote


 * Those last words are intended for people who demand that others "engage" with them in a discussion of what is "true". Bottom line: It doesn't matter. We're not here to decide what is true. We're just here to accurately report what has been published in reputable sources on this subject. If a reputable published source says centrifugal force appears in stationary polar coordinates (for example), then this must be reflected accurately in the article. Period.Fugal (talk) 20:39, 15 September 2008 (UTC)
 * Hi Fugal: Glad you got that off your chest. However, the discussion I'm looking for is a precise, well documented contribution to the articles. I do think that is what Wiki Talk pages are for. Brews ohare (talk) 21:13, 15 September 2008 (UTC)


 * You're not lacking an explanation. You're lacking an understanding.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * Fugal, thanks. Same to you. Brews ohare (talk) 19:46, 14 September 2008 (UTC)


 * Unfortunately, all any of the other editors here can do is provide you with explanations, not with understanding. You can obviously continue to not understand indefinitely, and you can continue to edit this and other articles based on your lack of understanding, which manifests itself in misrepresentations, novel narratives, original research, neologisms, and a persistent attitude of ownership, all of which are inappropriate for editing Wikipedia articles.Fugal (talk) 19:33, 14 September 2008 (UTC)
 * Fugal, I see. You can lead a horse to water, but you can't make him drown. Unsubstantiated pejorative remarks certainly advance things. Brews ohare (talk) 19:46, 14 September 2008 (UTC)


 * My remarks have been fully subtantiated, as have been the remarks of others who have explained the same things. You're not lacking for explanations or substantiation, you're just lacking in understanding. I think I've done more than part to help, but at some point it becomes clear that you simply are determined not to understand... and you're equally determined to prevent any understanding from entering these articles, which I think is unfortunate, although I suspect it will eventually be remedied.Fugal (talk) 23:31, 14 September 2008 (UTC)
 * Many assertions, no back-up. A case of revisionist history. Brews ohare (talk) 14:42, 16 September 2008 (UTC)

Suggestions
Fugal, your rewriting of history on Talk:Centrifugal force (rotating reference frame) contains no specifics, no engagement, and no facts. Two simple examples are your complete lack of response to Fugal's positions and to the subsection planar motion observed from a rotating frame. If you are serious, you must get down to brass tacks and stop lecturing. Brews ohare (talk) 13:03, 15 September 2008 (UTC)

As a "brass tacks" approach, take the subsection Polar coordinates in a rotating frame of reference and explain why (in your mind) the two different treatments of the terms $$ ( m r\dot\theta '^2\hat{\mathbf{r}} -m 2\dot r \dot\theta '\hat{\boldsymbol\theta})$$ (as fictitious force in one case, but not in the other) do not constitute two different usages of the terminology "fictitious force". It is not a case of different contexts inasmuch as both approaches describe exactly the same phenomena in exactly the same coordinate system and in exactly the same frame of reference. Brews ohare (talk) 19:07, 15 September 2008 (UTC)


 * The general unified solution to the very example you're talking about has been presented three or four times on this discussion page already, explicitly and in full, with equations and detailed explanation. There is obviously no point in duplicating it yet again.Fugal (talk) 20:39, 15 September 2008 (UTC)
 * Perhaps you refer to your Revision as of 21:30, 15 August 2008?
 * It was removed with extensive comments at Reasons for removal to which no response was received. In addition, many of the issues already were presented at Fugal's positions, so far ignored by you.Brews ohare (talk) 21:13, 15 September 2008 (UTC)
 * No I am not. I am referring to the explicit and detailed treatment of the specific example you have asked about, namely, a particle described in terms of a rotating system of polar coordinates.Fugal (talk) 03:12, 16 September 2008 (UTC)
 * Please bend a little and point out this discussion, or repeat if need be. Brews ohare (talk) 04:56, 16 September 2008 (UTC)


 * I am not looking for a "general unified solution"; just an exploration of a simple direct example. For example, take the subsection Polar coordinates in a rotating frame of reference. The derivations closely parallel those in the cited sources, viz: Taylor, and also Stommel and Moore, so it is hardly "narrative, neologism and whatever". Please explain why (in your mind) the two different treatments of the terms $$ ( m r\dot\theta '^2\hat{\mathbf{r}} -m 2\dot r \dot\theta '\hat{\boldsymbol\theta})$$ (as fictitious force in one case, but not in the other) do not constitute two different usages of the terminology "fictitious force". It is not a case of different contexts inasmuch as both approaches describe exactly the same phenomena in exactly the same coordinate system and in exactly the same frame of reference. Brews ohare (talk) 21:13, 15 September 2008 (UTC)


 * Already presented multiple times here on this discussion page.Fugal (talk) 03:12, 16 September 2008 (UTC)
 * Excuse me, but I can find not even one discussion (besides my own) of the terms $$ ( m r\dot\theta '^2\hat{\mathbf{r}} -m 2\dot r \dot\theta '\hat{\boldsymbol\theta})$$ on this page. Brews ohare (talk) 04:56, 16 September 2008 (UTC)


 * And I say again, by humoring you to this extent, we have been abusing the purpose of this discussion page, which is not to (in your words) "explore" the subject of the article. As I said, some of us have made the mistake of trying to explain a bit about the subject to you, in hopes that it would make the editing go more smoothly, but the folly of trying to reason with an "original researcher" has been demonstrated once again.Fugal (talk) 03:12, 16 September 2008 (UTC)
 * Sorry I used the word "explore" in a sense you misunderstood; how about "suggest revisions to"? Your use of the words "humoring", "abusing", "folly" etc. is very much in keeping with Wiki guidelines for this Talk page, eh? "Do as I say, not as I do"? Brews ohare (talk) 17:30, 16 September 2008 (UTC)


 * Look, as I said above, Wikipedia discussion pages are not intended to be a venue for discussing the subject of the article. As a courtesy, some people have been abusing the intent of these pages by trying to discuss the topic with you, hoping that if you understood it a little better, the editing would go more smoothly. But that obviously hasn't worked. The wisdom of the Wikipedia policies has been borne out yet again. We must simply eliminate all neoligisms and novel narrative from the article(s) (i.e., any statements that cannot be directly traced to a verifiable reputable source), and then we must add all the directly verifiable statements concerning centrifugal force in the context of curvilinear coordinates, with full citations and quotes where necessary. That's the only way forward that is consistent with Wikipedia policy.Fugal (talk) 20:39, 15 September 2008 (UTC)


 * Glad you have identified "the only way forward". It's good to know where you are headed. Please start a page to "add all the directly verifiable statements concerning centrifugal force in the context of curvilinear coordinates, with full citations and quotes where necessary." I'd suggest it as a separate page until it is thoroughly examined and its relation established to existing pages that do not aspire to be a "general unified approach to the overall subject". So far as I have seen, it will be thin pickings to find sources for this fundamental work, as all treatments of centrifugal force that I have seen avoid it entirely, except in the field of robotics where a Lagrangian approach is common. That field uses fictitious force in the unusual sense where centrifugal force is present (non-zero) even in inertial frames (the "coordinate" sense). (BTW, so does your Revision as of 21:30, 15 August 2008.) Besides being inappropriate for an article fundamentally based upon a centrifugal force that is zero in inertial frames, a curvilinear, unified, general approach probably falls into the category of an advanced page for specialists. If that is so, the "unified" page will stand on its own, rather than modify the existing pages. Brews ohare (talk) 23:56, 15 September 2008 (UTC)


 * Once again, please see the Wikipedia policy on "ownership". Verifiable material on the subject of any given article belongs in that article. Likewise, novel narrative and neoligisms do not belong in any Wikipedia article, so they should be removed from any article in which they appear.Fugal (talk) 03:12, 16 September 2008 (UTC)
 * As the existing pages are of narrow scope, and deliberately so, introduction of a "general unified approach", which most probably includes Christoffel symbols and metric tensors and maybe a little differential geometry, becomes a large overhead on these simpler examples. For that reason I merely suggested (see the word if ? ) that a separate page would be a better course. Brews ohare (talk) 14:39, 16 September 2008 (UTC)

Neologisms?
I would argue that the use of the terms "state-of-motion" fictitious force and "coordinate" fictitious force does not constitute introduction of neologisms, but is simply the application of adjectives to a noun, very parallel to the distinction "red dog" compared to "black dog".

The term "state-of-motion" fictitious force refers to the standard case of fictitious forces that vanish in an inertial frame of reference, as does the centrifugal force of this article. The second term "coordinate" fictitious force refers to the artificial forces introduced by treating all the terms introduced by a non-Cartesian coordinate system as "fictitious forces". The "coordinate" fictitious forces are present in every frame, including an inertial frame of reference. One might propose better names, of course. Maybe "classical-mechanical" fictitious force & "geometrical" fictitious force, for example. Brews ohare (talk) 20:01, 16 September 2008 (UTC)


 * None of the numerous verifiable sources found it necessary to make use of these expressions. The fact that you have found it necessary to invent neoligisms in order to express your alleged “dichotomy” in the subject demonstrates that your idea is original research. This research and the associated novel narrative and neoligisms do not belong in Wikipedia, per the established policies.


 * The term "black dog" is suitable for an article on dogs because the term appears in reputable and notable sources on the subject of dogs. But (for example) the term "cloudy dogs" would not be suitable, because it doesn't appear (as far as I know) in the literature on dogs.


 * More to the point, an article on dogs would be expected to acknowledge that dogs have different colors. If someone were to try to dominate the Dog article, flooding (spamming?) it with edits and discussion, claiming that this is two different usages of the word "dog", and asserting that the only real physical dogs are red dogs, and the things that are confusingly called "black dogs" in some fringe references of no importance are not really physical dogs at all, they are just mathematical dogs, then it would be appropriate for other editors to object, because this alleged dichotomy is not found in any reputable source.


 * And if the individual actually alleged a physical/mathematical dichotomy, not between red and black dogs, but between cloudy and non-cloudy dogs... i.e., alleging a dichotomy based on terms that don't even appear in the literature at all, well, again, it would be appropriate for other editors to object, and to strive to get this individual to respect Wikipedia policies.Fugal (talk) 15:11, 17 September 2008 (UTC)
 * That "fictitious force" is subject to two usages is well documented. I have chosen to select one obvious difference between usages: the requirement that fictitious force be zero in an inertial frame for those fictitious forces that also are called inertial forces, pseudo-forces, and d'Alembert forces, and the lack of this requirement for the fictitious forces defined as all but the second-time-derivative terms in the acceleration expressed in curvilinear coordinates.
 * As a reminder of the role of inertial frames; this quote from Arnol'd:


 * As a reminder of the second usage of fictitious force, here is a quote from Ge et al.


 * Divert yourself from "cloudy" dogs to treat this issue directly. Brews ohare (talk) 16:58, 17 September 2008 (UTC)


 * As always, your comments are based on your fundamental misconceptions as to the meanings of frames and coordinate systems. For the billionth time, a frame is simply an equivalence class of mutually stationary coordinate systems, and as such it may include both inertial and non-inertial coordinate systems. An inertial coordinate system is defined as one in which the space coordinates of any inertial path are linear functions of time. In introductory texts (and works that are not concerned with the dependence on spatial coordinates) a simplification is often introduced, by stipulating that the representative of any frame will be a rectilinear Cartesian coordinate system, which enables those works to then say without ambiguity that fictitious forces arise only in non-inertial frames. But this is a conditional statement, i.e., it is true only under the simplifying stipulations that those works present on the first few pages. (Unfortunately, beginning students are often unaware that they have only been presented with a simplified version. Some of them turn into physics cranks later in life, when they become exposed to the more general subject.) In more advanced works the general unsimplified view is taken, and in this context one must speak of specific coordinate systems, rather than of equivalence classes of coordinate systems, in order to avoid ambiguity. In this general context, one says that fictitious forces arise in non-inertial coordinate systems, which include systems with curved space axes or curved time axes or both. The point is that this general treatment of the subject does not contradict the simplied "Dynamics for Dummies" version, nor does it represent a different definition of the terms. It simply represents a more general view, sans the simplifying stipulations made in the introductory presentations.

Incidentally, since you were the one who introduced the red dog and black dog analogy, it seems odd that you would immediately admonish me for commenting in those terms. As to your wish (now) for the issues to be addressed directly, I can only say (again) that the issue has been addressed directly many many times. You aren't lacking explanations, nor substantiation, you are lacking only understanding of the subject ... and respect for Wikipedia policies.Fugal (talk) 19:42, 17 September 2008 (UTC)

Inertial frames
Fugal : An inertial coordinate system is defined as one in which the space coordinates of any inertial path are linear functions of time.

Isn't this definition circular? At a minimum we need a definition of an "inertial path". Maybe, a path followed by a particle subject to no forces (fictitious or otherwise)?(talk) 20:40, 17 September 2008 (UTC)


 * Of course it's circular. This is exceedingly well known, and has been pointed out and thoroughly discussed by every author on the foundations of science from Newton's day until today. Of course, one refers to "isolated" bodies, but that just begs the question of what is a sufficiently isolated body. As Einstein commented, "The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration." And of course this wasn't original to Einstein. For example, Mach pointed out that Newton's laws aren't really laws of motion, they are essentially the definition of inertial coordinate systems, but then this leads to the general problem of inductive knowledge, and so on. Newton himself was well aware of these issues, so there's nothing new here. Scientific knowledge is inherently provisional.Fugal (talk) 02:37, 18 September 2008 (UTC)
 * Thanks for that quotation. I was aware of this problem, but not of the quote. However, it seems to me that the orthodox way out this is DiSalle, who says in summary:
 * I hesitate to ask for you digress upon this "solution"; but perhaps you have another useful quote or source?? Brews ohare (talk) 04:44, 18 September 2008 (UTC)
 * My understanding is that a focus upon transformation properties of the laws of physics shows certain frames have simpler laws (because fictitious forces don't drop off rapidly with distance, for instance, and transform oddly, in fact vanishing in certain frames), and therefore are preferred. The alternative seems to be to suggest we don't know an inertial frame from any other frame: we can identify frames that are in uniform translation relative to one another as belonging to one family of frames, but in no way is such a specimen family preferred over another family exhibiting a common acceleration wrt the specimen family. For example, we cannot distinguish a rotating frame from a stationary frame; all we can say is that one rotates relative to the other. In particular, the rotating sphere experiment won't work. Assuming we stick within special relativity, which is your view? Brews ohare (talk) 05:14, 18 September 2008 (UTC)

Fugal : In this general context, one says that fictitious forces arise in non-inertial coordinate systems, which include systems with curved space axes or curved time axes or both.

Isn't this conclusion in contradiction with the classical mechanical view of the quote above from Arnol'd?(talk) 20:40, 17 September 2008 (UTC)


 * No, it isn't. You have to read carefully, and note the difference between frame and coordinate system, and recognize that Arnol'd has already "modded out" the variations in spatial coordinate systems within any given frame by stipulating (as in the two quotes that I provided to you previously) that we will take as THE representative of any frame a rectilinear Cartesian coordinate system, which just amounts to "modding out" any spatial coordinate effects, leaving only the temporal coordinate effects. This is just a simplification, so that almost all of the Christoffel symbols vanish, and the few that remain can be given cute names like centrifugal and Coriolis. The temporal coordinate effects are just as much "coordinate effects" as are spatial coordinate effects. There is nothing more or less "physical" or "mathematical" about them. And when it comes to simplicity, we can just as well (and often do) suppress variations in the time coordinate and put all the variations into the spatial coordinates, as is done in the numerous references that have been provided.Fugal (talk) 02:37, 18 September 2008 (UTC)
 * Here is the quote from Arnol'd once more:


 * On p. 130 (the very next page to the above quote) Arnol'd says (vector variable Q is the radius vector of a moving point in the moving coordinate system):


 * where the Euler force exists only in nonuniform rotation. [I've introduced the name "Euler force" following Lanczos]. The question is how these two quotes are to be combined.
 * I'd say the first quote requires that the inertial forces of the second quote to vanish in an inertial system, thereby distinguishing a system that is rotating from one that is not. (Obviously, they do vanish when &Omega; = 0. ) The entire formulation is in vector notation, and therefore independent of coordinate system (Cartesian or polar). If the radius vector Q is expressed in polar coordinates, $$m \mathbf{\ddot{Q}}$$ will contain a variety of terms related to the curvilinear coordinates (see here), and these are on the left side of the equation, not included in the inertial forces on the right side of the equation. Thus, the criteria for an inertial frame based upon vanishing of inertial forces is not affected by a switch to polar coordinates.
 * If instead the curvilinear terms in $$m \mathbf{\ddot{Q}}$$ are taken to the right side of the equation and all the terms on the right are called "fictitious forces", the resulting "fictitious forces" are clearly not the same as the original "inertial forces" and these newly coined "fictitious forces" do not vanish in an inertial frame. Hence, the need to recognize two usages for the term "fictitious force". Brews ohare (talk) 19:56, 18 September 2008 (UTC)

And finally, it seems to me you might be suggesting (particularly in your second statement above) that in a curvilinear system the second-time-derivatives of the coordinates are the applied force. In a curvilinear coordinate system that is what I've called the "coordinate" definition as exemplified by the quote above from Ge.(talk) 20:40, 17 September 2008 (UTC)


 * See above. All inertial forces are due to coordinate effects, so it's incorrect to call just some of them (the ones you've never thought about very much) "coordinate" effects while referring to others as "state of motion" effects. (It's also incorrect, and doesn't make sense, to refer to acceleration as a "state of motion", and you can't unambiguously extrapolate accelerations ... but this isn't the place for a tutorial on Fundamentals of Physics.)Fugal (talk) 02:37, 18 September 2008 (UTC)

It seems that you may be agreeing there are two terminologies, one you call the "simplification for beginning students" and one you call the "general unsimplified view ". Are we simply arguing over semantics? Is the difference just one of what merit is assigned to the two usages? Brews ohare (talk) 20:40, 17 September 2008 (UTC)


 * There are not two "terminologies". I went to the trouble of taking two of your own references, on which you've based your claims about two terminologies, and showed specifically with the exact quotes where they stipulated that they were restricting their considerations of spatial coordinates to rectilinear spatial coordinate systems, while allowing the temporal coordinate to be non-linear, in which case the statements they subsequently make about frames and inertial forces are correct. They are not correct, however, if the stipulation about spatial coordinates is removed, and the authors would surely not have objected to this statement. By the same token, the references that have been cited in which fictitious forces are derived in terms of stationary coordinate systems are also correct, because they have not stipulated rectilinear spatial coordinates. Of course, we could just as well stipulate that ALL our coordinates be rectilinear, in which case there are no fictitious forces at all.


 * Look, the explantion was contained in the edit to the article that you deleted. It specifically explained how the simplifed way of viewing of the subject, which is taken in the rest of the article, fits into the larger context of the general treatments, and how this also unifies the reputable references that derive centrifugal and other fictitious forces in terms of stationary coordinates. Viola, the so-called "confusing terminoligies" and "conflicting usages" evaporate when the subject is simply viewed clearly and correctly. It was all summarized in a paragraph or two, explaining, based on explicit quotes from numerous reputable sources, how all these pieces fit together. And you deleted it.Fugal (talk) 02:37, 18 September 2008 (UTC)

Discussion of Arnol'd
I wrote that “Newton's laws aren't really laws of motion, they are essentially the definition of inertial coordinate systems”, and you counter with “However, it seems to me that … the laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing them.” You do realize that you just repeated what I said, right?.Fugal (talk) 15:47, 19 September 2008 (UTC) You present (yet again) a quote from page 129 of Arnol'd. Unfortunately you jumped straight to page 129 without understanding pages 1 through 10, which is where the context is established for the rest of the book. Please look at page 6, where “inertial coordinate systems” are defined by a “state of motion”, but by the condition that the law of inertia takes the simple form x” = F(x,x’,t), where primed symbols represent derivatives of the coordinates with respect to time. Near the same page it says the only transformations between inertial frames are translations, rotations, and uniform motions. Both of these (along with all the rest of the discussion) explicitly signify that he is restricting “coordinate systems” to orthogonal rectilinear spatial coordinates? The transformation from Cartesian to polar coordinates (for example) is not just a translation, rotation, or uniform motion, so according to Arnol'd it is not an inertial coordinate system. He just isn't considering curvilinear spatial coordinates, so he is speaking in the restricted sense. This is exactly what I’ve been telling you. I’ve pointed out where this restrictive stipulation is introduced in all THREE of your sources.Fugal (talk) 15:47, 19 September 2008 (UTC) The rest of your comments are just repetitions of your previous erroneous comments. Please note that the thing you call the “equation of motion in polar coordinates” on your “planar” page is not even a coherent equation of motion, it’s just a disguised version of the rectilinear vector equation with some of the appearances of the position vector replaced with the angular coordinate. You essentially have one vector equation in three unknowns (namely, the two components of the position vector and the scalar angle). If you actually tried to integrate this equation you would immediately see the fallacy of what you’ve written. Again, the correct treatment of that very problem has been presented here on these discussion pages multiple times. Obviously the use of curved spatial axes introduces terms in addition to those introduced by the use of curved time axes, but it’s just as obvious that the same terms can be introduced by just one or the other. We are free to choose whatever system of coordinates we like. The point is that all the references you habitually cite have explicitly restricted themselves to rectilinear spatial coordinates, so no terms involving the spatial coordinates arise, whereas other (more sophisticated) references discuss the unrestricted view.Fugal (talk) 15:47, 19 September 2008 (UTC) You wrote that “The entire formulation is in vector notation, and therefore independent of coordinate system (Cartesian or polar).” Well duh. The equation F = ma is a vector equation, and it contains no fictitious forces, so according to your “reasoning” there are no fictitious forces in terms of any system of coordinates. Now, in one sense that’s true, i.e., if we use the true acceleration vector for “a”, then “F” will consist of just the true forces, and we can do this in terms of ANY coordinate system, regardless of whether it is accelerating or curvilinear or anything else. Of course, the expressions for “a” in terms of our chosen coordinates will depend on those coordinates. For some systems the vector “a” is just the second time derivatives of the space coordinates, whereas for other systems there are additional terms. Regardless of our coordinate system, the true acceleration “a” can always be expressed. But the subject of this article is a fictitious force, which arises when (and only when) we decide to use a fictitious acceleration rather than the true acceleration in the equations of motion. In other words, we use a fictitious acceleration A in place of the true acceleration “a”, but then the equation of motion becomes F+f = mA where f equals m(A-a). If we want, we can call f the fictitious force, which compensates for whatever fictitious acceleration we’ve chosen to use. Now, we have lots of choices, e.g., we can choose A = 0, in which case we get dynamic equilibrium and d’Alembert’s principle. On the other hand, we can choose A = second time derivatives of our space coordinates, which leads to the conventional fictitious forces. Of course, in the fully general context, the difference between this A and the true “a” will consist of terms that arise due to curved space axes as well as curved time axes. In a more restrictive context, with the stipulation that we will only use rectilinear space axes, the extra terms will then consist only of those arising from curved time axes. This is the restricted treatment that you were taught in Dynamics for Newbies. The point is that this is just a specialized treatment of a general subject.Fugal (talk) 15:47, 19 September 2008 (UTC) Again, these discussion pages are not to be used for discussions of the subject of the article. My best advice to you is to read a real book devoted specifically to this subject, say Friedman’s “Foundations of Space-Time Theories”, specifically Section III on Newtonian physics. This clearly describes the general context that encompasses all the discussions of “centrifugal force” to be found in the reputable literature.Fugal (talk) 15:47, 19 September 2008 (UTC)
 * I will look into your remarks further. An immediate question, however, is how do you react to the Rotating spheres example? In particular, that example seems to say that it is possible to determine one is in an inertial frame by comparing the tension measured in a string with the tension calculated using the laws of physics including only real forces. In other words, fictitious forces are zero in the inertial frame (and non-zero in a rotating frame). It would not matter what coordinate system was used. In contrast, if the curvilinear additions to the acceleration introduced by using curvilinear coordinates are treated as additional fictitious forces, this scheme will not work. Brews ohare (talk) 18:21, 19 September 2008 (UTC)

Principle of inertia functions as an organizing principle
Well, I react by saying you're completely and utterly wrong, as usual. First, the issue here is not the epistemological problem of how inertial coordinate systems are identified. That relates to the general issue of inductive knowledge and how the principle of inertia functions as an organizing principle for our knowledge... not relevant to this article. Second, the recognition of the fact that space-time coordinate systems contain space coordinates as well as time coordinates (either or both of which may diverge from inertial paths, does not in any way impede us in the identification of inertial coordinate systems (whether by the revolving globes or any other means). To the contrary, this recognition is an essential part of accomplishing such an identification. You keep saying things like "it doesn't matter what coordinate system you use", oblivious to the fact that the very same thing applies to time coordinates as to space coordinates. If you want to exclude the use of fictitious (coordinate dependent) acceleration, then there are no fictitious forces. On the other hand, if you allow the use of fictitious acceleration, then there are fictitious forces associated both with curved time axes and with curved space axes (unless you stipulate that you are considering only rectilinear space axes for simplicity).Fugal (talk) 22:04, 19 September 2008 (UTC)
 * Fugal: You definitely have put your finger on an important issue that underlies all this: the epistemological problem of how inertial coordinate systems are identified. Maybe it belongs in Inertial frame of reference. Anyhow it belongs somewhere. Maybe you could do something helpful here? If we take up this problem, what is your take on using the tension in the string joining rotating identical spheres to define inertial frames? Brews ohare (talk) 22:41, 19 September 2008 (UTC)

Coordinate-dependent acceleration
Fugal: ''If you want to exclude the use of fictitious (coordinate dependent) acceleration, then there are no fictitious forces. On the other hand, if you allow the use of fictitious acceleration, then there are fictitious forces associated both with curved time axes and with curved space axes (unless you stipulate that you are considering only rectilinear space axes for simplicity)''
 * We are at cross-purposes here. The approach called "coordinate" fictitious forces in Centrifugal force (planar motion) does associate fictitious forces with the choice of coordinate system (for example, polar vs. Cartesian). Moreover, the choice of coordinate system (polar or Cartesian) is available in any frame of reference, inertial or non-inertial. I believe this is the point of view you adopt as the point of view.
 * However, a different point of view is that there are no fictitious forces present in an inertial frame of reference. That statement is made explicitly in the quote from Arnol'd.
 * He goes on to say that there are fictitious centrifugal Coriolis and Euler forces in a rotating frame of reference, which is, of course, a non-inertial frame.
 * Your reply to this is The transformation from Cartesian to polar coordinates (for example) is not just a translation, rotation, or uniform motion, so according to Arnol'd it is not an inertial coordinate system. because Arnol'd says the only transformations between inertial frames are translations, rotations, and uniform motions. This last is not what Arnol'd says. The exact quote is:


 * This quotation (i) has no bearing upon the use of curvilinear coordinates; and (ii) indicates what can be done, not what cannot be done.
 * I find myself dismayed that you can misread this text so badly. Brews ohare (talk) 18:18, 20 September 2008 (UTC)


 * Your analysis of logical syllogisms is faulty. If every "inertial system" can be expressed as a rotation, translation, and uniform motion, then any system that CANNOT be so expressed is NOT an "inertial system" according to his statement. Curvilinear coordinates cannot be expressed that way, so they are not included in what Arnold calls "inertial coordinate systems". Then when he goes on to say fictitious forces appear only in non-inertial coordinate systems, he is perfectly correct, bearing in mind that curvilinear coordinate systems are not inertial coordinate systems according to his definition.


 * The quote is about Galilean transformations; not about the use of curvilinear coordinates. Brews ohare (talk) 14:55, 21 September 2008 (UTC)


 * He says the inertial coordinate systems are related by Galilean transformations, which shows that curvilinear coordinate systems are not included in the class of what he defines as "inertial coordinate systems. But you needn't infer that indirectly from the one quote you selected. He says this explicitly in the surrounding text. Please, please read the first nine pages in their entirety, and try to understand them. Here are the statements you should look for in particular:


 * "The expression "two non-simultaneous events occurring at one and the same place in three-dimensional space has no meaning as long as we have not chosen a coordinate system.... Consider the direct product RxR3 of the t axis with the three-dimensional vector space R3... we will call this space Galilean coordinate space.


 * We mention three example of Galilean transformations of this [coordinate] space... [rotation, translation, uniform motion]... Every Galilean transformation [of the coordinate space] can be written in a unique way as a product of a translation, rotation, and uniform motion.


 * [Now, please note the following, and try to understand it.]
 * A one-to-one correspondence phi1 M -> R x R3 is called a Galilean coordinate system. A coordinate system phi2 moves uniformly with respect to phi1 if [the transformation from one to the other] is a Galilean transformation.


 * Galileo's principle of relativity states that there is a class of Galilean coordinate systems [called the inertial coordinate systems] having the following properties... Inertial coordinate systems are related to each other by Galilean transformations." [Page 9]


 * Do you understand? He has defined a Galilean coordinate system (which he later in the book often calls just a "system") as having rectilinear space coordinates (R3), and he says inertial coordinate systems are related by Galilean transformations. This is true, given the stipulation that the spatial part of the coordinate systems are rectilinear (R3). It follows that curvilinear coordinate systems, which are not related to these Galilean coordinate systems by any Galilean transformation, are not in the class of what he calls "inertial systems".


 * Once again, I strongly recommend you acquire some good books on this subject, and read them from the beginnings, and think about what they are saying. Your misunderstandings don't begin on page 129, they begin on page 1. You'll have to let go of many of your pre-conceived notions in order to really understand the subject.Fugal (talk) 19:15, 21 September 2008 (UTC)


 * Again, I urge you to acquire a book devoted to this topic, like Friedman or Sklar or Earman or Ray or Reichenbach or any of the multitude of others who have written on this topic. Please, stop trying to get your education here. Go to a library. Read a book. Do Google searches. Take a class. Do something other than what you're doing, which simply isn't working.Fugal (talk) 21:27, 20 September 2008 (UTC)

This article has been falsified (so strongly POV that it is even incorrect)
I notice a colossal difference between this version which appears to be mainly the work of one person and the consensus version of only half a year ago: http://en.wikipedia.org/w/index.php?title=Centrifugal_force_(rotating_reference_frame)&oldid=196032047

In particular, the old version provides reliable sources that shows that the current version is already incorrect in the opening sentence. Moreover, the old version was very much NPOV while the new one only expouses a single POV and even falsely suggests that that POV is required for mapping to rotating frames.

This is the worst thing that can happen to a Wikipedia article - thus I'll put up the required banners. Harald88


 * Harald: You haven't said what you object to specifically. What changes would make you happy?
 * Contrary to your view, the opening (accurate) sentence is supported by numerous references that appear in the first paragraph.
 * In addition, you seem to be unaware that several other pages have been created that incorporate much of the material on centrifugal force from the ancient version you prefer. They are found at Fictitious force & Reactive centrifugal force. I believe you have over-reacted. Brews ohare (talk) 13:34, 19 September 2008 (UTC)


 * I think it's fine if at the start readers can fork to the different meanings. However, this is not the case when a reader types in "centrifugal force"; moreover, as rather well explained in the old version, the title "centrifugal force (rotating reference frame)" also applies to reactive centrifugal force. Apart of that, see what Fugal explains here below. Harald88 (talk) 08:07, 23 September 2008 (UTC)


 * The splitting of the article into multiple articles is somewhat problematic, and it's also been done incompletely and inconsistently. I suspect what Harald objects to (among other things) in the current article is that, even though the article has a disambiguation suffix (rotating reference frame), the text of the article contradicts this disambiguation. The first sentence says "In classical mechanics, centrifugal force is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a rotating reference frame." Recognizing the other articles, the first sentence here ought to say something like "In classical mechanics, the term "centrifugal force" has several different meanings, one of which is a fictitious force arising from the use of non-inertial coordinate systems, and a subset of these are the fictitious forces arising in rectilinear Cartesian coordinates rotating about a fixed axis. This limited subset is the subject of this article. For a discussion of centrifugal force in general, see Article "Centrifugal Force (General)". Then similar caveats would have to be included in the remainder of this article, replacing the existing assertions of universality for this small subset of the meaning.Fugal (talk) 16:31, 19 September 2008 (UTC)
 * I've tried to remedy this matter by modifying the lead. Brews ohare (talk) 18:07, 19 September 2008 (UTC)


 * That's not the way it's done in the wikipedia Fugal. We're not defining all forms of centrifugal force. We are defining and scoping the term centrifugal force for this article. The name of the article and the links at the top link to other 'centrifugal force's that there are. The general principle is that the wikipedia is and encyclopedia is NOT a Dictionary. It is inappropriate to have reactive centrifugal force in this article as it is physically distinct in every important respect, but simply shares the same name (and points in the same direction... but even then only sometimes.) The wikipedia's rules are quite clear on this. See WP:NOTADICT. The old article that Harrald refers to simply wasn't scoped correctly for the wikipedia.- (User) Wolfkeeper (Talk) 18:59, 19 September 2008 (UTC)


 * I think we should follow Wikipedia policy in editing these articles, and provide an accurate and well-reasoned presentation of the subject based on verifiable sources. This article begins with what seems to be a disambiguation statement by saying "In classical mechanics...". The problem is that all the other meanings described in the other related articles are also in classical mechanics, so it is incorrect to say (as the article currently does) that "In classical mechanics, centrifugal force is.. such-and-such".  In order for the introductory statement to be accurate, it needs to not conflict with the fact that (for example) the reactive centrifugal force is also a concept in classical mechanics.Fugal (talk) 21:43, 19 September 2008 (UTC)


 * The unit of English meaning is the sentence. If you read the entire sentence rather than cherry picking phrases from it, then I don't believe that that criticism has any merit at all. None of the other sentences around it support this interpretation of yours in any way ether, and the links to other meanings of the term 'centrifugal force' are as clear as could be.- (User) Wolfkeeper (Talk) 22:30, 19 September 2008 (UTC)


 * Fugal and Harald: The introductory sentence is In classical mechanics, centrifugal force (from Latin centrum "center" and fugere "to flee") is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. This is a pretty clear identification of centrifugal force in general terms. As such, regardless of what the rest of the article may say, what is wrong with it? It is supported by numerous citations. Brews ohare (talk) 22:36, 19 September 2008 (UTC)


 * Brews, I typed in "centrifugal force" as I was looking for a reference on how it is used in Newtonian mechanics; instead I was shown this article which falsely pretends that the term when used for rotating reference frames can only mean a fictitious force. Such a misleading and narrow-minded introduction is the very cause of never ending disputes in the existing literature, and which we had solved with the old article - perhaps the first time in history that a neutral complete overview was given. I have of course no objection to start with the old intro and then split up into two articles. Harald88 (talk) 08:15, 23 September 2008 (UTC)


 * Do you mean, what's wrong with it in addition to the thing wrong with it that had already been identified? How many things have to be wrong with it before you will conceed that it is wrong?  Once again, the sentence says "In classical mechanics, centrifugal force is such and such". But in classical mechanics centrifugal force is also other things, so the sentence is misleading, and conflicts with the other articles. The irrelevance of the cited references to this point has already been explained at length. An equal number of equally reputable references on the subject of classical mechanics have been cited which describe other things under the name "centrifugal force". Hence to say "In classical mechanics, centrifugal force is such and such" is self-evidently misleading. It ought to say something like what I suggested above, or something like "In classical mechanics, with rectilinear coordinates rotating about a fixed axis, centrifugal force is such and such".Fugal (talk) 01:16, 20 September 2008 (UTC)


 * The complete quote down to end of the first sentence goes:
 * For centrifugal force that isn't due to rotating reference frames, see centrifugal force (disambiguation).
 * For the external force required to make a body follow a curved path, see Centripetal force.
 * For general derivations and discussion of fictitious forces, see Fictitious force.


 * In classical mechanics, centrifugal force (from Latin centrum "center" and fugere "to flee") is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame."


 * This is clear, and follows WP:LEAD and the other norms of the wikipedia to the letter.- (User) Wolfkeeper (Talk) 02:31, 20 September 2008 (UTC)


 * The Wikipedia policy you referenced says the lead "should establish the context", and the sentence does attempt to do this, but it is erroneous in so far as it mis-identifies the context. It says "In classical mechanics, centrifugal force is such and such", but this contradicts the disambiguation, which forks to other "centrifugal force" articles that are also in classical mechanics. Hence the phrase "in classical mechanics" is obviously not sufficient to establish the context. Also, the unambiguousness of the statement contradicts the ambiguity that has already been acknowledged by the disambiguation statements. A more accurate opening sentence would be something like "In classical mechanics, the outward component of the fictitious (or inertial) force that appears when equations of motion are written in terms of a rectilinear Cartesian coordinate system rotating about a fixed axis is called centrifugal force."Fugal (talk) 05:56, 20 September 2008 (UTC)


 * You still get the same outward force on a coordinate stationary object even in polar coordinates though for the same non inertial frame, so that's not accurate.- (User) Wolfkeeper (Talk) 16:43, 20 September 2008 (UTC)


 * For example, expressing a position on Earth in terms of lattitude, longitude and altitude is an example of a polar coordinate system in a rotating frame of reference. Doing this is not at all uncommon.- (User) Wolfkeeper (Talk) 16:48, 20 September 2008 (UTC)


 * You say "you get the same outward force... even in polar coordinates...", but you should ask yourself what that really means. In other words, what does it mean to "get" a force in some specified system of coordinates? I'm sure you would agree that we don't affect any physical events by our choice of coordinates, although the description of those events may be affected. So, when you talk about "getting" a [fictitious] force "in" a specified system of coordinates, what PRECISELY do you mean?  See if you can article, in perfectly clear and unambiguous terms, precisely what you mean. As soon as you do this, I think the subject will become much more clear to you.Fugal (talk) 19:27, 20 September 2008 (UTC)


 * It means that if I model a weight on a spring balance that is flying in an aircraft around the Earth in a polar coordinate system referring to a non inertial frame that rotates around the Earth with the aircraft, then I get the same answer as if I use a rectilinear coordinate system that refers to that same frame and the same as that which I get to within measurable accuracy in an actual aircraft.- (User) Wolfkeeper (Talk) 00:49, 22 September 2008 (UTC)


 * Fugal: Wolfkeeper has said the force depends on the choice of non-inertial frame, not upon whether the coordinates in that frame are polar or Cartesian or oblate-spheroidal. That is pretty clear and unambiguous. It agrees with your remark: I'm sure you would agree that we don't affect any physical events by our choice of coordinates, although the description of those events may be affected. Brews ohare (talk) 20:18, 20 September 2008 (UTC)

Just for the record, I slightly modify my stand in this issue below on this page, based on the discussions and in view of the existence of a disambiguation page: "In addition to what Frugal stated [...] about the misleading intro of this article, what really is wrong is the fact that readers (like happened to me!) do not encounter the disambiguation page but instead fall directly on this page which only gives one opinion about the meaning of "centrifugal force". Thus, the first banner (POV) really refers to the fact that, as I wrote a few days ago, but some may have missed: "I think it's fine if at the start readers can fork to the different meanings. However, this is not the case when a reader types in "centrifugal force". Instead they are confronted with the Single View that in classical mechanics "centrifugal force" is a fictitious force. Thus, my main objection is that the linking to this article is unacceptably POV. I don't know how to fix this; I would agree with removing the first banner (POV) if "centrifugal force" links to the disambiguation page instead of to this article. Harald88 (talk) 13:55, 25 September 2008 (UTC)" Harald88 (talk) 14:09, 25 September 2008 (UTC)


 * Again for the record, after long discussion below the status was strongy improved; removed one banner and moved one banner to problematic section. Harald88 (talk) 12:58, 28 September 2008 (UTC)

A frame is just a class of coordinate systems (continuation of above discussion)

 * No, it isn't clear and it isn't unambiguous. A frame is just a class of coordinate systems, and the challenge to Wolf is to explain what he means when he says you "get" a certain force in a certain frame but you do or do not "get" the same force in certain coordinate systems within that frame. Remember, the physics doesn't change for a choice of coordinate systems, nor does it change for a choice of a set of coordinate systems (i.e., a frame). Fictitious forces are fictitious. So what does it mean to "get" a [fictitious] force in a certain coordinate system (or a certain class of coordinate systems) but not in other? This is what I'm hoping Wolf can ponder, and hopefully begin to get a glimmer of understanding of this subject. It wouldn't hurt you to ponder it as well.Fugal (talk) 21:05, 20 September 2008 (UTC)


 * No, a frame can have one or more coordinate system(s). A frame of reference is a set of axes which you use to measure positions, positions which may then be expressed in a coordinate system. Coordinate systems are not the same as reference frames, and it's common to measure a position according to multiple coordinate systems on Earth for example. This should be self-evident.- (User) Wolfkeeper (Talk) 02:14, 21 September 2008 (UTC)


 * You say "a frame is a set of axes which you use to measure positions", and then you go on to say "positions may then be expressed in a coordinate system". How exactly do you "measure positions" without a coordinate system? A set of axes IS a coordinate system. Hence the name "coordinate axes". Look, this has all been explained (as has everything else) previously. A frame is an equivalence class of mutually stationary coordinate systems. And one again, the choice of a coordinate system, or a class of coordinate systems, does not change any physical events. It may change the terms of your description of the events, but it doesn't change the events themselves. You see, your persistent refusal to either consult with a reputable source or the THINK about these things yourself is what prevents you from making any progress, and hence these articles remains stalled in its current deplorable state.Fugal (talk) 03:28, 21 September 2008 (UTC)


 * No. Do you have a good reference saying that a frame of reference is exactly the same thing as a coordinate system? Because they're self evidently not the same. A frame of reference has an origin and a way of determining direction. A coordinate system is applied relative to that. A frame of reference can be a physical thing, or a mechanical construct. A coordinate system is not a mechanical construct. They are not the same.- (User) Wolfkeeper (Talk) 21:17, 21 September 2008 (UTC)


 * As I said in the message to which you are responding, a frame is NOT a coordinate system, it is an equivalence class of mutually stationary coordinate systems. (Do you understand what this means?) But YOU gave your own definition, i.e., you said "a frame is a set of axes which you use to measure positions", to which I responded that a set of axes used to measure positions is a coordinate system, and hence your subsequent comments were non-sequiturs. So what exactly are you asking now? You want references for the fact that a frame is an equivalence class of coordinate systems? I suggest you read any of the many excellent books on this subject, such as Friedman's "The Foundations of Space-Time Theories".Fugal (talk) 23:26, 21 September 2008 (UTC)


 * No. You said: A frame is just a class of coordinate systems,


 * and explain what he means when he says you "get" a certain force in a certain frame but you do or do not "get" the same force in certain coordinate systems within that frame. It means you're talking about a different situation than scoped by this article.- (User) Wolfkeeper (Talk) 00:40, 22 September 2008 (UTC)


 * No, you misunderstood the question. Again, the question is: What do YOU (Wolfkeeper) mean when you say you "get" a certain force in a certain frame? This is vitally important.Fugal (talk) 02:25, 23 September 2008 (UTC)


 * Fictitious forces are fictitious. Uhhh. How about no? Fictitious means it doesn't exist at all in reality, that they are unphysical. Fictitious forces do exist, here they're a manifestation of inertia. They do physically exist. They can kill you.- (User) Wolfkeeper (Talk) 00:40, 22 September 2008 (UTC)


 * No, fictitious forces cannot kill you. What kills you is the actual (absolute) acceleration to which you are subjected, and this actual absolute acceleration is proportional to the applied actual forces. Fictitious forces do not contribute at all to your absolute acceleration. Your comment is the kind of misunderstanding that I'm trying to eliminate from the article, by insisting that it be written clearly and correctly.Fugal (talk) 02:25, 23 September 2008 (UTC)


 * So what does it mean to "get" a [fictitious] force in a certain coordinate system (or a certain class of coordinate systems) but not in other? It means you are talking about something that this article is not covering, and is not the normal most common definition of the term 'centrifugal force'.- (User) Wolfkeeper (Talk) 00:40, 22 September 2008 (UTC)


 * First, I note again your non-response to the substantive question (which perhaps is just as well, considering that your previous response gives ample evidence of your level of understanding of this subject). Second, for the billionth time, you are entitled to pass judgement on what is "normal", and wikipedia policy is NOT to limit articles to just the "most common" point of view, but to represent all notable points of view to be found in reputable sources. Hence your comments are completely misguided.Fugal (talk) 02:25, 23 September 2008 (UTC)


 * Here's a reference for what is a Cartesian coordinate system [Korn & Korn] and a curvilinear coordinate system [Korn & Korn]. This (and all other definitions of coordinate system in the mathematical literature) makes no reference to motion, or observer. In contrast, all references to inertial and non-inertial frames of reference refer to motion. For example, [Landau] and [Iro]. Evidently, the two concepts are not the same: one is math, the other is physics. Obviously also, if one can connect a Cartesian coordinate system with an inertial (or a non-inertial frame), the math defines ipso facto any curvilinear coordinate system one might wish to relate to that Cartesian coordinate system. You have only to exercise the coordinate transformations found in the curvilinear link preceding. That is, if the curvilinear coordinates are [q1, q2, … ] and the Cartesian coordinates are [x1, x2, …] there are equations relating the two sets of the form:
 * $$ q_1 = q_1 (x_1, \ x_2,\ ...)$$ &ensp; and so forth.
 * Hence, any Cartesian coordinate selection can be converted to any curvilinear set. You then end up with a curvilinear coordinate system in that inertial (or non-inertial ) frame. Likewise all physical laws transform using the same substitutions to the physical laws as expressed in that frame using that curvilinear coordinate system. Obviously, if two frames are related by a Galilean transformation, then any associated Cartesian coordinate systems also are so-related. Again, ipso facto, a curvilinear coordinate system in one frame is related to a curvilinear coordinate system of the same species in the other frame. Brews ohare (talk) 22:23, 21 September 2008 (UTC)
 * I would add that the mathematical idea of coordinate system is not restricted in any way to three dimensions nor to the interpretation of what the coordinates may mean in any particular application. For example, see [Vladimir Igorevich Arnolʹd, Mark Levi, Joseph Szücs]. The need to use a 3+1 space interpretation of coordinates in a inertial (or non-inertial) frame of reference is another indication that a frame makes use of a coordinate system, but is itself different from a coordinate system. Brews ohare (talk) 00:38, 22 September 2008 (UTC)
 * The fact that a frame can select any of a number of coordinate systems, for example any of a set of Cartesian coordinate systems that differ only in orientation, or differ only in location of the origin, indicates that a frame can be viewed as the "equivalence class of coordinate systems related by rigid translations and rotations of space and translations in time" [Brown]. Of course, such transformations can be applied as readily to curvilinear coordinate frames as to Cartesian frames. One also can call the set of all inertial frames a Lorentz equivalence class, see Kiehn. Brews ohare (talk) 03:19, 22 September 2008 (UTC)
 * All reputable sources on dynamics recognize that time is one of the coordinates of the coordinate system. Are we really down to the level of arguing about whether time is a coordinate? An endless number of reputable references can be supplied to substantiate the fact that time is a coordinate in the science of dynamics, and that inertial coordinate systems include a time coordinate. The comments of Brews ohare are simply incorrect. Quoting from a book describing purely spatial coordinates does not contradict the fact that dynamics is carried out in coordinate systems that include a time coordinate. Perhaps we should ask for this point to be reviewed by a wider audience of scientifically literate editors, to see what they thing?Fugal (talk) 23:17, 21 September 2008 (UTC)


 * You confuse the mathematical term "coordinate system" with the physical application of this mathematical construction in which a coordinate system is applied to describe physical events in a frame of reference. For this application of the mathematical construct, the coordinates are given physical interpretations in terms of space and time. For this application, a Cartesian coordinate system is not essential of course, and many other types of coordinate system are employed depending on how they simplify the problem. For example, an arc-length coordinate system might be used, or a polar coordinate system. I'm sure you know this - you're simply playing games here. Brews ohare (talk) 12:34, 22 September 2008 (UTC)


 * Again, you completely miss the point. In dynamics the coordinate systems are four-dimensional, including a time dimension. (Otherwise, there could no such thing as a "rotating coordinate system".) Also, please do try to bear in mind that you aren't arguing with me, you're arguing with Grunbaum, Earman, Friedman, Stommel, Beer, Johnston, etc. etc., in other words, all the reputable sources that present the view of this subject that you are trying to suppress. Wikipedia policy is to accurately represent all notable views on the subject in a proportionate way. The current article strictly excludes all but one POV. This is not in accordance with Wikipedia policy, and I'm trying to correct it. I've provided plenty of references from the most reputable sources to show the existence of a very notable view (actually several notable views) of this subject, and I am working to incorporate these, in a proportionate way, into the article. It seems to me that you have a strong feeling of "ownership" over this article, and you absolutely refuse to allow any view other than your own personal point of view to be represented. In the long run, I don't think you will be able to maintain the level of personal ownership of this article.Fugal (talk) 00:17, 24 September 2008 (UTC)
 * You amaze me by suggesting that the fact time is a coordinate has a role in all this. You also wander off-topic to repeat how impeccable your arguments always are blah-blah. Here is the question you raised:
 * So what does it mean to "get" a [fictitious] force in a certain coordinate system (or a certain class of coordinate systems) but not in other?
 * And here is the rub: there are two usages of "fictitious force". In the approach of Stommel and Moore, in a inertial frame there are fictitious forces if (and only if) you use curvilinear coordinates. On the other hand, in a non-inertial frame there are "additional" fictitious forces due to acceleration of the frame relative to an inertial frame. The quotations I have provided (with links where you can read the entire discussion surrounding these quotes) provide their discussion for the case of polar coordinates.
 * Despite this answer to your question, I am sure you will say that I have misread Stommel and Moore, but that you will not go into any detail why that is so. Instead, you will wander off and explain your noble quest for sanity in a desert of ignorance. Brews ohare (talk) 08:21, 24 September 2008 (UTC)

Introductory material
Fugal: You might have a point that a better intro could be drafted in terms of some ethereal approach to the subject that you understand. Unfortunately, that approach is outside of the common attack upon the subject as presented in Arnol'd, for example, Taylor for example, or Stommel and Moore for example.


 * You're mistaken. As has already been explained repeatedly and at length, the references you mentioned (along with many others) explicitly support what I'm saying, and contradict what you are saying. I've pointed out that you mis-understand and therefore mis-represent those references. For example, Stommel and Moore say


 * "In this chapter we have faced the fact that there is something of a crisis in intuition that arises from the introduction of the polar coordinate system, even in a non-rotating system reference frame. When we first use rectilinear coordinates to understand the dynamics of a particle, we commit our minds to the simple expressions x" = F_x, y" = F_y. We think of the accelerations as time rate-of change [per unit mass] of the linear momentum X' and y'. Then we express the same situation in polar coordinates that partly restore the wanted form. In the case of the radial component of the acceleration we move the r(theta')^2 term to the right hand side and call it a "centrifugal force."Fugal (talk) 19:49, 20 September 2008 (UTC)


 * Fugal:This quotation indicates that Stommel and Moore (p. 36) treat the additional terms in the acceleration in polar coordinates as fictitious forces, even in an inertial frame. See this [link]. That is not an issue. I call this the "coordinate" usage of the terminology "fictitious force". Then on [p. 55] (in Chapter III on "Rotating Frames") they say the centrifugal force in the rotating frame has additional centrifugal "force" &Omega;2r due to the system's rotation rate &Omega; in absolute space. This additional centrifugal force of theirs is exactly the "state-of-motion" centrifugal force that vanishes in a non-rotating frame. It appears to me to be just a matter of semantics whether one calls these additional terms "additional terms" or "state-of-motion" terms. So in terms of the math, everybody is on the same page. The dispute, I'd say, is over this: does every author use the Stommel-Moore approach, or not. The answer is clearly "not". Some authors treat the "additional terms" as the entire fictitious force and treat the the coordinate-based terms that enter the acceleration in every frame of reference as simply that: terms introduced by the coordinate system. For example, Taylor does exactly this. So whatever importance one might attach to these two methods, there are two usages.
 * This discussion of Stommel and Moore is just the same as that in the centrifugal force (planar motion) article. Brews ohare (talk) 14:16, 21 September 2008 (UTC)


 * Again, all fictitious forces are "coordinate based", so it makes no sense to call some of them "coordinate based" and others "state of motion based". That is simply a novel narrative that you have personally fabricated, not supported by any reputable sources, and as such it doesn't belong in Wikipedia.Fugal (talk) 20:14, 21 September 2008 (UTC)
 * Fugal: My treatment of Stommel and Moore follows their approach closely with numerous links that leave no doubt as to the accuracy of my portrayal of their stance. A complete and detailed treatment is in centrifugal force (planar motion). Anyone (but you) can understand it and compare it with the original text. Your abusive response that does not attempt anything, but simply inventories various nasty adjectives, indicates that there is no purpose in trying to talk to you. So I won't. Cheerio. Brews ohare (talk) 20:45, 21 September 2008 (UTC)


 * There was nothing abusive in my response, unless you consider that anyone who disagrees with you, and backs up their disagreement with detailed explanations and extensive references, is "abusive". Once again, there is an article on rotating reference frames, and then another article was created, in which you claim (intermittantly) that you (1) describe planar motion, and (2) describe the more general view of centrifugal force, not restricted to the rotating reference frame point of view. But all the quotes in this second article (the one NOT on rotating reference frames) come from the section "Rotating Reference Frames" from Stommel and Moore. And there is no sign of an accurate presentation of the more general view. So when you say there are "numerous links that leave no doubt as to the accuracy of my portrayal of their stance", you are, I believe, mistaken, for the reasons explained on this discussion page.Fugal (talk) 23:35, 21 September 2008 (UTC)


 * Likewise in McQuarrie's "Statistical Mechanics" he says


 * "Since the force here is radial, it is convenient to use polar coordinates. Taking x = r cos(theta) and y = r sin(theta) [i.e., stationary polar coordinates] then... If we interpret the term [r(theta')^2] as a force, this is the well-known centrifugal force..."


 * And so on. I've also provided links to online sources, such as John Baez's web page, on which he derives the fictitious centrifugal force in stationary polar coordinates.


 * Look, you continue to delete and ignore the above words of Stommel (for example), and then you turn to the section of his book entitled "Rotating Reference Frames" where you extract some text that refers to (suprise) rotating reference frames, and then you claim that this represents the entirety of the subject according to Stommel and Moore! In accord with Wikipedia policy, I'm steadfastly assuming good faith on your part, but frankly, if someone asked me to explain how, in good faith, anyone could continue making these kinds of mis-representations, I would be unable to answer.Fugal (talk) 19:49, 20 September 2008 (UTC)
 * I plead innocent of deleting or ignoring the discussion by Stommel. Please look at centrifugal force (planar motion) and my earlier remarks. Brews ohare (talk) 14:16, 21 September 2008 (UTC)


 * When the current article says that In classical mechanics, centrifugal force is [the terms arising from curved time axes, but from curved space axes], it is making a claim that is contradicted by Stommel and Moore (not to mention the numerous other references that have been cited). Your plea of innocence is false.Fugal (talk) 20:14, 21 September 2008 (UTC)


 * The term 'Centrifugal force' really is used to describe force terms in polar coordinates even in inertial frames; indeed I have added that quite clearly to other articles. But it's a question of NPOV. What do most people mean when they use the term 'Centrifugal force'. Above I have shown evidence that in most cases they are referring to rotating reference frames. That being the case, we end up with the article that we have here. Cherry picking references from text books to an opposing usage doesn't count. Nobody here says that the term isn't used that way. It's about not giving undue weight.- (User) Wolfkeeper (Talk) 20:23, 20 September 2008 (UTC)


 * That's not correct. The current article does say that "in classical mechanics, centrifugal force is such and such". and the "such and such" is just one of things that the term centrifugal force represents in classical mechanics. So the article is wrong and misleading. You simply can't make the kind of categorical statement that you obviously wish to make in this article. It needs to be toned down, to accurately reflect the entirety of the reputable literature on this subject, rather than just the one particular point of view that you favor. And please note that "undue weight" does not imply that every point of view other than the one that is presented in 51% of the published sources is to be suppressed. All points of view represented by a significant and notable portion of the reputable literature are to be represented in the article. And the situation here is even less supportive of exclusion, because the 49% of the published texts that present the more encompassing view happen to be the more advanced and sophisticated ones, whereas the 51% of the texts that present the restricted and simplistic view are the introductory texts, and almost all of them admit right up front that they are presenting a restricted view of the subject. Furthermore, the two views are not even contradictory, if one understands them. There simply is no justification for excluding from this article all but the one limited point of view that you personally favor.Fugal (talk) 05:34, 21 September 2008 (UTC)


 * You are right that there is another usage for the term centrifugal force in the literature. However, I'd say the cited references in centrifugal force (rotating reference frame) all support the view presented.


 * Well, first, that is not correct, for the reasons explained on this Discussion page. Second, even if it was correct, it wouldn't be a defense of the POV unbalance, it would be a symptom of it. The criticism is that the page is biased toward one particular POV to the exclusion of all the others. It makes no sense for you to try to defend this by saying that only references supporting that particular POV are presently included in the article. Honestly, this discussion is being reduced to tutorials on the application of elementary logic and reason. At this rate, it will be centuries before we ascend to the level of actually discussing the science of dynamics.Fugal (talk) 19:52, 21 September 2008 (UTC)


 * I'd say further that the standard and predominant viewpoint of classical mechanics is this one,


 * As already explained, predominant does not imply exclusive. In order to justify the categorical attitude of the present article you need to show that any other POVs are held by an insignificant or non-notable minority... which is clearly not the case. The number of references containing different POVs on this subject is actually about equal to the number supporting the POV of this article... and this doesn't even consider the fact that the real predominant view is that the concept of centrifugal force shouldn't even be used at all! I can supply plenty of quotes of authors asserting strenuously that it is simply a misguided and worthless and ambiguous concept. All these views should represented in the article, not just the single POV that you personally prefer.Fugal (talk) 19:52, 21 September 2008 (UTC)


 * inasmuch as the very definition of an inertial frame is one where fictitious forces vanish.


 * Again, your misunderstanding of this point has been explained over and over and over.


 * As an example, look at the citation, which has exactly the same formulas for the fictitious forces as Arnol'd and as Taylor. It's my understanding, however, that you do not agree that there are two usages, but in fact only this secondary usage I call the "coordinate" usage. Brews ohare (talk) 15:24, 21 September 2008 (UTC)


 * Your understanding is wrong, as I've explained over and over and over. The references you've cited all stipulate that they are restricting their considerations to rectilinear spatial coordinates, so the contributions to the fictitious forces arising from curvilinear coordinates don't come into discussion. Other authors take the more general unrestricted view.Fugal (talk) 19:52, 21 September 2008 (UTC)


 * Thus, the available literature treats the matter in a manner consistent with the articles. If you wish to make a more fundamental attack upon the subject it therefore falls upon you to write the appropriate text and provide the appropriate back-up from available texts.


 * I did just that.... and you summarily deleted it, giving as the justification your usual fallacious claims that have been refuted countless times.Fugal (talk) 19:59, 21 September 2008 (UTC)


 * Regardless of your success in this endeavor, the existing pages will stand, as they present the vastly dominant viewpoint that everyone can find in the associated citations.


 * Ah, now we see the true colors. Regardless of what any other editors try to do, "the existing pages will stand". This is simply an inappropriate attitude. You do not own these articles.Fugal (talk) 19:59, 21 September 2008 (UTC)

So far, you have repeatedly said that everything necessary has already been provided by you. However, your criteria for clear and documented presentation falls a bit short for the Great Unwashed. Speaking for myself, I simply have a vague shadow in my mind of what you are looking for, and attempts to get more specifics from you is like trying to return defective merchandise.

You apparently feel you are talking to dummies, but if that really is what you are doing, calling them dummies is not going to smarten them up. You'll have to bend a bit, and explain 2 + 2. Brews ohare (talk) 11:53, 20 September 2008 (UTC)


 * I've given you several references, such as Friedman, that explain all this in great detail. Wikipedia discussion pages are not supposed to be used to discuss the subject of the article, but to discuss reputable verifiable sources. As a courtesy, I've tried to bend the rules and explain some things, but that obviously hasn't worked. Tim Rais also tried to explain some things to you, and it didn't work. The references I've provided to you haven't helped either. Are you absolutely sure this is the fault of the explanations? I personally found Tim's explanations to you to be quite clear and correct. And yet you found them to be utterly inscrutible. Again, on the assumption of good faith, I'm unable to account for this.Fugal (talk) 19:49, 20 September 2008 (UTC)


 * It's not enough to be clear and correct. We agree it's a clear and correct meaning. But there's only one meaning allowed per article, and that's not the dominant one. It would just simply be undue weight to include it here: WP:UNDUE. It is covered elsewhere though.- (User) Wolfkeeper (Talk) 20:23, 20 September 2008 (UTC)


 * No, what was clearly and correctly explained is that this is all just different ways of looking at the very same thing. You are trying to promote one particle POV on this subject, which is inappropriate, per Wikipedia policy. Fugal (talk) 21:14, 20 September 2008 (UTC)


 * Even if we assume you're correct, your argument is of the same form as arguing that electrostatics and magnetism are two sides of the same thing, namely, electromagnetism. Well, yeah. But we still have separate articles on electrostatics and magnetism. Likewise even if you were to successfully argue that polar coordinate centrifugal force and non inertial frame centrifugal force are essentially the same thing, will this article disappear? No, because it helps the users understand physics.


 * And, we already tried adding as much of the curvilinear tensor stuff here, and the consensus was to take it out. So your argument is moot, either way. Either you're wrong and then your argument doesn't matter. Or you're right, and it doesn't matter.- (User) Wolfkeeper (Talk) 02:14, 21 September 2008 (UTC)


 * [This reply was deleted by Brews ohare. I'm restoring it.] Other editors have objected to all the forks, and those editors might also object to forking electrostatics and magnetism, but that is not the point I've been making. The point I've been making is analogous to saying that an article on electrostatics should not begin with the sentence "In physics, electromagnetism consists of electrostatics". That is simply an incorrect and misleading statement. Electrostatics is a special case of electromagnetism, i.e., a restricted part of a more general subject. The problem with the current article is that it seems determined to give the reader the impression that this one specialized sub-set of the subject of centrifugal force in classical mechanics constitutes the entire proper content of the subject. That is false and misleading, and it ought to be fixed. And it could be fixed rather easily. Just unclench and describe what the article's context is in an honest way, that accurately represents the published literature on the subject.Fugal (talk) 03:40, 21 September 2008 (UTC)


 * Fugal, well said! The fact that I came directly on this page instead of on the disambiguation page, together with the false impression of the introduction sentences makes me wonder if someone purposefully tried to impose his POV on this topic, in opposition to what Wikipedia stands for. Does anyone know if this is a regretful coincidence or manipulation? Harald88 (talk) 14:06, 25 September 2008 (UTC)

Improper Removal of POV and Dispute Tags
I think it should be noted that, on at least two recent occasions, POV and Disputed Content tags have been unilaterally removed from the article, without the agreement of the parties that inserted the tags, despite the fact that Wikipedia policy (as well as the tag templates themselves) specifically state that such tags should not be removed until the dispute is resolved on the associated Discussion page. The individuals who inappropriately removed the tags (Brews ohare in one case and Wolfkeeper in the other) are the same two editors who have been cited by at least four other editors as displaying clear signs of "ownership", and have been requested by several editors to take a break from editing this article, since they have lost all perspective on the subject. I think the unilateral removal of tags from "their" article is further evidence of an inappropriate attitude of ownership. At some point, I think some mediation is going to be required. If nothing else, it would prevent these outright violations of Wikipedia policy, so that the discussion could continue within the approved rules.Fugal (talk) 05:13, 21 September 2008 (UTC)

I should have made it clear that the tags in question had not been present for long periods of time, with no recent attention being paid to them. In such cases, it may be reasonable for someone to just delete tags that seem obsolete. In both the cases I'm referring to, the tags were place, and then unilaterally removed within hours, by Brews ohare and Wolfkeeper, respectively, over the clear objections of those who inserted the tags.Fugal (talk) 05:21, 21 September 2008 (UTC)
 * "Just for the record", the tag removal was accompanied in one instance by a major re-write of the article that removed all controversial material. That removal was instigated by PeR. In the second case, the reasons for placing the tag weren't presented, and the removal of the tag was accompanied by an explanation that was not contested. Brews ohare (talk) 15:00, 21 September 2008 (UTC)


 * Brews ohare's statements above are incorrect. As explaiined previously (and as anyone can check for themselves by looking at the history of the article), both of the improper removals followed the placements of the tags by just hours, and there were no re-writes. Brews is answering these charges by referring to a completely different set of tags. This illustrates the danger of unilateral action, because Brews always thinks he knows what people are objecting to, and he's (unfortunately) always wrong. Since he never works for genuine resolution of the issues on the Discussion page (which is what is supposed to happen), he just goes on acting based on his misunderstandings.


 * As to Brews' statement that explanations for the removals were given and "not contested", this is both self-evidently false (just look at this Discussion page!) and is not a valid excuse in any case, because the tags are not to be removed until AFTER resolution has been reached on the discussion page. Brews and Wolf seem to think they are entitled to unilaterally remove tags, and simply place a statement in the removal edit summary. Then when people who placed the tags, who are not obsessed with this article the way Brews is, come back some days later, they find that the tag was unilaterally removed just hours after they placed it, and when they challenge Brews about it, he says "well no one contested the removal". Then the person puts the tags back, explaining why on the Discussion page (as appropriate), and Brews or Wolf immediately removes them again unilaterally, and so it goes.


 * This is quite obviously NOT the way POV and Disputed content tags are supposed to work. Also, please note that people are encouraged to avoid putting contentious objections into the tags themselves, because the tags sit on the article, and should not contribute to the dispute. The customary preferred approach is to simply point to the discussion page for details of the dispute, which is where resolution is to be reached, NOT in the edit summary comments.


 * The high-handed unilateral treatment of POV and Disputed content tags is symptomatic of the abuses that Brews and Wolf have been practicing in their editing of this article. It is quite obvious that the issues were not resolved... simply ask Harald (for example) if he considers that the issue prompting him to place the tag has been resolved. Or ask me if I think the issue prompting my placement of a tag has been resolved, or look at this very Discussion page to see if you think the issue over POV and Content has been resolved. For Brews to say that the removal of these tags was "uncontested" is self-evidently false. And the fact that he can make such a self-evidently false statement with a straight face is just more evidence of his complete loss of perspective on this subject.


 * Ideally, the people placing tags should be the ones to remove them. They are certainly not to be removed without reaching resolution of the issue, and this does NOT mean that within Brews or Wolfs mind the issue has been resolved, it means that a consensus has been reached on the discussion page. Brews has demonstrated that he can posted 50 or 60 messages per day to this Discussion page, and if each of his posts is not answered to his personal satisfaction, he considers that the issue has been resolved in his favor. This really has to stop. I say again that we need some administrative help on this page.


 * I'm going to put to POV tag back on the page, and I trust (in good faith) that it will not be removed by Brews or Wolf until resolution has been reached on this Discussion page, per Wikipedia policy.Fugal (talk) 18:11, 21 September 2008 (UTC)


 * These tags will be there forever, because there is absolutely no possible method to reach agreement with you. Your approach is to blah-blah, ignore attempts at clarification, then refer to these clarifications as garbage, and finally to say that you have presented a definitive view time and again (claiming in addition, acceptance by a host of imaginary editors, something like the Verizon "team" that follows all their customers). What you really have done, of course, is to repeat your same stance over and over again and repeatedly characterize any attempt at discussion as the argument of the silly and uneducated. Enjoy the tags. Brews ohare (talk) 20:51, 21 September 2008 (UTC)


 * As I understand it the purpose of these tags was because Fugal is claiming that one phrase in one sentence might be interpreted by someone in a way that is contrary to what the rest of the sentence, and every other sentence around it says. Given that, I feel that tagging the entire article is completely unnecessary and ridiculous, and I have removed it. I encourage people that are considering tagging an article to instead tag the particularly sentences or paragraphs that they have an issue with.- (User) Wolfkeeper (Talk) 21:24, 21 September 2008 (UTC)


 * To prove my point, within just a couple of hours of my restoring the improperly removed tags, Wolfkeeper summarily removed them, with the edit summary "Ridiculous bad-faith tags removed". Then we find the above comments from Brews and Wolf, in which Brews attempts to justify unilateral removal of dispute tags on the grounds that "there is absolutely no possible method to reach agreement with you", but of course he fails to acknowledge that the tag wasn't placed by me, it was placed (most recently) by Harald, and that Brews was also unable to reach agreement with Tim Rias. And of course he seems oblivious to the fact that it is the nature of a dispute that people disagree. The fact that he is unable to get the (several) people who believe he is wrong to change their minds does NOT constitute grounds for him to unilaterally declare that the disagreement has been resolved in his favor.  Sheesh.


 * As to Wolfkeeper's comments, I probably don't need to add much. He makes my point for me. He feels himself entitled to unilaterally ajudicate all disputes, and make unilateral rulings on the validity of other's people's statements, and to violate Wikipedia rules at will, by unilaterally removing dispute tags without resolution of the issue on the discussion page. I repeat that we are badly in need of some administrative assistance with this article. In particular, the latest removal of the POV and unbalanced tags by Wolfkeeper, combined with his explicit accusation of bad faith (which is also in violation of Wikipedia policy) is bordering on vandalism.Fugal (talk) 22:46, 21 September 2008 (UTC)


 * We know what you're doing. You're just trying to give undue weight to your interpretation of this particular topic. That's all these tags are ever used for. It shouldn't be like that, but that's what they are, in practice used for. If this was done like that based simply on my opinion, you would have a strong case. Instead, this article has been carefully scoped to match the most common definition of the term 'centrifugal force' and references to use of that term in that way are already in the article. More importantly, analysis of google searches has been done above to show that that seems to be the most common significant usage on the web; so this does not seem to be undue weight in any way.- (User) Wolfkeeper (Talk) 04:23, 22 September 2008 (UTC)


 * Other definitions are found elsewhere in the wikipedia. Normally a very general definition is good for articles. But the most general usage of the term (any center fleeing force) isn't appropriate here because the wikipedia is not a dictionary and does not define terms it's about topics. Your attempts to show that centrifugal force as defined for polar coordinate systems is on topic here hasn't really worked, because that force physically behaves differently and because although they may become the same in a very general tensor treatment, that tensor treatment has been judged to be off-topic here (and not by me.) In my opinion, what you're trying to achieve is pointless and not obviously useful for the likely readership of the article, and tagging the article only hurts your case and the wikipedia.- (User) Wolfkeeper (Talk) 04:23, 22 September 2008 (UTC)


 * I can't speak for others who have tried to place the NPOV tag and had it summarily removed, but my intent in placing the tag was simply to indicate that the NPOV of the article is disputed (which is a simple statement of fact, because I for one dispute it), and readers should consult the Discussion page for details of the dispute. In working toward a resolution of the dispute, I've begun with the first sentence of the article, but I don't mean to imply that it is the only sentence that needs work. It's just the first one. I'm specifically trying NOT to give undue weight to any particular view of the subject. Indeed, my whole objective of my proposed re-wording. I've read your opinion about dictionaries and terms versus topics previously, and I and others have commented that the "bark" of a tree and the "bark" of a dog should certainly be two different topics, but it is much less clear that the concept of centrifugal force in classical mechanics should be regarded as multiple different topics. In all cases, there is a general meaning of an outward tendency associated with rotation in some sense. So it isn't totally unreasonable to say that this constitutes a single topic, albeit a topic with several different nuances, contexts, and formalisms. Hence I don't see any justification for your unilateral removal of tags from the article.Fugal (talk) 15:59, 23 September 2008 (UTC)

Wolfkeeper erases Brews Ohare's comments?
For the record, I see from the "history" page that Brews Ohare posted several comments, and then some minutes later they were all removed (without explanation) by Wolfkeeper. This leaves me unsure about whether to respond to the erased comments or not. I've noticed that Brews Ohare frequently posts numerous furious comments, and then minutes later edits them and sometimes removes them, which is confusing enough when trying to carry on a discussion, but now that Wolfkeeper has taken on the job of deleting Brews Ohare's comments, it has become even more confusing. Oddly enough, these are the same two editors who have improperly deleted Dispute tags from "their" article. Curious.Fugal (talk) 05:47, 21 September 2008 (UTC)
 * Wolfkeeper: Can you explain why this was done? I do not believe my remarks were intemperate or inflammatory, with the possible exception of reflecting some of Fugal's recommendations for my self-education back to him with a "likewise". Brews ohare (talk) 05:56, 21 September 2008 (UTC)
 * I've reinstated some of my remarks; please do not remove them. Brews ohare (talk) 15:07, 21 September 2008 (UTC)
 * I see what happenned. There is one new comment from Wolfkeeper added in the edit that removed the comments from Brews. Probably Wolf was editing a version of the discussion page that he chose from the history links, and in the mean time Brews added a bunch of edits and saved them, and then Wolf saved his edit of an earlier version, which obliterated Brews's edits. By editing from a link on the history page, it seems to not give an "edit conflict" message.Fugal (talk) 18:19, 21 September 2008 (UTC)
 * Yes, it happens occasionally, I've never managed to pin down exactly what triggers it. I never knowingly remove other people's comments from a talk page (unless they are clearly vandalisations, which doesn't apply here). I can only apologise, as I do here, when it happens. It's very annoying, and there is no warning. Some kind of race condition in the UI perhaps.- (User) Wolfkeeper (Talk) 20:21, 21 September 2008 (UTC)

Brews ohare Deletes Fugal's comments
Now I've noticed that Brews ohare deleted my reply to Wolfkeeper in the "Introductory Comments" section above. I assume this, too, was inadvertent, but it does suggest that two particular editors here could stand to cool down a bit, and be a little more careful and deliberate with their messages.Fugal (talk) 23:03, 21 September 2008 (UTC)
 * Sorry, inadvertent. Brews ohare (talk) 03:23, 22 September 2008 (UTC)

= The neutrality of this article is disputed. =

This dispute is stated as follows:

There are two uses for the terminology centrifugal force. The dispute is over which of these usages is most commonly used and which should be the basis of this article.

According to one usage, centrifugal, Coriolis and Euler terms (or forces per unit mass) arise only by virtue of physical acceleration of a frame of observation. An example of this usage is Iro:

The term "pseudo-force" is a synonym for centrifugal, Coriolis and Euler forces. Another example is Arnol'd: or in Hawley:

or in Shadowitz:

An alternative presentation of this viewpoint can be found in Taylor.

According to a second usage, these terms arising from physical acceleration are only "extra" centrifugal, Coriolis and Euler terms (or forces per unit mass). Besides these motion-induced contributions, all terms in the mathematical expression for acceleration other than the second time derivatives of the coordinates chosen should be included. (In curvilinear coordinates, in the mathematical expression for acceleration various additional terms arise that may be first or zero-order time derivatives in the coordinates, varying with the choice of curvilinear system. These terms are zero in a Cartesian coordinate system.)

To illustrate the second viewpoint, here is the discussion for an inertial frame (where centrifugal force is zero according to the first viewpoint) from Stommel and Moore:

Later, in discussing a frame rotating at angular rate &Omega;, Stommel & Moore state:

These two quotations from Stommel and Moore illustrate the second viewpoint that centrifugal force exists in inertial frames, and is supplemented by "additional" centrifugal force when the system rotates. Brews ohare (talk) 16:46, 22 September 2008 (UTC)


 * The above statement of the dispute is disputed. Indeed, the actual dispute is over precisely the neoligisms and novel narrative POV embodied in the above "statement of the dispute". Brews ohare contends that there is a dichotomy in the subject between what he calls "state of motion fictitious forces" and "coordinate fictitious forces". These terms, and this dichotomy, are not to be found in any published reputable source. Hence they are not verifiable per Wikipedia policy, and the article should not be based on that point of view. In contrast, reputable sources have been cited to substantiate that ALL fictitious forces are based on the chosen coordinates. In addition, it's worth noting that the only reason anyone is hung up on precisely how to characterize the distinction between two acceleration terms is due to the tactic adopted by some editors here of trying to exclude aspects of the subject of this article by claiming that they are different "definitions", as opposed to the same definitions in different contexts. I believe this tactic (dictionary versus encyclopedia) was originally adopted in order to suppress some kooky ideas of a former editor, but the tactic is no longer useful, and it largely responsible for driving the discussion down this dead-end of arguing about how precisely to characterize the distinction between two acceleration terms.


 * So, a more accuate statement of the dispute is: The subject of "centrifugal force" in classical mechanics is complicated and has many facets and nuances, and is regarded in many different ways in the technical literature. Many authors discourage the introduction of any fictitious forces, and they maintain that the science of dynamics has no need for the concept of fictitious. Other go to the opposite extreme, and adopt the d'Alembert principle of making EVERYTHING into fictitious forces, thereby reducing dynamics to statics. Among those who reject the utility of fictitious forces, many argue that the term "centrifugal force" ought to be reserved for an actual force, namely, the reactive force. There are other authors who believe the only legitimate use of the term is as the outward inertial force on a particle following a curved path when described in terms of an instantaneously co-moving inertial coordinate system. More advanced texts on the foundations of mechanics take a more general view of fictitious forces. Hence, even within the "fictitious force" camp, there are numerous points of view. The current article has been narrowed in scope to just one small sub-region of this convoluted topic. I believe this has been done merely as a tactic to allow the "owners" of the article to avoid making any changes. That's fine, if they really narrow the scope, but the text of the article hasn't been updated to fully reflect the narrowness of the scope. It continues to make catagorical statements about what "centrifugal force" means in classical mechanics. So the dispute is over this POV aspect of the article. I believe some revisions of the text are needed to eliminate the residual POV aspects of the article. Some other editors have expressed agreement with this, while others maintain that the current article should not be tampered with in any way. These two editors (Brews and Wolf) believe they "own" this article, and they should be able to dictate what it says. I disagree. I think the article needs to be written in a NPOV way, in accord with Wikipedia policy.Fugal (talk) 16:04, 22 September 2008 (UTC)


 * The "nonexistent dichotomy" in terminology is supported by direct quotes from published sources. No citations support the fog being spread over the entire subject by this respondent. Brews ohare (talk) 16:57, 22 September 2008 (UTC)


 * What Brews refers to as "fog" is explained very clearly in the reputable literature, such as Firedman's "Foundations of Space-Time Theories", as well as in Stommel and Moore, and several other references that have been cited and quoted on these page. Moreover, the quotations that Brews claims support his case actually do not. For example, he displays the statement "An additional force due to nonuniform relative motion of two reference frames is called a pseudo-force." Well, that's a perfectly true (if somewhat sloppily expressed) statement. But from this Brews infers that converse, i.e., he thinks that statement asserts the propositions that a pseudo-force is an additional force due to non-uniform relative motion of two reference frames. In other words, when Brews reads that all gold glitters, he jumps to the conclusion that everything that glitters is gold. So the discussion devolves into these silly examinations of rudimentary logic. This is not just an isolated case. My observation is that Brews consistently mis-construes what he reads and quotes. In many many case I've gone to the trouble of finding his source and explaining in detail how he has mis-understand, but he never gets it. This is why I think it probably won't be possible to achieve consensus until some additional editors joint the discussion, to bring a broader perspective with less of a vested interest and sense of "owership".Fugal (talk) 18:27, 22 September 2008 (UTC)

In support of the present organization of the article

 * There is no dispute that centrifugal, Coriolis and Euler terms (or forces per unit mass) arise by virtue of physical acceleration of a frame of observation. Supporting special consideration of these forces alone, rather than all the terms of the second view, is the observation that these motion-related forces are coordinate-system independent and therefore have a claim to reality in an accelerating frame. That is not true of the second terminology, in which (i) the coordinate contributions vary with the choice of coordinate system, not only in form but in quantity and direction (in a stationary frame, they are zero in Cartesian coordinates and non-zero in polar coordinates, for example); and (ii) the coordinate contributions always are present regardless of whether the frame physically accelerates or is stationary. Thus, the first view has claim to physical reality, while the second view has an accidental nature originating in mathematical choices and not in physical consequences.


 * Of course, logic is not an argument in Wikipedia; the real issue is the predominant usage, and there is no doubt that the predominant view in texts and journals on the subject of classical mechanics is that centrifugal, Coriolis and Euler terms (or forces per unit mass) arise only by virtue of physical acceleration of a frame of observation. This predominance is established in the article by numerous citations to popular treatments, undergraduate texts and technical monographs of great authority.


 * A related concern in Wikipedia could be accessibility and utility of the article. The article name should reflect common usage. The first viewpoint is the one closest to the common perception of centrifugal force as illustrated in the examples of a centrifuge, the graviton amusement park ride, and in cornering a car or banking an airplane. In these examples the centrifugal force is very obviously the result of physical acceleration. Thus, the first viewpoint is most transparent to the readership most likely to consult the article.


 * A case can be made, however, that in some areas, notably in robotic design where the state-space of the robot is described by numerous coordinates describing orientation of links and extensions of links, the second viewpoint is predominant. Obviously, the "coordinate system" in this field is a more abstract concept than 3D-coordinates in Euclidean space. Needless to say, this field of study is not the subject of this article on centrifugal force.


 * It should be noted as well that a more technical article centrifugal force (planar motion) provides a detailed discussion of both viewpoints in a more appropriate context. Brews ohare (talk) 14:53, 22 September 2008 (UTC)

Opposed to the present organization of the article
The case opposing the present wording of the article is presented below in this discussion page (in the section entitled "Proposal for..."), along with a specific proposal for re-wording of the introduction to make it NPOV. I think that proposal clearly shows the kinds of changes that are needed (in my opinion) to eliminate the objectionable POV aspects of the existing article.

So, in this section, I'll just comment on the above statements from Brews in which he supports the current wording of the article. Unfortunately, it appears to me that each of the sentences in his defense of the current article is either factually incorrect, a non-sequitur, or misleading. These issues have all been repeatedly explained already on this discussion page, but maybe it's worth taking it one sentence at a time, and summarizing what is wrong with each of those statements.

(1) "There is no dispute that centrifugal, Coriolis and Euler terms (or forces per unit mass) arise by virtue of physical acceleration of a frame of observation."

That sentence is false. In fact, the entire dispute is over the muddled and ambiguous phraseology contained in that sentence. It talks about things "arising by virtue of", which is not scientifically meaningful, and it talks about "physical acceleration", in an effort to distinguish this from non-physical acceleration (as called by Brews "coordinate acceleration"), and it refers to "frame of observation" in an effort imbue the word "frame" with some kind of additional authority... again, not supported in any reputable literature. That single sentence embodies most of the neolegisms, novel narrative, and original research that Brews has tried to insert into this and several other Wikipedia articles.

(2) Supporting special consideration of these forces alone, rather than all the terms of the second view, is the observation that these motion-related forces are coordinate-system independent and therefore have a claim to reality in an accelerating frame.

That sentence is false. All fictitious forces are fictitious. None of them have coordinate-independent existence. The concept of "motion-related forces" is another neologism of Brews ohare, not supported by the reputable literature. Brews does not understand that, in classical dynamics, the coordinate systems have four (not just three) coordinates, time being a coordinate. What Brews calls "motion-dependent forces" is just his novel way of describing the effect of coordinate basis vectors changing as a function of time, which is not qualitatively different than the effects of coordinate basis vectors changing as a function of space, as explained in many reputable reference sources.

(3) That is not true of the second terminology, in which (i) the coordinate contributions vary with the choice of coordinate system, not only in form but in quantity and direction (in a stationary frame, they are zero in Cartesian coordinates and non-zero in polar coordinates,

That statement is based on a false premise, because (as noted above) all fictitious forces depend on the choice of coordinate system. We can choose a coordinate system with basis vectors that change in time or in space or both.

(4) The coordinate contributions always are present regardless of whether the frame physically accelerates or is stationary.

Again we find the neoligism "physical acceleration" (as opposed to non-physical acceleration?) applied to the concept of a frame, but a frame does not have a unique acceleration (allowing for rotation), and a frame is simply an equivalence class of mutually stationary coordinate systems, so the assertion of a fundamental dichotomy between frames and coordinate systems is unfounded.

(5) Thus, the first view has claim to physical reality, while the second view has an accidental nature originating in mathematical choices and not in physical consequences.

That is pure original research (and, by the way, false). Wikipedia articles are not supposed to be based on Brews ohares personal philosophical musings about what is "physical" and what is "mathematical". His ideas are not supported by any reputable sources (not to mention that they are also false).

(6) The real issue is the predominant usage...

That is false. The Wikipedia policy says that coverage in an article should be proportionate to the coverage in reputable published sources. It does not say we are to identify the view that is most commonly discussed (51%), and exclude all other views of the subject. This is especially important in this case, because there are so many different and inter-related views of this subject. So it isn't a question of identifying just one "predominant usage" (which, in any case, has changed over time...).

(7) There is no doubt that the predominant view in texts and journals on the subject of classical mechanics is that centrifugal, Coriolis and Euler terms (or forces per unit mass) arise only by virtue of physical acceleration of a frame of observation.

That is not true. We can start to make lists of all the books on dynamics, and count how many take each of the various points of view on "centrifugal force", but the answer will vary greatly from one decade to the next, and even for books written at roughly the same time, there are a multitude of views. Many (I actually suspect most) authors of books on Dynamics just mention the concept of centrifugal force in passing, often accompanied by a remark like "Sometimes people pretend this acceleration term is a force, and call it the centrifugal force, but it really isn't a force, so don't do this". Others (although not many) go whole hog in the other direction, and adopt d'Alembert's principle. Then there are a lot of books that use the "pilot's" frame of reference, in the osculating plane, and they split up the inertial force into just two components, normal and tangent to the path, calling the normal component the centrifugal force. And so on. I frankly don't know how a complete survey of references books would turn out, but I suspect one would also find examples (such as those on some web links) where the author claims to define centrifugal force in terms of rotating coordinates, but then actually derives it in terms of stationary polar coordinates. I'm not sure how to "count" sources like that. In any case, I think it's fair to say that the "predominance" mentioned by Brews is not a fact in evidence. Moreover, as noted above, even if we identify the one particular usage that has a majority or plurality of references, this still does not justify the exclusion of all the other views. Wikipedia policy says all views in reputable sources should be given proportionate coverage. Surely no one disputes that there are multiple views of this subject to be found in the reputable literature.

(8) This predominance is established in the article by numerous citations to popular treatments, undergraduate texts and technical monographs of great authority.

That sentence is false. An equal number of references (of equal authority) have been presented in which different views are presented, but those references have been suppressed by the self-appointed "owners" of this article. In addition, most of the references that Brews claims support his POV actually don't. He fails to read and/or understand the context established by those references.

(9) The article name should reflect common usage.

That sentence is false. I don't know on what basis Brews makes this claim, but in any case, the common usage of a term like "centrifugal force" doesn't necessarily have much to do with the scientific useage of that term, and it isn't clear how to go about verifying "common usage" as opposed to the usage in the scientific literature. This too easily slides into original research, as we find in Brews's next sentence.

(10) The first viewpoint [i.e., Brews' POV] is the one closest to the common perception of centrifugal force as illustrated in the examples of a centrifuge, the graviton amusement park ride, and in cornering a car or banking an airplane.

That sentence is a non-sequitur. The identification of the common perceptions of amusement park rides with the scientific coordinate-based notion of a fictitious force (which is the first viewpoint, although Brews doesn't understand this) has not been established. The common perception is unlikely to identify anything as a "fictitious force".

(11) In these examples the centrifugal force is very obviously the result of physical acceleration.

That too is a non-sequitur, because the "first viewpoint" assigns non-zero centrifugal force to objects that aren't moving at all. It is entirely coordinate-system dependent. But surely the common perception would reject the idea of a free-standing stationary object being subjected to some gigantic centrifugal force (in terms of some arbitrarily chosen frame of reference).

(12) Thus, the first viewpoint is most transparent to the readership most likely to consult the article.

Since all the previous sentences have been falsified, the "thus" does not follow.

(13) A case can be made, however, that in some areas, notably in robotic design where the state-space of the robot is described by numerous coordinates describing orientation of links and extensions of links, the second viewpoint is predominant.

Possibly, but if so, it is not particularly significant. More to the point, a case can be (and HAS BEEN) made that viewpoints other than the one Brews favors are predominant in those parts of the literature that are specifically concerned with the foundations of dynamics, in which the axioms and definitions are closely examined.

(14) Obviously, the "coordinate system" in this field is a more abstract concept than 3D-coordinates in Euclidean space.

Well, that's true, but this shows once again that Brews erroneously thinks the "coordinate systems" in dynamics are just three dimensional. That is incorrect. The coordinate systems in dynamics are four dimensional, including the time dimension. Even the introductory references that Brews prefers all make this perfectly clear.

(15) Needless to say, this field of study is not the subject of this article on centrifugal force.

That sentence is false. The very concept of centrifugal force (as a fictitious force) is an abstraction, and depends on the choice of the (four-dimensional!) coordinate system. To claim that this is "not the subject of this article" is simply bizzare.

(16) It should be noted as well that a more technical article centrifugal force (planar motion) provides a detailed discussion of both viewpoints in a more appropriate context.

That sentence is completely false. First, we must note that the distinction between the viewpoints that Brews is referring to has nothing to do with "planarity", so it would make no sense for an article identified as being on "planar motion" to be the place where this is discussed. Oddly enough, just a couple of days ago, Brews was indignant at the suggestion that the "planar motion" article was mis-named, because it's purpose was obviously not to discuss planar motion. He responded that it most certainly WAS about planar motion, and implied that anyone who suggests that it was intended to be a discussion of the alternate viewpoints on centrifugal force is a damned liar. Now we find that, well, as a matter of fact, after all, he now claims that this is exactly what the article is about. Why he thinks this should go under the heading of "planar motion" is anyone's guess.Fugal (talk) 18:11, 22 September 2008 (UTC)
 * The above line-by-line critique is Fugal's opinion, no doubt, but is it supported by any fact or anybody? Brews ohare (talk) 18:21, 22 September 2008 (UTC)


 * Should we adopt the practice of appending to every comment a question as to whether it contains (or is even supported by) any facts or people? It is my contention that none of Brews ohare's comments are factual (as detailed above), and they are not verifiable from reputable published works. In contrast, by position is fully supported by published works, as has been discussed in detail on this discussion page. Verifiability is the basic criterion that we have to follow. The Neoligisms, novel narrative, original research and slanted POV material should be removed from the article.Fugal (talk) 20:59, 22 September 2008 (UTC)


 * As Fugal already noticed, the dispute is not as interpreted above. In particular, the dispute is not about "which of these usages is most commonly used and which should be the basis of this article"; that misunderstanding is probably the cause of the problem. Instead, please read the article on NPOV. Harald88 (talk) 08:22, 23 September 2008 (UTC)

Harald: Sorry for the confusion caused here. Of course, the point is not one of excluding one viewpoint. The point is that the most common viewpoint and the one basic to the view of such texts as Taylor and of Arnol'd and of Landau and Lifshitz and of Whittiker is the one based upon centrifugal forces that vanish in a non-rotating frame, and are present in a rotating frame. The contrary usage that takes terms introduced by changing to a curvilinear coordinate system and interprets them as fictitious forces, thereby introducing terms that are present even when the system is not rotating, finds application predominantly in a Lagrangian formulation of the problem in terms of "generalized coordinates". In such an abstract formulation, it is mathematically handy to treat every $$\ddot{q_k}$$ as a so-called "acceleration" and everything else as a "fictitious force".

So here is the dilemma: if the standard usage of centrifugal force is used, as in the present article, the result is an article consonant with the vast majority of the literature and with the common use of "centrifugal force". If instead the $$\ddot{q_k}$$ formulation is used, then (i) immediately one has to make the subject more abstract to get across the idea of generalized coordinates, and (ii) immediately one has to issue a disclaimer that this viewpoint is not what is commonly understood by centrifugal force. As a third option, one can say the "centrifugal force sometimes means this and sometimes means that". This unfortunate intro (which I guess contradicts Wiki policy that there be "one" subject per topic) then must be followed by a digression on the various meanings.

IMO the present organization is the best option. Somewhere something could be added that there is an alternative $$\ddot{q_k}$$ usage. However, this minority usage should not upset the entire presentation, making the straightforward present article into an abstract maze.

NPOV may not be the issue. (NPOV suggests different interpretations of the same subject, more than different usages of a terminology.) Whatever the case for applicability of NPOV, NPOV doesn't mean we have to lean over backwards so far that we fall down. Brews ohare (talk) 16:09, 23 September 2008 (UTC)


 * Brews, there seems to be something wrong about your remark that:
 * "The point is that the most common viewpoint and the one basic to the view of such texts as Taylor and of Arnol'd and of Landau and Lifshitz and of Whittiker is the one based upon centrifugal forces that vanish in a non-rotating frame, and are present in a rotating frame. The contrary usage that takes terms introduced by changing to a curvilinear coordinate system and interprets them as fictitious forces, thereby introducing terms that are present even when the system is not rotating, finds application predominantly in a Lagrangian formulation of the problem in terms of "generalized coordinates"
 * For, if those views are contrary, then we have a 3D contrarian view: The view of Newtonian mechanics is that only "real" forces are admitted; in any frame - even rotating - inertial coordinate systems are chosen for the laws of mechanics, using only real forces. In the case of rotating reference frames, these are usually mapped to inertial reference systems for the determination of forces and the calculation of Coriolis acceleration - without anything fictitious, according to the Newtonian interpretation that gravity is a real force.
 * Apart of that, as Frugal correctly states here below, a discussion of fictitious forces certainly doesn't address my objections to the current article as stated at the outset, as it is a wrong intro for people who type "centrifugal force". Harald88 (talk) 14:27, 25 September 2008 (UTC)
 * Hi Harald: There are two approaches to handling rotating frames. One approach, which you mention, is to work in an inertial frame with only the real forces due to interactions between bodies. A second approach is to work directly in the rotating frame, where use of Newton's laws requires introduction of fictitious forces. This introduction allows problems to be solved without translation back to an inertial frame. Here is the quote from the article (where links can be found):


 * Brews ohare (talk) 15:10, 25 September 2008 (UTC)
 * I don't think the above comment address the point that Harald raised. In fact, the above comments just give another display of the very problem that Harald mentioned. Brews talks about "the most common viewpoint", and then morphs this into "the standard viewpoint", and then concludes that the present article is fine, i.e., no other viewpoints need to be acknowledged or given representative treatment. This is precisely what's wrong with the article. The NPOV policy does not say we are to identify the "most common" POV and limit the article to that. All notable POVs (to be found in reputable sources) are to be given representative and proportionate coverage. The current article does not do this. It is rigidly restricted to one POV. Brews' comments do nothing to justify this violation of NPOV policy.


 * I will also note that Brews' identification of other viewpoints with Lagrangian formalism is skewed, and shows that he still does not understand the other points of view described in the numerous reputable references that have been cited here. This makes the discussion and resolution of the issue that much more difficult.Fugal (talk) 16:38, 23 September 2008 (UTC)


 * I did suggest reference be given to the $$\dot{q_k}^2$$ terminology. Please read again.


 * Your comment is a non-sequitur. Your reference to that terminology is precisely what reveals that your understanding is skewed. Please read again (or for the first time, if necessary).Fugal (talk) 21:18, 23 September 2008 (UTC)


 * Please support your statement that my view is skewed.


 * Already done (several times). The only new wrinkle is that you've discovered the terminology of generalized coordinates and Lagrangian mechanics, which you seem to think somehow resolves the issue of fictitious forces in general space and time coordinates per the numerous reputable references (which, be it noted, do not refer to generalized coordinates or Lagrangian mechanics). Hence your excursion into Labrangian mechanics is pointless.Fugal (talk) 21:18, 23 September 2008 (UTC)


 * Please provide Google book links to the relevant portions of "numerous reputable references".


 * Already done. More importantly, references to actual books, that one accesses in a library, have also been provided. So far, providing you with references has not proven to be productive.Fugal (talk) 21:18, 23 September 2008 (UTC)


 * Please help make the discussion less vague and tendentious.


 * I've provided the exact wording for the introductory sentence, and there is absolutely nothing vague or tendentious about it. If you would care to actually discuss it, and the rest of the sentences in the article, instead of your original research, that would be good.Fugal (talk) 21:18, 23 September 2008 (UTC)

=Lagrangian formulation= You may recall this quotation from Ge et al.: Brews ohare (talk) 16:54, 23 September 2008 (UTC)


 * Indeed. Just another of the multitude of references that supports my point and contradicts yours. The words you've quoted there are almost verbatim from one of the very first messages I posted to this discussion page, eons ago, and of course was roundly berated for my amazing ignorance of the subject. Sheesh.Fugal (talk) 21:18, 23 September 2008 (UTC)


 * Another vague rewrite of history to suit yourself. The use of Lagrangian generalized coordinates includes all curvilinear coordinate systems (e.g. polar) as special cases. So it just is a simpler and more general thing to write $$\dot{q_k}^2 $$ than to write out the more restricted case of the polar form. You may also note that this usage of centrifugal is the form that is non-zero in an inertial frame unless a Cartesian coordinate system is used. Thus, this quote is meant only to illustrate this usage does occur. The quotes from Iro, from Arnol'd and from Hawley & Holcomb here illustrate the other usage. Brews ohare (talk) 08:53, 24 September 2008 (UTC)


 * I don't see it as a "vague re-write of history", I think it's just stating something that you yourself have just confirmed. The reference you “reminded me” of is just another reference that confirms my position and contradicts yours. Remember, my position is that there are multiple treatments and views of this subject, and the more general view subsumes the more restrictive view. Indeed the Lagrangian formalism is an even more general view, that subsumes and unifies an even larger set of concepts. It allows arbitrary coordinates, but if those are restricted to ordinary space and time coordinates it reduces to the general treatment of fictitious forces, and if it is restricted still further it reduces to the specialized treatment of time-dependent fictitious forces. The definition of "centrifugal force" is the same throughout these layers of specialization. It merely reduces to fewer and fewer components are we restrict more and more.Fugal (talk) 18:19, 24 September 2008 (UTC)
 * I agree that "there are multiple treatments and views". Or, more closely, two treatments: " state of motion" and "coordinate" based. I agree that the Lagrangian approach allows arbitrary coordinates. If these are restricted to ordinary space and time, it reduces to the "coordinate" view of fictitious forces that persist even in inertial frames. This is not a general view, however, because it results in centrifugal force in an inertial frame. That means it does not encompass the view that centrifugal forces do not so occur. Thus, your picture of a general formulation that can be specialized to deal with all usages is an ephemera. Brews ohare (talk) 18:46, 24 September 2008 (UTC)


 * The key point is that, from the general level covering all fictitious forces in terms of space and time coordinates, we can specialize in one way and arrive at the restricted view that you favor, or we can specialize another way, and arrive at the exitence of fictitious forces in stationary curvilinear coordinates, which is also notably represented in the dynamics literature. Hence this unifies all the views of "centrifugal force", and is consistent with all the references that have been cited.Fugal (talk) 18:19, 24 September 2008 (UTC)
 * Unfortunately, not. See above. Brews ohare (talk) 18:46, 24 September 2008 (UTC)
 * In contrast, your position is that there is only ONE notable view of the subject of fictitious centrifugal force in the literature, and you try to defend this (in my opinion, ridiculous) position by claiming that all the other points of view on fictitious forces in the literature are really talking about a "different subject"(!) Your latest tactic is to try to identify all the other views with Lagrangian mechanics, in the hopes that you can then sweep them aside. However, as I pointed out previously, the references discussing fictitious centrifugal force in stationary coordinates do not refer to Lagrangian formalism, so your effort to define them as such is "original research" and a novel narrative, just another failed attempt to circumvent Wikipedia NPOV policy.Fugal (talk) 18:19, 24 September 2008 (UTC)
 * That is not my position; I contend there are two views. Introduction of Lagrangian formalism was simply to generalize the treatment of one of these two views, not to discredit it. Brews ohare (talk) 18:46, 24 September 2008 (UTC)
 * As to your customary accusation of vagueness, I’ve presented a line-by-line examination of each of the 16 sentences in your case supporting the present article, and you’ve conspicuously declined to address any of them (let alone all of them). It seems to me you can’t legitimately charge me with being vague or unresponsive in my criticism. You may very well not understand my criticisms, but that is not due to vagueness in the statement of those criticisms.Fugal (talk) 18:19, 24 September 2008 (UTC)
 * There is no point in responding to criticisms of positions that I do not hold. Brews ohare (talk) 18:46, 24 September 2008 (UTC)


 * Excellent. More progress! So you don't hold any of those positions, and hence you agree that the article's current POV character needs to be fixed so that it accurately represents, in a NPOV way, the entire subject of fictitious centrifugal force in rotating reference frames, and this NPOV approach needs to avoid stating (as the first sentence of the article presently does) that centrifugal force means [precisely what Brews ohare thinks it means, not what jot more or one jot less!]. I'm all in favor of these badly needed improvements.  See the current proposal for an improved introduction sentence.Fugal (talk) 22:06, 24 September 2008 (UTC)


 * Not exactly. I'm just overwhelmd at trying to explain myself in the face of many misconceptions. Brews ohare (talk) 22:37, 24 September 2008 (UTC)


 * The misconceptions are all yours, as has been clearly explained here multiple times, and not just by me. Tim Rias explained the same thing, as do the authors of many reputable sources that have been provided to you. I can't account for your inability to understand. Perhaps you just don't WANT to understand? In any case, the situation isn't helped by you first evading any defense of your positions by claiming that you don't hold those positions, and then immediately going back to espousing those positions. If you find that you can't defend your ideas, maybe you should think about getting some new ones?Fugal (talk) 02:09, 25 September 2008 (UTC)

= This article or section may be inaccurate or unbalanced in favor of certain viewpoints. =

This flag is present for exactly the same reason as the first tag on neutrality. Brews ohare (talk) 12:56, 22 September 2008 (UTC)

= Proposal for making the intro NPOV and accurate =

Here's an example of the kind of introduction that I think would be appropriate, accurate, and NPOV for the current article. Let me just present this first, and then explain why I think this would be an improvement.


 * In classical mechanics, when the motion of a particle is described in terms of a Cartesian coordinate system rotating about a fixed axis, the kinematic acceleration of the particle relative to the coordinate system differs from the absolute acceleration of the particle by the appearance of three terms, called the centrifugal, Coriolis, and Euler accelerations. In the Newtonian equation of motion, F = ma, these three components of the acceleration "a", multiplied by the mass m, are sometimes brought over to the force side of the equation, and treated as fictitious forces. When this is done, the symbol "a" represents just the kinematic acceleration of the particle relative to the rotating coordinates, and the fictitious forces are called the centrifugal, Coriolis, and Euler force, respectively.

The omission of the Latin origin (to flee the center, etc) is intentional, because it seems to me that eptymology is more suitable for a generic article on all the meanings of the term centrifugal force. Also, this proposed wording may seem slightly prolix, but I think this article presents special challenges, because we've split up the topic into fairly small sub-topics, and it therefore becomes necessary to be fairly specific, in the lead, about precisely what sub-topic is being covered. We also, in order to avoid POV, need to avoid any unwarranted implication of preference for this sub-topic, or of disparaging the other sub-topics, all of which go by the same name. It isn't Wikipedia's place to make such judgements, per the NPOV groundrule. I haven't mentioned the fact that many (perhaps even most) modern texts discourage the use of fictitious forces altogether, although I think it might be appropriate to mention this later in the article.

I'm certainly not insistent on these exact words for the header. I'm just trying to give an idea of what I think it would take (along with similar changes in the rest of the article) for me to support removal of the POV tag. Fugal (talk) 14:47, 22 September 2008 (UTC)


 * Before going into details about the use of fictional force, it is essential that when typing in "centrifugal force" Wikipedia users do not come upon an article that suggests that it can only mean a fictitious force ("rotating reference frame" is ambiguous for this issue, since mapped rotating reference frames are also used in Newtonian mechanics, without any fictitious force). I think the old intro should be used instead, and that can link to the two different articles that explain the different uses. Harald88 (talk) 08:33, 23 September 2008 (UTC)


 * I agree that this article should not state or imply that the only meaning of "centrifugal force" is the "fictitous force in rotating frames" meaning, not that that is the only context (within classical mechanics) in which the term "centrifugal force" is used. In fact, my proposed introduction for this article was drafted specifically to eliminate that implication from the opening sentence. Bear in mind that the present article has been spilt off, so the subject of this article is not the overall subject of centrifugal force, it is specifically limited to the fictitious/rotating frame aspect. As such, I don't think the original intro would be fully appropriate. To cover the overall subject, what's needed is a completely different article (maybe the old article that you are referring to) under the title "Centrifugal Force (General)" or some such. The generic introduction would be suitable for that article. Then this article would be a sub-article, focusing specifically on the fictitious/rotating frame context.


 * It has occurred to me that this restricted article would more naturally cover all three of the conventional fictitious forces in rotating reference frames, because otherwise we will need three different sub-articles, one for fictitious centrifugal in rotating frames, one for fictitious Coriolis in rotating frames, and one for fictitious Euler in rotating frames... not to mention others to cover the case when the axis of rotation is not fixed. So maybe the present article should be re-named something like "Fictitious Forces in Rotating Frames". I'm not sure.


 * In any case, what I'm trying to do here is create an introduction for an article specifically about the fictitious centrifugal force in rotating frames. As I see is, the problem with the existing intro sentence is that it says "Centrifugal force is such-and-such", but this implies exclusivity. The way to fix that (which is also the way reputable texts are usually written) is to reverse the order of implication, by saying "Such-and-such is called centrifugal force." This is simply a true statement, and does not imply that nothing else is called centrifugal force. Hence I believe my draft proposal accomplishes your stated intent, although there remains the question of how the overall subject of centrifugal force is to be covered. That's a bigger issue, and will require (in my opinion) another article. Eventually it would be nice to combine all the articles on centrifugal force into one, but that may take awhile, given the current attitude of two currently very active editors.Fugal (talk) 15:14, 23 September 2008 (UTC)


 * This article about physics is independent of the coordinate system used, so how can specifying the Cartesian coordinate system be in any way helpful? Certainly some things are easier to show in one coordinate system or other, but the physics is the same.- (User) Wolfkeeper (Talk) 18:44, 22 September 2008 (UTC)


 * You get exactly those same 3 forces (centrifugal, euler, coriolis) in polar coordinates which is applied to a non inertial frame in addition to the 'centrifugal force' that appears relative to the coordinate axes. They'll resolve differently in the coordinate system, but they'll still point in exactly the same directions and be of the same intensity.- (User) Wolfkeeper (Talk) 18:49, 22 September 2008 (UTC)


 * So I can't get behind this, it's implying things that are actually wrong; or more accurately, it's a bad definition of what the article is about, because it's overly narrow (see Not_a_dictionary- (User) Wolfkeeper (Talk) 18:49, 22 September 2008 (UTC)
 * Besides your well-founded objections, the proposed intro is unclear, both as to terminology and as to what is meant by the terms it defines. If it is elaborated upon to become clear, it will be wrong. Brews ohare (talk) 19:55, 22 September 2008 (UTC)


 * I should have commented specifically on Wolf's statement, when he said "This article about physics is independent of the coordinate system used...". That's the key problem with the Brewskeeper understanding. Once again, all fictitious forces are fictitious. The only coordinate-independent acceleration is the absolute acceleration, and if we use that, there are no fictitious forces at all. So it's completely wrong to say that the subject of this article is independent of the coordinate systems used. That entire subject of this article is nothing but coordinate dependent things, namely, fictitious forces.Fugal (talk) 21:10, 22 September 2008 (UTC)


 * This article is NOT Centrifugal force (coordinate dependent things)!!! This article is Centrifugal force (rotating reference frame). It is about a pseudo force that appears in rotating reference frames, and completely independently of what coordinate system is in use, because it makes absolutely no difference to the size, direction and scale of the force that appears. There may be additional fictional forces as well due to the coordinate system you pick, but that's not the same thing at all. You agreed to the name of the article after all Fugal. - (User) Wolfkeeper (Talk) 19:53, 24 September 2008 (UTC)


 * Once again, all fictitious forces are "coordinate dependent things", so your comment is a complete non-sequitur.Fugal (talk) 23:21, 24 September 2008 (UTC)


 * You're seriously with a straight face claiming that the centrifugal force due to the rotation of the Earth on a stationary object on Earth, depends on the coordinates you use?


 * Indeed I am. Centrigugal force (in the sense that we are discussing here) is a fictitious force. Your stationary object on the Earth has a definite absolute acceleration which corresponds to the absolute forces (in Newton's sense) to which it is subjected. If you describe the motion of that object in terms of an inertial coordinate system (in the full sense of that term), the object is not subject to ANY centrifugal force. That's why it's called a fictitious force. It is entirely dependent on the coordinate system you choose. You could just as well choose a coordinate system in terms of which that object is presently being subjected to a million tons of centrifugal force, in any direction you choose. Honestly, if this isn't totally clear to you, then you really have no business editing this article.Fugal (talk) 02:27, 25 September 2008 (UTC)


 * Why is it then, that the references overwhelmingly talk about non inertial reference frames, if, according to you, they should be talking about some magical property of some coordinate systems?


 * People are free to choose whatever coordinate system they find most convenient. But this choice is strictly arbitrary. Again, if what I just said isn't perfectly clear and obvious to you, then you shouldn't be editing this article.Fugal (talk) 02:27, 25 September 2008 (UTC)


 * No. There's a subtle point here. You can use coordinate systems and coordinate transformations to translate from one reference frame to another, but they are not the same thing. Coordinate systems are not reference frames.- (User) Wolfkeeper (Talk) 00:29, 25 September 2008 (UTC)


 * Once again, frames are equivalence classes of mutually stationary coordinate systems. And although I encourage you to continue your voyage of discovery in elementary physics concepts, I don't think you should tie up the editing of this Wikipedia article. These discussion pages are not supposed to be placed for people to come and extort a free education.Fugal (talk) 02:27, 25 September 2008 (UTC)


 * The proposed intro is quite clear and perfectly correct. The main point that still hasn't been grasped by some editors here is that all fictitious forces are coordinate-dependent. Bear in mind that the coordinate systems used in dynamics are four-dimensional, because they include a time coordinate along with the three space coordinates. If any of the coordinate axes are curved (relative to inertial paths), then the expression for the acceleration in terms of those coordinates have additional terms. When these are brought over to the force side of the equation, they are called fictitious forces. Now, your position is that it only makes sense to bring over the extra terms arising from curved time axis, but not the terms arising from curved space axes. The point I’ve been trying to make (which is the same point Tim Rias was making) is that there’s no justification for this bifurcation, and the published literature contains explanations of the fact that this is purely arbitrary. Of course, it’s true that we can treat just the time-dependent terms as fictitious forces if we so choose, even if we are working in curved space coordinates, but only in a superficial sense. This is because the choice of which terms to call accelerations and which terms to call forces is, strictly speakiing, arbitrary, and independent of our choice of coordinate system. But by convention we associate these two choices, by saying that our acceleration will be a certain specified function of our coordinates. Ordinarily we say acceleration is the second time derivative of the space coordinates, assuming Cartesian space coordinates. After making the force/acceleration partition on this basis, we can then obviously convert the Cartesian coordinates to polar or any other space coordinates, but the partition was based on the resolution of the acceleration as the second time derivative of Cartesian coordinates. If, instead, you actually work entirely in curvilinear coordinates, and you define the force/acceleration partition on that basis, then the extra fictitious forces due to the varying spatial axes appear (as described in Stommel and Moore, for example).  If you think it would help, I wouldn’t mind adding some words to the proposed introduction to make this more clear. But I personally think it’s a bit too much detail for the intro, and would be better later in the article.Fugal (talk) 20:15, 22 September 2008 (UTC)


 * Here's another version of the proposed introduction that might be more paletable, based on the above discussion:


 * In classical mechanics, when the motion of a particle is described in terms of a reference frame rotating about a fixed axis, the kinematic acceleration of the particle relative to the reference frame differs from the absolute acceleration of the particle by the appearance of three terms, called the centrifugal, Coriolis, and Euler accelerations. In the Newtonian equation of motion, F = ma, these three components of the acceleration "a", multiplied by the mass m, are sometimes brought over to the force side of the equation, and treated as fictitious forces. When this is done, the symbol "a" in the equation of motion represents just the kinematic acceleration of the particle relative to the rotating frame, and the fictitious forces are called the centrifugal, Coriolis, and Euler force, respectively.


 * Then at some later point in the article the subtlety of frames versus coordinate systems can be mentioned, at least to the extent of explaining how the terms selected to be treated as forces are chosen.Fugal (talk) 20:47, 22 September 2008 (UTC)


 * The proposed language is simply an example of words reduced to meaningless. After debating this topic for months, the editors decide that they cant make sense of the topic being discussed and so confirm the opinion that they are completely oblivious to the fact that their definition of centrifugal force is simply meaningless metaphysical claptrap that has no value other than the appearance of meaning when it has none that the average person can understand. Getting rid of David Tombe, has only catered to the fools who dont understand what they are doing. I say say bring back Tombe and let him write this as you guys are going nowhere with it as it now stands  [unpunctuated and unsigned message, apparently left by IP server 71.251.184.32.]


 * I'm not sure if the above comment was some kind of vandalism, or was meant to be taken seriously. Let me just say that the proposed introduction to this article, which is explicitly limited to just the fictitious force in rotating frames, is not meaningless. It is a correct and clear introductory statement for the subject of this article, and it is intentionally worded in such a way as to avoid giving the impression that this is the only (or the best) context or point of view for "centrifugal force". It simply makes a statement of fact, that when certain acceleration terms based on a rotating reference frame about a fixed axis are brought over and treated as forces, they are called centrifugal, Coriolis, and Euler forces. This does not imply that nothing else is properly called centrifugal force, nor does it imply that this is the only (or the most general) context in which centrifugal force is defined.Fugal (talk) 21:59, 23 September 2008 (UTC)


 * If anyone wishes to point out any errors in the draft proposal, I'm happy to consider them. So far I don't see any substantive objections, nor any substantive defense of the existing sentence to be replaced. I'll give it awhile longer, to see if anyone has any objections to making the change.Fugal (talk) 21:59, 23 September 2008 (UTC)


 * I object strenuously to your proposal and have given my reasons, which you pooh-pooh as misguided and as already dealt with by your snow job of vague allusions to wonderful arguments made in the distant past, with refutations blithely ignored. Brews ohare (talk) 23:46, 23 September 2008 (UTC)


 * As far as I can see, your only comment was on the original draft, and you have not commented on the revised proposal, intended to accommodate the comments received. Here it is again, with a couple more minor tweaks:


 * In classical mechanics, when the motion of a particle is described in terms of a reference frame rotating about a fixed axis, the kinematic acceleration of the particle relative to the reference frame differs from the absolute acceleration of the particle by the appearance of three terms, called the centrifugal, Coriolis, and Euler accelerations. In the Newtonian equation of motion, F = ma, these three components of the acceleration, multiplied by the mass, are sometimes brought over to the force side of the equation, and treated as fictitious forces. When this is done, the symbol "a" in the equation of motion represents just the kinematic acceleration of the particle relative to the rotating frame, and the fictitious forces are called the centrifugal, Coriolis, and Euler force, respectively.


 * This wording is, I believe, provides an accurate, clear, and NPOV introduction to this article. If anyone wishes to point out any inaccuracy, lack of clarity, or disproportionate leaning toward are particular POV, please do so. Lacking any substantive objections, I think we should make this change.Fugal (talk) 00:02, 24 September 2008 (UTC)


 * That is your opinion. It is not mine. As an introductory paragraph it has several failings. First, it employs a number of technical terms that make it hard to follow for the uninitiated. Among these are "kinematic acceleration", "absolute acceleration" (what is this anyway?). Brews ohare (talk) 05:28, 24 September 2008 (UTC)


 * Are you saying you don't know what absolute acceleration is? And you don't know the difference between absolute acceleration and kinematic acceleration relative to an arbitrary frame? Holy smokes.  No wonder we're having so much trouble communicating. Sheesh... all I can think of to do is suggest that you acquire a good book on introductory physics and mechanics. I also have to suggest that you might want to consider whether a person who is unacquainted with the concept of absolute acceleration is really equipped for the job of editing an article on dynamics.


 * In any case, if you think the readers of this article aren't familiar with the conceptual distinction between kinematics and dynamics (covered in every introductory text), then I wouldn't mind omitting the adjective "kinematic", since it was just intended to emphasize the point that it is relative (rather than absolute) acceleration.


 * Second, it doesn't indicate the idea of force away from a center, which is the hallmark of centrifugal force that everyone understands intuitively. Brews ohare (talk) 05:28, 24 September 2008 (UTC)


 * A fair point. So, taking your comments into account, my revised proposal is this:


 * In classical mechanics, when the motion of a particle is described in terms of a reference frame rotating about a fixed axis, the acceleration of the particle relative to the reference frame differs from the absolute acceleration of the particle by the appearance of three terms, called the centripetal, Coriolis, and Euler accelerations. In the Newtonian equation of motion, F = ma, these three components of the acceleration, multiplied by the mass, are sometimes brought over to the force side of the equation (with the opposite signs), and treated as fictitious forces. When this is done, the symbol "a" in the equation of motion represents just the acceleration of the particle relative to the rotating frame, and the fictitious forces are called the centrifugal, Coriolis, and Euler force, respectively. The centrifugal force is directed outward from the axis of rotation.


 * Third, it employs a mathematical manipulation POV (shuffling terms) that is very unreal and intuitively phony. Brews ohare (talk) 05:28, 24 September 2008 (UTC)


 * That's not a valid criticism, because the very subject of this article is fictitious forces in rotating reference frames, and these are explicitly defined as the result of "shuffling terms" (as you put it). See, for example, Goodman and Warner's "Dynamics" for example. Just about any reputable reference book on Dynamics introduces these fictitious forces by first writing the basic equation F = ma in terms of a rotating system of coordinates, and noting the appearance of the extra acceleration terms, and then saying we can bring these terms over to the force side and treat them as if they are forces. This is nearly verbatim from almost every Dynamics text I've ever seen. The article needs to be written in a way that accurately represented the published reputable sources. This is what the proposed wording does.Fugal (talk) 16:20, 24 September 2008 (UTC)
 * How do you respond to this? An interesting discussion of the reality of fictitious forces is provided by Kompaneyets:
 * "'Naturally, the acceleration of a point caused by noninertiality of the system is absolutely real, relative to that system, in spite of the fact that there are other, inertial, systems relative to which this acceleration does not exist. In [the equation for acceleration] this acceleration is written as if it were due to some additional forces. These forces are usually called inertial forces. In so far as the acceleration associated with them is in every way real, the discussion (which sometimes arises) about the reality of inertial forces themselves must be considered as aimless. It is only possible to talk about the difference between the forces of inertia and the forces of interaction between bodies.'" Brews ohare (talk) 18:14, 24 September 2008 (UTC)


 * I completely agree that discussions about the reality of [fill in the blank] are aimless, because there's no clear scientific meaning for the term "reality". One can talk meaningfully about whether a force is "fictitious" only because that word has (in this context) a well-defined meaning, namely something that is not a force in the Newtonian sense, viz, something that is not associated with absolute acceleration. But one can't talk meaningfully about whether a force is "real". One might criticize the author for failing to heed his own words when he asserts that relative acceleration is "absolutely real", but one may forgive this, since it's a mere (somewhat dippy) tautology, i.e., relative acceleration is absolutely real relative acceleration. (Needless to say, no one would mistake this for a claim that relative acceleration is absolute acceleration.)


 * The quoted comment asserting that inertial forces do not represent interactions between bodies is somewhat sporty, and would raise eye-brows in more sophisticated circles, because we do not know whether inertia is ultimately attributable to interactions between bodies. Mach and (more recently) Wheeler have argued that it must be, even though the interaction is clearly dis-similar to ordinary binary interactions. See Wheeler's 1992 book on the origin of inertia (or the rest of the vast literature on this subject). (Moreover, if the Higgs particle were to be found at the LHC, the idea of inertia as an interaction would become less speculative.)


 * Overall the quotation doesn't have any particular bearing on the issues being discussed here. I personally wouldn't cite it as an example of great insight or sophistication, but it doesn't say anything exactly wrong.Fugal (talk) 19:30, 24 September 2008 (UTC)


 * The pertinence of the quotation is that centrifugal force can injure you, and mathematical shuffling of terms from one side of an equation to the other hardly captures the reality. Brews ohare (talk) 19:57, 24 September 2008 (UTC)


 * No, that's completely wrong. Only absolute acceleration can "injure you. In the absence of absolute acceleration, you are in free-fall. Fictitious forces are not associated with absolute acceleration - by definition. Hence, once again, you are as wrong as it is possible to be. You plainly have not the slightest understanding of this subject, and aren't even equipped with the vocabulary or the conceptual background to discuss it rationally. You ask me what absolute acceleration is, and you tell me you're astounded that time coordinates have anything to do with dynamics and fictitious forces. Now you claim that fictitious forces can "injure" someone, and so on. And you purposefully misconstrue every reference and quote presented to you. And you present no rational justification for suppressing what is obviously a variety of views on the subject of fictitious centrifugal force in rotating frames. What am I to do? Please give some thought to the possibility that you don't know what you're talking about.Fugal (talk) 20:19, 24 September 2008 (UTC)


 * Thing is, fictitious forces can at the root be real inertia. XKCD says it best: .- (User) Wolfkeeper (Talk) 05:29, 25 September 2008 (UTC)

= Applicability of NPOV = According to NPOV, The neutral point of view is a means of dealing with conflicting verifiable perspectives on a topic as evidenced by reliable sources.

I'd argue that two usages of a term do not constitute two "perspectives" of a topic. An analogy might be two different definitions of a word. In Encarta:
 * Centrifugal: (physics) away from center: acting, moving, or pulling away from a center or axis.

which is apparently the common usage. In Lagrangian mechanics one might say a second usage is:
 * Centrifugal: (Lagrangian formulation) All terms in the expression for $$\ddot{q_k}$$ involving  $$\dot{q_k}^2$$. (see Ge)

Do these two usages constitute two "perspectives". I'd say not, because they both can be applied to the very same problem and produce the very same math. All that is different is the names given to things. Brews ohare (talk) 16:33, 23 September 2008 (UTC)


 * Brews, thanks for your clarification! I now see that your disagreement is due to a misunderstanding: the Newtonian use of "centrifugal force" corresponds to one subset of "away from centre", while the fictitious use corresponds to a different meaning of the same words (with proponents and opponents on either side, often refusing to admit the existence of the other). The big dividing line is due to 'two usages of "Centrifugal:(physics)" and the polarized views that correspond with these.
 * Funny enough, the old article dealt with eliminating the kind of misunderstanding that now occurs on this page. Please study the intro of the old page to which I referred above, complete with examples and references. Harald88 (talk) 13:22, 26 September 2008 (UTC)


 * The entire subject of fictitious centrifugal force consists of "giving different names to things". The absolute acceleration expressed in terms of any chosen system of space-time coordinates contains several components. We can choose to name ALL of these components "forces", and we get d'Alembert's principle and dynamic equilibrium, or we can choose to name SOME of the components "forces" while still calling others "accelerations", and we get various forms of fictitious forces, or we can choose to name NONE of the acceleration terms as forces, in which case there are no fictitious forces at all. Obviously this is just a single topic, with a number of points of view that can be adopted at the convenience of the analyst.Fugal (talk) 16:51, 23 September 2008 (UTC)
 * "Obviously" this article covers two topics that unfortunately have the same name: centrifugal force ("state-of-motion") and centrifugal force ($$\dot{q_k}^2$$), two terminologies that can be adopted at the convenience of the analyst. Brews ohare (talk) 16:58, 23 September 2008 (UTC)


 * Since it's been established that your ideas about "state of motion forces" are original research, not to be found in any reputable published source, I think it would help the discussion if you would refrain from invoking those ideas here. This discussion page is intended strictly for discussion of the Wikipedia article, which excludes original research. Thanks. Fugal (talk) 20:42, 23 September 2008 (UTC)


 * The use of "state-of-motion" centrifugal forces by which is meant the use of the term "centrifugal force" in the sense of a centrifugal force that vanishes in an inertial frame of reference, is clearly presented in this section of the Talk page and supported by citations and quotations from published sources with links provided.  Brews ohare (talk) 21:27, 23 September 2008 (UTC)


 * Can it be that you still don't realize that the phrase "a centrifugal force that vanishes in an inertial reference frame" simply begs the question, because the decision to use a "frame" (an equivalence class of coordinate systems) rather than a specific coordinate system already entails the decision to mod out the effects of the varying space basis vectors, i.e., to leave the space-based acceleration terms on the acceleration side, and just move the time-based acceleration terms over to the force side. Look, I shouldn't have to keep explaining this to you over and over and over, like Tim Rias tried to do. The simple brute fact you have to deal with is that the literature (within the science of dynamics) on the subject of centrifugal force (as a fictitious force) includes NOTABLE points of view that differ from what is presently represented in this article. I know you don't like it, but you can't change the facts. Wikipedia policy demands that all the notable points of view contained in reputable sources must be given proportionate representation in the article, and it must be accurate representation. Since you, by your own admission, do not understand this point of view (and in Friedman, for example), and since you clearly have no intention of learning it, I think at some point you may need to relinquyish your "ownership" of this article and allow improvements to be made.Fugal (talk) 21:47, 23 September 2008 (UTC)

Response
Fugal: Can it be that you still don't realize that the phrase "a centrifugal force that vanishes in an inertial reference frame" simply begs the question, because the decision to use a "frame" (an equivalence class of coordinate systems) rather than a specific coordinate system already entails the decision to mod out the effects of the varying space basis vectors, i.e., to leave the space-based acceleration terms on the acceleration side, and just move the time-based acceleration terms over to the force side.


 * What possible basis do you have for this statement? Centrifugal force (in one use of the term) does exist in every frame that rotates, and does not in a stationary frame. Your notion of "moding" out the effects of of varying basis vectors is a figment of your imagination. Can you find one citation to support your view? Please do not be content with simply stating a title: provide page numbers a Google link and an exact quotation. Brews ohare (talk) 05:24, 24 September 2008 (UTC)


 * Sixty seconds of googling turns up the books
 * (1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press.
 * (2) "Methods of Applied Mathematics" By Francis B. Hildebrand, 1992, Dover, p 156.
 * (3) "Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books.
 * (4) "Essential Mathematical Methods for Physicists" By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.


 * and the academic web pages


 * http://math.ucr.edu/home/baez/classical/inverse_square.pdf (irrelevant Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Here Brews ohare is lying. The web page derives the centrifugal force in stationary coordinate system. Anyone is free to click on the link and see for themselves that Brews is simply lying.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/CORIOLIS.PDF (says "Such a force is called an “effective” or “fictitious” force. The acceleration due to such a force is caused solely by the motion of the observer." Doesn't support you at all. Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Again, the web page derives the centrifugal force in stationary coordinate system. Anyone is free to click on the link and see for themselves that Brews is simply lying. The fact that the author of the page later repeats the sophomoric mantra, even though it directly contradicts his own equations, is a useful lesson in itself.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * http://www-math.mit.edu/~djk/18_022/chapter02/section04.html (duplicates Stommel and Moore, nothing new.Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Here Brews says "nothing new", i.e., it is simply more evidence in support of my claims and contradicting his. I agree it's not new. In fact, it's getting very old. But for him to simply dismiss the very references that he begged me to provide, based on the fact that they confirm exactly what I told him, is, well, rather odd.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * http://www.phy.umist.ac.uk/~mikeb/lecture/pc167/gravity/central.html (duplicates material on using a potential to express centrifugal force - no bearing upon discussion Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Here Brews is lying again. The web page derives the centrifugal force in stationary coordinate system. Anyone is free to click on the link and see for themselves that Brews is simply lying.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * http://www.cbu.edu/~jholmes/P380/CentralForce.doc (Stommel-Moore again; nothing new. Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Again the dismissal as "nothing new" because it's just yet another reference that confirms my point. Unbelievable.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * http://www.myoops.org/twocw/mit/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/1BEBB815-1441-4698-8D09-3C0E378291F3/0/spring_pendulum.pdf (Stommel-Moore again; nothing new. Brews ohare (talk) 17:52, 24 September 2008 (UTC))


 * Again the dismissal as "nothing new" because it's just yet another reference that confirms my point. What a truly disgraceful display of intellectual dishonesty.Fugal (talk) 04:18, 25 September 2008 (UTC)


 * and you can also check any numnbe of old-fashioned books in a library, such as


 * (5) Marion and Thornton [ref by Tim Rais, "the term appearing in the (polar coordinate) formula is called the centrifugal force"]
 * (6) "Dynamics", Goodman and Warner, Wadsworth Publishing, 1965, p 238.
 * (7) "Statics and Dynamics", Beer and Johnston, McGraw-Hill, 2nd ed., p 485, 1972.
 * (8) "Foundations of Space-Time Theories", Princeton Univ Press, 1989, p 163-180.


 * I would also remind you of Tim Rias's comment when I presented all these references to you previously:


 * "I'm going to support Fugal on this. The term present in equations in polar coordinates and the term present in rotating reference frames are two sides of the same coin. (i.e. they are terms coming from the non-trivial connection coefficients involved in calculating the acceleration.) I think this article should cover both. Especially, since there is a whole bunch of textbooks that don't really distinguish between the two. (Marion and Thornton is one of them.)


 * To this quick list of references, demonstrating incontrovertibly the notability of the point of view that you claim does not exist, I would also add all of the references that you have cited in support of your preferred point of view, because (as has been explained over and over and over...) you misunderstand those references, and you fail to realize that they actually are perfectly consistent with all these other references.Fugal (talk) 15:29, 24 September 2008 (UTC)


 * Hi Fugal: Tim's statement "The term present in equations in polar coordinates and the term present in rotating reference frames are two sides of the same coin. (i.e. they are terms coming from the non-trivial connection coefficients involved in calculating the acceleration.)" espouses the Stommel-Moore view; "connection coefficients" is a reference to the extra terms in the acceleration stemming from use of curvilinear coordinates. The "two sides of the same coin" comment is prejudicial in favor of this view, which is only one of two views.
 * I have not claimed this Stommel-Moore POV does not exist, and I provided the references 1 -4 myself in the articles as examples of the view that allows centrifugal force to be non-zero in inertial frames. That is not the argument. The argument is that this view is not the only view, and is not the primary view.


 * Well, we've actually made some progress here!  We've established that there are multiple views of this subject. Now, in accord with Wikipedia policy, the views must all be given proportionate coverage in the article. The problem is that the article does not do this, because it begins in the very first sentence by asserting that, in classical mechanics, centrifugal force is [insert Brews ohare's preferred view]. This sentence is not consistent with NPOV, because it clearly and unequivocally states that centrifugal force IS [Brews' preferred view]. My proposal for starting to make the article NPOV is to reverse the structure of the sentence, to make it true without being POV. Hopefully you can get behind this effort to make the article accurately reflect all the notable POVs, as you have yourself admitted exist, in accord with Wikipedia policy.Fugal (talk) 20:34, 24 September 2008 (UTC)


 * You have not responded to the question I wanted citations for, which was in reference to the "moding" out of curvilinear coordinates. The "moding" term you have invented is the way you conclude that the "state-of-motion" quotes "actually are perfectly consistent with all these other references" espousing the "coordinate" approach. Brews ohare (talk) 17:30, 24 September 2008 (UTC)

Fugal: The simple brute fact you have to deal with is that the literature (within the science of dynamics) on the subject of centrifugal force (as a fictitious force) includes NOTABLE points of view that differ from what is presently represented in this article. I know you don't like it, but you can't change the facts.


 * Prove it. Take the time to actually dredge up these references and again, provide page numbers and exact quotations. Personally, I cannot find any such detail on this Talk page. I'd say the citations and quotations I have presented thoroughly document two usages. You have not attempted to address any of this presentation in similar detail. You simply claim it has been done, but in fact it has not. Brews ohare (talk) 09:01, 24 September 2008 (UTC)


 * Already done, over and over and over again. Here's the problem, as I see it. I spoon feed you a web link book like Stommel and Moore, which derives in black and white the centrifugal force in terms of stationary polar coordinates, and then you turn to a different chapter of that book, devoted to rotating reference frames, and point out that it refers to rotating reference frames, and on this basis you assert that Stommel supports your claim that there is no notable point of view in the literature for fictitious centrifugal force in stationary coordinates. You do the same for each of the other references, or else you say they are not accessible to you (apparently you don't live near a library). Now, in accord with Wikipedia policy, I assume good faith on your part, but quite frankly, I cannot account for your behavior on the basis of that assumption.Fugal (talk) 15:29, 24 September 2008 (UTC)


 * Stommel and Moore do, as you say, "derive in black and white the centrifugal force in terms of stationary polar coordinates". I have no argument about this, and have quoted them to this effect, providing web links to the appropriate section of their book. My reference to their Chapter on rotating frames was not used to discredit this idea. It was used to point out that they say there is "additional" centrifugal force in a rotating frame. If you disagree with me about these quotes, take them apart and reconstruct them to support your ideas above. Finally, I have not said that no-one uses the Stommel-Moore view. What I have said is that there are many authors that do not do so, for the simple reason that the Stommel-Moore usage blurs the basic distinction between inertial and non-inertial frames of reference. That failure muddles the  Stommel-Moore presentation, and is the reason they have to keep reminding the reader about which frame of reference they are in. Brews ohare (talk) 19:20, 24 September 2008 (UTC)


 * Again, your views on the subject are not relevant, nor are your mistaken ideas about blurriness. Moreover, you have yourself just conceeded the entire discussion. Your ownly justification for suppressing the view of the subject presented in all the references I've provided is that none of those are notable or reputable or some other reason within Wikipedia policy for excluding them. You are not able to provide any such reason. Your comment that some things are additional centrifugal forces do not make them a separate subject it would due to the fact that additional centrifugal forces arise if you change from one accelerating frame to an even more accelerated frame. Fictitious forces are relative by definition, i.e., they depend on the system of reference in terms of which they are defined. Your inability to understand this should not be allowed to perpetually prevent improvements from ever being made to this article.Fugal (talk) 20:10, 24 September 2008 (UTC)


 * The point is that some authors call them "additional" and some authors say they aren't additional, they are everything. Brews ohare (talk) 21:34, 24 September 2008 (UTC)


 * No, some discuss them and call them additional, and others avoid discussing them by either talking in terms of frames or else by stipulating rectilinear space coordinates (as Arnold). You can't honestly believe that Arnold (or any other author) would deny the appearance of additional acceleration terms in curvilinear space coordinates. Be serious.Fugal (talk) 22:12, 24 September 2008 (UTC)


 * I also differ with you that the other quotations I have drawn from Iro, Arnol'd see here etc. etc. exemplify the Stommel-Moore view. To the contrary, these other authors all use the view that there is zero centrifugal force in an inertial frame. This point is particularly clear in Taylor's treatment of the co-rotating frame (pp. 358-359). Brews ohare (talk) 19:39, 24 September 2008 (UTC)
 * You have attempted the argument that these authors have inherently ruled out curvilinear coordinates from the outset, and so these quotes only apparently support the zero centrifugal force in an inertial frame position. However, I find nothing in these references that supports that view of implicit elimination of all but Cartesian coordinates. I have responded to you directly in the case of Arnol'd, where you claimed his description of a Galilean transformation excluded the use of polar coordinate systems in inertial frames. That view was shown to be nonsense, and further quotes can be marshaled if you wish to pursue this contention. Brews ohare (talk) 17:52, 24 September 2008 (UTC)


 * I also differ with you that the other quotations I have drawn from Iro, Arnol'd see here etc. etc. exemplify the Stommel-Moore view. To the contrary, these other authors all use the view that there is zero centrifugal force in an inertial frame. You have attempted the argument that these authors have inherently ruled out curvilinear coordinates from the outset, and so these quotes only apparently support the zero centrifugal force in an inertial frame position. However, I find nothing in these references that supports that view of implicit elimination of all but Cartesian coordinates. I have responded to you directly in the case of Arnol'd, where you claimed his description of a Galilean transformation excluded the use of polar coordinate systems in inertial frames. That view was shown to be nonsense, and further quotes can be marshaled if you wish to pursue this contention.  Brews ohare (talk) 17:52, 24 September 2008 (UTC)


 * Your misunderstanding on this has already been explained over and over and over again. As I explained to you, Arnol'd's "systems" are rectilinear coordinate systems. On the basis of that clearly stated stipulation, his statements are correct, and fully consistent with all the rest of the literature on this subject. Your refusal to understand this should not be allowed to perpetually prevent improvements from ever veing made to this article.Fugal (talk) 20:10, 24 September 2008 (UTC)


 * I'm afraid your assumption that Arnol'd has deliberately excluded all but Cartesian coordinates is unsupported. If you wish to pursue this matter, provide something other than your misinterpretation of Galilean transformations. Brews ohare (talk) 21:37, 24 September 2008 (UTC)


 * A thorough explanation of Arnold's stipulation of rectilinear coordinates has already been given (along with pointing out the same explicit stipulation in your other two references). Once again, Arnold defines reference "systems" as what he calls systems of galilean coordinates, which is the explicit stipulation. For those who have trouble understanding this, he then defines the acceleration in the equation of motion as the second time derivatives of the space coordinates. This (again) shows inequivocally that his space coordinates are rectilinear. Then for those who still don't get it, he says that all inertial coordinate systems are related by translation, rotation, and state of motion transformations of the coordinates, which shows (for the THIRD TIME) that his systems are restricted to rectilinear space coordinates. This has been explained repeatedly now. Honestly, it isn't that difficult. I very much agree with Tim Rias when he said it seems as if you are not really trying to understand. I might even go further, and say it seems you are trying to NOT understand.Fugal (talk) 23:33, 24 September 2008 (UTC)

In addition to what Frugal stated somewhat higher about the misleading intro of this article, what really is wrong is the fact that readers (like happened to me!) do not encounter the disambiguation page but instead fall directly on this page which only gives one opinin about the meaning of "centrifugal force". Thus, the first banner (POV) really refers to the fact that, as I wrote a few days agao, but some may have missed: "I think it's fine if at the start readers can fork to the different meanings. However, this is not the case when a reader types in "centrifugal force". Instead they are confronted with the Single View that in classical mechanics "centrifugal force" is a fictitious force. Thus, my main objection is that the linking to this article is unacceptably POV. I don't know how to fix this; I would agree with removing the first banner (POV) if "centrifugal force" links to the disambiguation page instead of to this article. Harald88 (talk) 13:55, 25 September 2008 (UTC)
 * Harald: Regardless of whether one adopts Fugal's view that terms always enter the centrifugal force, even in non-rotating frames, or the view that such terms are excluded, "centrifugal force" is a fictitious force. So this aspect of the page is not the problem IMO. Brews ohare (talk) 15:25, 25 September 2008 (UTC)
 * No, careful here Brews, that's not entirely accurate. Reactive centrifugal force is still regarded as a centrifugal force, but is real.- (User) Wolfkeeper (Talk) 16:11, 25 September 2008 (UTC)
 * Agreed. I was making the (perhaps erroneous) assumption that Reactive centrifugal force was outside this discussion. Brews ohare (talk) 16:36, 25 September 2008 (UTC)
 * Harald, we had to decide where to link to. To determine what most people consider the term 'centrifugal force' to mean, I did a websearch. (See Talk:Centrifugal_force_(rotating_reference_frame) above).- (User) Wolfkeeper (Talk) 16:11, 25 September 2008 (UTC)


 * About 50% used the term in this way. The others used it in a different way, but no other way even came close.- (User) Wolfkeeper (Talk) 16:11, 25 September 2008 (UTC)


 * The bottom line is, we went with that. That's why it's not a POV issue of any of the editors, we measured the way people currently actually seem to use the term and have tried to followed it for the redirect. If you think about it, that's a NPOV.- (User) Wolfkeeper (Talk) 16:11, 25 September 2008 (UTC)


 * So the tag is just misplaced. That's not how it came to be like that, and the reason it's like that is evidence based. It's not perfect, but it's at least a method for determining this.- (User) Wolfkeeper (Talk) 16:11, 25 September 2008 (UTC)


 * Wolfkeeper, it's not necessarily wrong to directly link to the most used meaning, as long as the user doesn't have to search for other any meaning other than the one that is most common - especially since the meaning of the word itself is a point of dispute in the literature and thus a POV. Below I explained the two options in detail. Harald88 (talk) 13:02, 26 September 2008 (UTC)

Proposal for new page
I propose a new page Centrifugal force (generalized coordinates) that would present the formulation in Lagrangian mechanics, introduce the $$\dot{q_k}^2$$ formulation of centrifugal force and illustrate the procedure with an example of robot design. The disambiguation page would list this topic as well. Then this entire debate could be squelched and the tags on this article removed. Brews ohare (talk) 17:43, 23 September 2008 (UTC)


 * You can certainly create a page on generalized coordinates if you like (although you may be overlapping with the existing article on Lagrangian mechanics), but there will still remain a need to accurately reflect the topic of centrifugal force (in the fictitious force sense) in terms of non-inertial space-time coordinate systems, as discussed in the literature. And of course there will still be a need to remove the incaccurate and POV material from this existing article. My proposal for getting started on that task is presented in the previous section here on this discussion page. Hopefully we can reach a speedy agreement on the necessary changes to this article.Fugal (talk) 20:39, 23 September 2008 (UTC)


 * When someone types in "centrifugal force", that person should be directed to either a general page or an an introduction that leads the reader without prejudice to the right article. Thus I propose to make either a disambiguation page that links to all meanings (likely the best option), or else a page like the existing one but with the old introHarald88 (talk) 07:59, 24 September 2008 (UTC)


 * We already have a disambiguation page Centrifugal force (disambiguation), and it's already linked from this article. The scope of the disambiguation page is all forces that act away from some kind of rotation centre. The default article you get when you type in 'centrifugal force' is based on analysis of which definition seems to be the most common on the internet out of the reliable sources that discuss it. The definition used is overwhelmingly the same as this article; very few use other definitions. It seems that in most cases that this is probably the article the user needs or would most expect to arrive at.- (User) Wolfkeeper (Talk) 18:00, 24 September 2008 (UTC)


 * http://en.wikipedia.org/w/index.php?title=Centrifugal_force_(rotating_reference_frame)&oldid=196032047
 * plus new links. And don't forget, and as rather well explained in the old version, "centrifugal force (rotating reference frame)" also applies to reactive centrifugal force so that it's not an appropriate title. Unambiguous would be "centrifugal force (fictitious)". Harald88 (talk) 07:59, 24 September 2008 (UTC)
 * Careful here. The old article talked about reactive centrifugal force, that's completely orthogonal to rotating reference frames; you can either, neither or both. If they're orthogonal they're not the same thing, if they're not the same thing, under the wikirules they belong in different articles, the only thing they share is the name, but the wikipedia is not a dictionary. Reactive centrifugal force now has its own article. It's mostly the article you helped to write Harald.- (User) Wolfkeeper (Talk) 03:41, 25 September 2008 (UTC)
 * Hi Harald: What do you mean by your phrase "centrifugal force (rotating reference frame)" also applies to reactive centrifugal force? I'm guessing you are saying Reactive centrifugal force also refers to a rotating frame, not that the fictitious force and the reactive force are the same thing? Brews ohare (talk) 08:33, 24 September 2008 (UTC)


 * To both, see the old version to which I referred once more here above and which contains a disambiguation table (not by me, and which certainly should be added to the disambiguation page - which I again cannot find back!). The old version does not (only) "talk about reactive centrifugal force" but gave a neutral discussion of the contrary uses of the term; and it stresses the point that the reactive force may be observed in any frame. Real centrifugal force is the reaction force to centripetal force and both these forces occur with rotational force. For example taking the rotating earth frame and including the rotation effect of the earth in apparent gravitation, this action-reaction pair is still measured on a merry-go-round. Harald88 (talk) 13:05, 26 September 2008 (UTC)


 * I support Harald on this. The "top" page on the subject of centrifugal force should encompass the entire subject, perhaps with links to sub-articles giving more in-depth discussion of sub-topics (if needed). I also agree that the title of the current article is problematic, because the phrase "rotating reference frames" is not sufficient to isolate the very specific sense of the term treated in this article. Unfortunately, even the term "fictitious", while somewhat more precise, still is not sufficient to single out the specific topic of this article, because there are (at least) two other contexts for fictitious forces discussed in the literature (one of which encompases all the fictitious force aspects). In addition, the present article actually isn't limited to centrifugal force (in its restricted sense), because it contains a lot on Coriolis and even some on the Euler force, which is understandable, since these three are almost inseparable conceptually. This is why, in the previous section, I suggested that a more appropriate title for this article would be something like "Fictitious Forces in Rotating Frames". This still wouldn't match the content exactly, but it would be much closer.Fugal (talk) 14:28, 24 September 2008 (UTC)


 * Yes, that's much better and I think rather unambiguous. Harald88 (talk) 13:03, 26 September 2008 (UTC)


 * The only page that encompasses all of the subject is the disambiguation page. Really 'centrifugal force' is just a term for any centre fleeing force. Given that disambiguation pages properly disambiguate terms and articles aren't about terms (that's what dictionaries do), it's probably never going to be a proper encyclopedia article.- (User) Wolfkeeper (Talk) 18:35, 24 September 2008 (UTC)


 * The whole "dictionary" canard has been debunked long ago. (This isn't about bark.) The subject of centrifugal force, including its variety of meanings, both as it has evolved through history, and in current usage, is itself a subject. In all the encyclopedia's I've checked, all the meanings are covered in a single article... or else there is not article at all on the subject. I've never seen an encyclopedia with multiple articles on (for example) reactive and fictitious. All the meanings, usages, and points of view are so closely interconnected and overlap so much that it's quite inefficient to try to discuss them all separately.Fugal (talk) 23:45, 24 September 2008 (UTC)


 * The page we have for that is the disambiguation page. I personally don't think that the different forces that you have there, some that are real forces that oppose centripetal force, some that are fictitious forces that are reference frame related, and some that are coordinate related are the same things at all. They act in different directions at different times. It is indeed more like bark (as in shout) and bark (as in dog) and bark (as in tree).- (User) Wolfkeeper (Talk) 01:39, 25 September 2008 (UTC)


 * Indeed we won't need to make more of a summary stub out of the disambiguation page, together with the nice disambiguation table that I referred to. However, at the moment that page is more or less hidden while it should be the departure point after typing "centrifugal force". Please can anyone who knows how to do so, do that? Then for me, the first banner (NPOV) may be removed from this article. Harald88 (talk) 13:04, 26 September 2008 (UTC)


 * But I think even if you did manage to do that, to make a full article page from the disambiguation page, the evidence that we have is that it still probably wouldn't be the page that the users want/need when they type in 'centrifugal force'.- (User) Wolfkeeper (Talk) 18:35, 24 September 2008 (UTC)


 * The acceptable alternative was also already indicated: If everyone comes upon this page, then this page has to have an accurate and neutral [NPOV] introduction that immediately links to the disambiguation page. And then again for me it's OK to delete the first of the two banners. 128.178.153.55 (talk) 12:55, 26 September 2008 (UTC)


 * What evidence is that? Fugal (talk) 23:45, 24 September 2008 (UTC)


 * The fact that most references specifically refer to rotating reference frames and that this article is about rotating reference frames?- (User) Wolfkeeper (Talk) 01:39, 25 September 2008 (UTC)


 * As it stands, this article is not just about rotating reference frames, despite it's parenthetical disambiguation. Look at the following two assertions:
 * A car is a Chevrolet.
 * A Chevrolet is a car.


 * LOL. You completely messed that up. The one I usually use is: 'all lions are cats but...'- (User) Wolfkeeper (Talk) 03:41, 25 September 2008 (UTC)


 * Can you see a difference between them? They look somewhat similar, but one of them is false and the other is true. Now look at the following two assertions:
 * Centrifugal force is an outward fictitious force in a rotating frame.
 * An outward fictitious force in a rotating frame is called Centrifugal force.
 * Again, can you detect a difference between these two? They may look somewhat similar, but the first is false and the second is true. The current article begins with a sentence of the first form, which implies that all centrifugal force is such-and-such, contrary to the disambiguation. What's needed is to change from the first form to the second. Do you understand this?


 * We're defining the usage of the term for the article, not the world. That's what you don't understand, the term has multiple, distinct, definitions. When you look in a dictionary, there's more than one definition. In the wikipedia, each article only deals with one definition. That's why there are multiple articles. The polar centrifugal force is different from the rotating reference frame centrifugal force is different from the Reactive centrifugal force. The article is about a concept, it's not defining or contrasting terms for the world; encyclopedias don't define terms, they describe concepts, ideas, topics, subjects. That's why I don't mind if you reorder that sentence, it doesn't matter, but if you do, you've proven you don't really understand.- (User) Wolfkeeper (Talk) 03:41, 25 September 2008 (UTC)


 * In addition, I asked for the evidence that "most references specifically refer to rotating reference frames", and you just repeated the assertion. What is the actual EVIDENCE to which you referred? Looking at the six reference books on dynamics that I happen to have at my desk, your assertion is false. And I would guess that the results of a genuine survey of the literature would be dependent on the decade of publication, and the particular sub-discipline, e.g., mechanical engineering, aeronautics, fluid mechanics, dynamics, fundamental physics, mathematical physics, foundations of mechnaics, celestial mechanics, auto mechanics, and so on and on. I seriously doubt that you are in possession of enough "evidence" to make a judgement, aside from your own personal point of view.Fugal (talk) 02:48, 25 September 2008 (UTC)

Who says centrifugal force vanishes in an inertial frame?
Taylor says:

Hand and Finch say:

Arnol'd says:

Landau & Lifshitz say:

Goldstein says:

The above quotations indicate that some very reputable writers in the arena of classical mechanics use the term centrifugal force to describe a force that vanishes in a non-rotating frame where the angular rate of rotation is zero. Brews ohare (talk) 21:16, 24 September 2008 (UTC)

It may be noted further that the above results follow immediately from simple time differentiation in a coordinate-independent vector notation, and in no way place any restriction upon what coordinates one may elect to use, be they polar or Cartesian or arc length. In other words, centrifugal force is zero in a non-rotating frame (according to the usage of these authors) regardless of coordinate system. In addition, the vector derivation does not require any "implicit assumption" that an inertial frame must be associated with a Cartesian coordinate system, nor any "implicit assumption" disallowing curvilinear coordinates. See Fictitious force or Rotating reference frame for details. Brews ohare (talk) 21:24, 24 September 2008 (UTC)


 * Once again, a frame is an equivalence class of mutually stationary space-TIME coordinate systems, and hence the reference to a "frame"(or, equivalently, the stipulation of rectilinear space coordinates, as I showed you in all your references) implicitly signifies that any acceleration terms related to curved space axes will be kept on the acceleration side of the equation.Fugal (talk) 21:58, 24 September 2008 (UTC)
 * Of course, this is merely a convention, and we can just as well keep ALL of the acceleration terms on the acceleration side of the equation (which is the predominant recommendation in most modern dynamics texts), but we can also bring the acceleration terms related to curvature of the time axes over to the force side. The whole point is that this is arbitrary.Fugal (talk) 21:58, 24 September 2008 (UTC)
 * The same situation can be represented in infinitely many ways, and the choice of which, IF ANY, accelerations to treat as forces is arbitrary, and someone who understands this is not at all baffled when they see some people deriving the centrifugal force on a revolving particle in terms of a rotating cartesian coordinate system and others deriving the very same thing in terms of a stationary polar coordinate system, and so on.Fugal (talk) 21:58, 24 September 2008 (UTC)


 * Maybe its arbitrary, but different authors have made different choices. They are not the same. Centrifugal force consists of fewer or of more terms depending upon the author, and for some authors only terms involving the rotation of the system can contribute to fictitious forces, and the ones due to coordinate system selection (polar, arc-length, etc.) cannot. For others, all the terms matter. Consequently, centrifugal force vanishes in a non-rotating system for some authors, and not for others. Brews ohare (talk) 22:22, 24 September 2008 (UTC)


 * No, you're just getting confused because you don't pay attention to how the context is defined. Whether or not centrifugal force vanishes in a non-rotating system (or in a rotating system for that matter) depends entirely on your definition of "system" and on your decision about what, if any, acceleration terms to treat as fictitious forces. If someone stipulates that a "system" has rectilinear space coordinates, then obviously no extra acceleration terms due to curved space coordinates will appear, so there will be extra terms if, and only if, the "system" has a curved time axis, i.e., is accelerating in some way. Of course, even in this case, we aren't required to call the acceleration term a force, but we may choose to do so. If, on the other hand, a "system" is defined to be any space-time coordinate system, allowing curvilinear coordinates, then extra terms will appear (for moving objects) due to the space axes being curved. Again we then must decide whether to call these terms what they are (accelerations) or to call them forces. It's exactly the same. This is why all those references I gave you (which you promptly ignored, as you have before, and no doubt will again) are able to arrive at the centrifugal force for a particle in terms of stationary coordinates. Thus (for the billionth time) your POV attitude is inappropriate and unjustified.Fugal (talk) 00:05, 25 September 2008 (UTC)


 * It's all one simple unified subject... to anyone who understands it. And this is what is confirmed by ALL the references that have been cited. That's why the article needs to be written in a NPOV way, to accurately represent the full range of the subject as it appears in the literature.Fugal (talk) 21:58, 24 September 2008 (UTC)


 * It's unified except that different incompatible uses for the term centrifugal force are in use. Brews ohare (talk) 22:22, 24 September 2008 (UTC)


 * No, it's all unified, as fully and explicitly explained here (even extending it to the still more unifying formalism of Lagrangian mechanics, as you yourself have admitted), except that certain individuals are unable or unwilling to understand it. The fictitious sense of the term centrifugal force has precisely the same definition at all levels. The differences are only in which terms are stipulated to be zero by specialized choices of coordinates.Fugal (talk) 00:05, 25 September 2008 (UTC)


 * Sorry, Fugal. I don't agree with your interpretation, and do not find sufficient detail to make a case for it. Brews ohare (talk) 05:04, 25 September 2008 (UTC)


 * It's not that that they're not unified, I'm sure they are, it's that they're not the same, even though they're unified. Unified just means you can put them into one set of equations/tensor/whatever, but they're still different terms/solutions/roots/whatever to the equation. I mean that's what 'The differences are only in which terms are stipulated to be zero by specialized choices of coordinates.', that's what that boils down to. They're not the same terms. As I say, magnetism and electrostatics are unified, but they're still different. Yes, you can (sometimes) turn centrifugal force (rotating reference frame) into centrifugal force (polar coordinates) by changing references frames, just like you can turn electrostatics into magnetism by changing reference frames. But they're still different, they behave differently, they are defined differently and have different articles. Right?- (User) Wolfkeeper (Talk) 05:02, 25 September 2008 (UTC)
 * Yes, all authors would agree on the form of Newton's second law, for example, in polar coordinates, and in either a rotating or a stationary frame. So the unifying feature is Newton's second law. It also is true that looking at this law everyone agrees on, some terms vanish when the angular rate of rotation &Omega; = 0, and some do not. Some authors have chosen to group into the concept "centrifugal" only terms that vanish when &Omega; = 0 (see here), and other authors have chosen differently (see here), so that only some of their "centrifugal" terms vanish when &Omega; = 0, leaving them with a non-zero "centrifugal force" when &Omega; = 0. Brews ohare (talk) 20:59, 25 September 2008 (UTC)

David Tombe
Please note that I have unprotected User talk:David Tombe to allow a further unblock request to be made. The indefinite block remains in force. You might want to review any such request. -- The Anome (talk) 15:30, 25 September 2008 (UTC)

Redirect discussion
I've copied the key discussion (or what I think is the key discussion) of what the correct destination for the redirect should be to the redirect page's talk page. I would suggest that any conversation carry on over there, rather than being scattered to the 4 winds here.- (User) Wolfkeeper (Talk) 16:25, 25 September 2008 (UTC)

Talk:Centrifugal force.- (User) Wolfkeeper (Talk) 16:25, 25 September 2008 (UTC)
 * I do not find any recent discussion at Talk:Centrifugal force (disambiguation). Brews ohare (talk) 16:40, 25 September 2008 (UTC)
 * I see, you made a new page altogether at Talk:Centrifugal force. Sorry for the confusion. Brews ohare (talk) 16:43, 25 September 2008 (UTC)

Consensus?
Regarding this article in particular (Centrifugal force - rotating reference frames) there seems to be general agreement that the reputable published literature in classical mechanics includes discussions of something called “centrifugal force” in the fictitious sense that are not covered in this article (intentionally, since they are not restricted to the rotating frame context). In addition, there seems to be general agreement that, within classical mechanics, the term “centrifugal force” also has other (non fictitious) meanings, such as the reaction force. There is also a normal/tangential context for fictitious forces which we haven’t yet touched on.

So, in view of this consensus, I say again that the first sentence of the present article is unacceptably POV, because it says “In classical mechanics, centrifugal force is [the subset of a subset of centrifugal force described in this article]”. The sentence is too categorical. The lead sentences are supposed to accurately delineate the context. The present opening sentence reads like it is saying "cars are Chevys", whereas what it ought to be saying is that Chevy's are cars.

In addition, the first sentence could be improved for clarity and accuracy and verifiability. In all the reputable references I've seen, the fictitious centrifugal force is introduced by presenting the equation of motion, will the all acceleration terms, and then saying that one can, if desired, move some terms over and call them forces. This is representative of the published literature on this subject, so for Verifiability, the article should reflect this.

Combining both of these considerations (NPOV and Verifiability to reputable sources), I think a suitable first sentence for this article (bearing in mind the very restricted subject of this article, and the fact that it will be placed below a more generic article on the entire subject of centrifugal force in classical mechanics) would be as follows:

'''In classical mechanics, when the motion of a particle is described in terms of a reference frame rotating about a fixed axis, the acceleration of the particle relative to the reference frame differs from the absolute acceleration of the particle by the appearance of three terms, called the centripetal, Coriolis, and Euler accelerations. In the Newtonian equation of motion, F = ma, these three components of the acceleration, multiplied by the mass, are sometimes brought over to the force side of the equation (with the opposite signs), and treated as fictitious forces. When this is done, the symbol "a" in the equation of motion represents just the acceleration of the particle relative to the rotating frame, and the fictitious forces are called the centrifugal, Coriolis, and Euler force, respectively. The centrifugal force is directed outward from the axis of rotation.'''

I think this contains essentially the same information as the current lead, but worded in an NPOV and Verifiable way that accurately reflects the reputable literature on this subject. Fugal (talk) 22:24, 25 September 2008 (UTC)
 * Two problems.
 * This proposal does not deal with the issue of reactive centrifugal force. I don't think this is problem, because it is dealt with in Reactive centrifugal force and because that topic is of marginal interest, but Harald does.
 * The subject of this article is Centrifugal force (rotating reference frame). It is not about the acceleration of the particle relative to the reference frame differs from the absolute acceleration of the particle.
 * The present intro reads:"In classical mechanics, centrifugal force (from Latin centrum 'center' and fugere 'to flee') is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. The other two fictitious forces are the Coriolis force and the Euler force.[1][2] This article discusses the important case of a reference frame rotating about a fixed axis." I believe the objection to this intro is the use of the words "non-inertial frame", because Fugal would like to have centrifugal force present in every frame. Is that correct? But you don't have to take this sentence as all-encompassing: it leaves open the possibility that centrifugal force occurs in other circumstances too; the stated case is just a case where it does appear. All parties do agree that it appears in rotating frames. So maybe this intro is flexible enough after all? Brews ohare (talk) 23:46, 25 September 2008 (UTC)


 * Sorry but no, "All parties do agree that it appears in rotating frames" is a misunderstanding due to lack of precision, as now explained above. And as now also emphasized above, it still fails to accommodate people in general who typed in "centrifugal force". Again, if this article does not serve as general page for "centrifugal force", it's almost acceptable IMHO.
 * About almost: please see the intro of the old (general) page which shows that your intro is not correct for Newtonian mechanics in which a rotating coordinate system can be used as reference for measurements, while this is mapped to an inertial system for the laws (in fact that is how I was taught classical mechanics, and how Coriolis accel. etc. were derived).
 * http://en.wikipedia.org/w/index.php?title=Centrifugal_force_(rotating_reference_frame)&oldid=196032047
 * Regards, Harald88 (talk) 13:41, 26 September 2008 (UTC)


 * Regarding objection #1, I think that is a non-objection, because everyone agrees that this particular article is not about the reactive force. The point is that, since there are other meanings, this article's opening sentence is incorrect, because it asserts that "in classical mechanics, centrifugal force is [what's discussed in this article]". This is too categorical, and need to be qualified. Regarding objection #2, the phrase to which you object is the scientifically accurate description of the subject of this article, i.e., fictitious centrifugal force in rotating reference frames. This is fully supported by all the reputable literature, and your personal beliefs to the contrary are not relevant. Regarding objection #3, no, you have not correctly grasped my objection to the existing opening sentence, and no, the existing opening sentence doesn't meet the NPOV requirements.


 * Here's another proposal, trying to find some kind of common ground. Again, these words are fully supported by, and representative of, the descriptions of fictitious centrifugal force in rotating frames to be found in the literature, and it accurately and clearly establishes the limited context of this article.


 * In classical mechanics, when Newton's law F = ma is expressed in terms of a reference frame that is rotating about a fixed axis, the acceleration "a" of a particle contains terms involving the rotation rate of the frame. These frame-dependent terms are sometimes brought over to the force side of the equation (with reversed sign), and treated as fictitious forces. One of these fictitious forces points directly outward from the axis of rotation, with magnitude proportional to the square of the rotation rate of the frame. In much of the literature on classical dynamics, this term is called centrifugal force.


 * The issue of whether or not it makes sense to dedicate an article just to this subset of all fictitious centrifugal forces is a separate question. I personally think it's brain-dead to enshrine this little arbitrarily delineated, time-dependent but not space dependent, subset of fictitious forces, since it means that ultimately there will be about five or six separate articles on what can actually be presented in a single unified all-encompassing way from the modern point of view, but that's a separate issue. At the moment, I'm just trying to get agreement on the correct description of this little sub-topic. Hopefully, in the long run, once all the editors understand the correct definition of this sub-topic, and then place it along side the correct definitions of the other sub-topics (e.g., fictitious force derived in curvilinear coordinates), and realize that they are essentially identical, we will be able to achieve some coherence in this overall subject. But I'm afraid we have a long ways to go before we get to that point.Fugal (talk) 14:49, 26 September 2008 (UTC) —Preceding unsigned comment added by Fugal (talk • contribs)

= Harald's views =

Harald has me a bit confused because his comments are scattered all over the page. This section is an attempt to consolidate his views.

Views on reactive centrifugal force

 * the title "centrifugal force (rotating reference frame)" also applies to reactive centrifugal force. Harald88 (talk) 08:07, 23 September 2008 (UTC)
 * And don't forget, and as rather well explained in the old version, "centrifugal force (rotating reference frame)" also applies to reactive centrifugal force so that it's not an appropriate title. Unambiguous would be "centrifugal force (fictitious)". Harald88 (talk) 07:59, 24 September
 * Brews, I typed in "centrifugal force" as I was looking for a reference on how it is used in Newtonian mechanics; instead I was shown this article which falsely pretends that the term when used for rotating reference frames can only mean a fictitious force. Such a misleading and narrow-minded introduction is the very cause of never ending disputes in the existing literature, and which we had solved with the old article - perhaps the first time in history that a neutral complete overview was given. I have of course no objection to start with the old intro and then split up into two articles. Harald88 (talk) 08:15, 23 September 2008 (UTC)
 * "I think it's fine if at the start readers can fork to the different meanings. However, this is not the case when a reader types in "centrifugal force". Instead they are confronted with the Single View that in classical mechanics "centrifugal force" is a fictitious force. Thus, my main objection is that the linking to this article is unacceptably POV. I don't know how to fix this; I would agree with removing the first banner (POV) if "centrifugal force" links to the disambiguation page instead of to this article. Harald88 (talk) 13:55, 25 September 2008 (UTC)" Harald88 (talk) 14:09, 25 September 2008 (UTC)
 * In particular, the dispute is not about "which of these usages is most commonly used and which should be the basis of this article"; that misunderstanding is probably the cause of the problem. Instead, please read the article on NPOV. Harald88 (talk) 08:22, 23 September 2008 (UTC)
 * Brews, thanks for your clarification! I now see that your disagreement is due to a misunderstanding: the Newtonian use of "centrifugal force" corresponds to one subset of "away from centre", while the fictitious use corresponds to a different meaning of the same words (with proponents and opponents on either side, often refusing to admit the existence of the other). The big dividing line is due to 'two usages of "Centrifugal:(physics)" and the polarized views that correspond with these.
 * Funny enough, the old article dealt with eliminating the kind of misunderstanding that now occurs on this page. Please study the intro of the old page to which I referred above, complete with examples and references. Harald88 (talk) 13:22, 26 September 2008 (UTC)
 * Wolfkeeper, it's not necessarily wrong to directly link to the most used meaning, as long as the user doesn't have to search for other any meaning other than the one that is most common - especially since the meaning of the word itself is a point of dispute in the literature and thus a POV. Below I explained the two options in detail. Harald88 (talk) 13:02, 26 September 2008 (UTC)
 * Indeed we won't need to make more of a summary stub out of the disambiguation page, together with the nice disambiguation table that I referred to. However, at the moment that page is more or less hidden while it should be the departure point after typing "centrifugal force". Please can anyone who knows how to do so, do that? Then for me, the first banner (NPOV) may be removed from this article. Harald88 (talk) 13:04, 26 September 2008 (UTC)
 * The acceptable alternative was also already indicated: If everyone comes upon this page, then this page has to have an accurate and neutral [NPOV] introduction that immediately links to the disambiguation page. And then again for me it's OK to delete the first of the two banners. 128.178.153.55 (talk) 12:55, 26 September 2008 (UTC)
 * And as now also emphasized above, it still fails to accommodate people in general who typed in "centrifugal force". Again, if this article does not serve as general page for "centrifugal force", it's almost acceptable IMHO. Regards, Harald88 (talk) 13:41, 26 September 2008 (UTC)


 * The old version does not (only) "talk about reactive centrifugal force" but gave a neutral discussion of the contrary uses of the term; and it stresses the point that the reactive force may be observed in any frame. Real centrifugal force is the reaction force to centripetal force and both these forces occur with rotational force. For example taking the rotating earth frame and including the rotation effect of the earth in apparent gravitation, this action-reaction pair is still measured on a merry-go-round. Harald88 (talk) 13:05, 26 September 2008 (UTC)

Harald: I understand what reactive centrifugal force is, of course.

Your initial proposal for Centrifugal force (fictitious) is too general, as Centrifugal force (rotating reference frame) talks only about a reference frame rotating about a fixed axis. For example, centrifugal force (fictitious) also arises in the local reference frame in which the particle appears stationary.

How about adding a cross reference to this subject at the top of the page like this: I have done this for your perusal. Brews ohare (talk) 15:53, 26 September 2008 (UTC)


 * That's fine with me! Now readers are properly informed with links - thus I'll now remove the NPOV banner (which I had placed). There is still an issue with the intro and the quality of the new set of articles as identified (thanks to you!) just here below ("Views on inertial frames"). Harald88 (talk) 12:25, 28 September 2008 (UTC)

Views on inertial frames

 * The view of Newtonian mechanics is that only "real" forces are admitted; in any frame - even rotating - inertial coordinate systems are chosen for the laws of mechanics, using only real forces. In the case of rotating reference frames, these are usually mapped to inertial reference systems for the determination of forces and the calculation of Coriolis acceleration - without anything fictitious, according to the Newtonian interpretation that gravity is a real force. Harald88 (talk) 14:27, 25 September 2008 (UTC)


 * About almost: please see the intro of the old (general) page which shows that your intro is not correct for Newtonian mechanics in which a rotating coordinate system can be used as reference for measurements, while this is mapped to an inertial system for the laws (in fact that is how I was taught classical mechanics, and how Coriolis accel. etc. were derived). http://en.wikipedia.org/w/index.php?title=Centrifugal_force_(rotating_reference_frame)&oldid=196032047 Regards, Harald88 (talk) 13:41, 26 September 2008 (UTC)

Harald did not reply as yet to this response to these statements:
 * Hi Harald: There are two approaches to handling rotating frames. One approach, which you mention, is to work in an inertial frame with only the real forces due to interactions between bodies. A second approach is to work directly in the rotating frame, where use of Newton's laws requires introduction of fictitious forces. This introduction allows problems to be solved without translation back to an inertial frame. Here is a quote (also in the article) from :


 * Brews ohare (talk) 15:10, 25 September 2008 (UTC)

You might take a look at Rotating reference frame or Fictitious force for more details. Brews ohare (talk) 15:56, 26 September 2008 (UTC)


 * HI Brews, as I explained, the standard way to handle rotating frames with classical mechanics is not as you describe here above: that would provide horribly complex descriptions! Instead, the way I was tought from Alonso&Finn (and this is certainly the standard way) is to map the rotating frame to the most appropriate inertail frame - this is for example done for GPS. The description of motion is relative to the rotating frame, without the introduction of anything fictitious. This is very well described and referenced in the old version of this article (together with the derivation of Coriolis acceleration) to which I referred you several times.
 * From the fact that you don't know this although this very article that you are editing explainend it half a year ago, I can only conclude that the current set of articles does not reach the level of half a year ago, and at several places misleading statements must have slipped in (to be identified: what stamenents in this article as well as in the split-of ones are responsible for that misunderstanding?).
 * Note that your quotation "Treat the fictitious forces like real forces, and pretend you are in an inertial frame" is perfect for the intro to this article, IMHO.
 * Regards, Harald88 (talk) 12:25, 28 September 2008 (UTC)
 * Whether the math is more complicated in the inertial frame or in the rotating frame is a question of the problem. For example, in some Coriolis force problems (e.g. the trajectory of a particle on a carousel) the path is simple (e.g. just a circle) while in the inertial frame it is a more complicated path.
 * In the case of meteorology, it looks like most of the time the Earth is chosen as the frame of reference and Coriolis forces are invoked directly. There is no resort to inertial frames.

Brews ohare (talk) 13:22, 28 September 2008 (UTC)


 * The path relative to to the rotating frame is the same with and without fictitious forces; and the Coriolis force cannot be calculated without accounting for the rotation speed relative to the ECI frame. Thus it appears that you either did not read or not understand the above explanation, nor the old article! Harald88 (talk) 19:35, 1 October 2008 (UTC)


 * Harald, just because there's other equivalent ways to do it, it doesn't follow in any way that he didn't read or understand the earlier version.- (User) Wolfkeeper (Talk) 20:03, 1 October 2008 (UTC)
 * Harald, the point was not what can be done, nor how to do it differently. The point is what the common practice is in meteorology - if that is what you are aiming at. Namely, an Earth frame is used throughout, as per the quote added to the article on this topic. Brews ohare (talk) 23:17, 1 October 2008 (UTC)

= Correct definition for Centrifugal force (rotating reference frame) =

At the moment, I'm just trying to get agreement on the correct description of this little sub-topic. Fugal (talk) 14:49, 26 September 2008 (UTC)

Here is an observation, repeated from earlier:
 * The present intro reads:"In classical mechanics, centrifugal force (from Latin centrum 'center' and fugere 'to flee') is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. The other two fictitious forces are the Coriolis force and the Euler force.[1][2] This article discusses the important case of a reference frame rotating about a fixed axis." I believe the objection to this intro is the use of the words "non-inertial frame", because Fugal would like to have centrifugal force present in every frame. Is that correct? But you don't have to take this sentence as all-encompassing: it leaves open the possibility that centrifugal force occurs in other circumstances too; the stated case is just a case where it does appear. All parties do agree that it appears in rotating frames. So maybe this intro is flexible enough after all? Brews ohare (talk) 23:46, 25 September 2008 (UTC)

I have only a non-specific response on this observation from Fugal:
 * Regarding objection #3, no, you have not correctly grasped my objection to the existing opening sentence, and no, the existing opening sentence doesn't meet the NPOV requirements. Fugal (talk) 14:49, 26 September 2008 (UTC)

Fugal, I hope you can provide a more definite guidance to your objections, taking into account my discussion of the intro immediately above. In particular, in looking at these comments, here is the key point: however the quotations from the authors of various camps are interpreted, all these authors would agree that when &Omega; is non-zero, additional terms in the acceleration are produced; that is, regardless of interpretation, centrifugal force is present when &Omega; is non-zero. Hence, my opinion that the present intro is inclusive of all interpretations of centrifugal force (except reactive centrifugal force). Brews ohare (talk) 20:57, 26 September 2008 (UTC)

I am hopeful also that the addition of the template direction to Reactive centrifugal force will satisfy Harald. Brews ohare (talk) 16:29, 26 September 2008 (UTC)


 * As has been explained repeatedly, the objection to the first sentence of the existing article is that it incorrectly and inadequately establishes the limited context of the article. It implies that the context of the article is classical mechanics, which is true but incomplete, because there are other usages of centrifugal force within classical mechanics (such as the reactive force), which can and do pertain to "rotating reference frames", so the disambiguation parenthetical of the title combined with the context of "classical mechanics" still is not nearly sufficient to accurately establish the very restricted context of this article. Even if the intro said it is talking only about the fictitious force sense of centrifugal force, it still would not be sufficient, because we have agreed that the literature in classical mechanics encompasses views of centrifugal force that are more general and comprehensive than the restricted view that is the specialized subject of this article.


 * Accordingly, I've proposed wording that I believe accurately and adequately establishes the context of the present article. Per Wikipedia policy, I think this would be a more suitable introductory sentence for this article.


 * In classical mechanics, when Newton's law F = ma is expressed in terms of a reference frame that is rotating about a fixed axis, the acceleration "a" of a particle contains terms involving the rotation rate of the frame. These frame-dependent terms are sometimes brought over to the force side of the equation (with reversed sign), and treated as fictitious forces. One of these fictitious forces points directly outward from the axis of rotation, with magnitude proportional to the square of the rotation rate of the frame. In much of the literature on classical dynamics, this term is called centrifugal force.


 * By the way, when this was proposed above, Brews declined to make any objection at all, so I hardly think he is in a position to be making unctious statements like "I hope you can provide a more definite guidance to your objections". It should also be noted that he extracted just the single sentence from my reply to him, in which I simply stated that his hypothesized paraphrase of my objection was incorrect, and he neglected to mention that this sentence was embedded in a full, clear, and explicit explantion of my objection. I continue to assume good faith on Brews' part, but I also continue to find myself unable to account for his behavior on the basis of that assumption.


 * Let me also assure the other editors, who have expressed objections to "all these forks", that I remain convinced that the article ultimately should be unified, and that the present forking is just a tactic to evade the NPOV rules of Wikipedia by splitting off every POV other than the one Brews and Wolf favor into separate articles (which they have stated they believe will be ignored). But before we can make progress against this abuse, I think we need to accurately and clearly establish the restricted context of this particular article. Hence my effort to reach agreement on an accurate intro to this article.Fugal (talk) 17:32, 27 September 2008 (UTC)


 * One more point: My proposal for a lead paragraph for this article does not include the eptymology of the term (i.e., the latin meaning to flee from the center), because this applies to each and every one of the forked articles on centrifugal force, and yet it is not presented in any but this particular sub-article. It should either be repeated in each of the sub-articles (and more such sub-articles are needed, to cover for example the normal-tangential view of inertial centrifugal force), or else it should be given just once in the top level article. Of course, as I mentioned above, ultimately the subject of centrifugal force ought to be consolidated into a single article, so the Latin source would naturally just appear there, but with the existing tactical fragmentation, it needs to be placed in a NPOV position, not just in this particular article. My proposal is to just put the Latin source in the disambiguation article for now, since it applies to ALL of the disambiguated articles.Fugal (talk) 17:55, 27 September 2008 (UTC)

Response to Fugal
Even if the intro said it is talking only about the fictitious force sense of centrifugal force, it still would not be sufficient, because we have agreed that the literature in classical mechanics encompasses views of centrifugal force that are more general and comprehensive than the restricted view that is the specialized subject of this article Fugal (talk) 17:55, 27 September 2008 (UTC)

The present intro reads: "In classical mechanics, centrifugal force (from Latin centrum 'center' and fugere 'to flee') is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. The other two fictitious forces are the Coriolis force and the Euler force.[1][2] This article discusses the important case of a reference frame rotating about a fixed axis."

This wording says exactly what you want: it points out the more general meaning exists, and specifies the restricted topic of the article in hand. Brews ohare (talk) 18:45, 27 September 2008 (UTC)

there are other usages of centrifugal force within classical mechanics (such as the reactive force), which can and do pertain to "rotating reference frames" Fugal (talk) 17:55, 27 September 2008 (UTC)

The page does have a "for-see" link for reactive centrifugal force. It also has a disambiguation link. There is little possibility that a reader of this article will be unaware of the article reactive centrifugal force.

The number of readers interested in reactive centrifugal force is dwarfed by those interested in the meaning on this page. As Harald's old (general) page states: "Although this sense was used by Isaac Newton,[1] it is only occasionally used in modern discussions.[2][3][4][5]". There is no need to go further overboard to accommodate this little-used meaning.

Your proposed wording also is inadequate to encompass this case, and will rely upon these links to connect to Reactive centrifugal force. Brews ohare (talk) 18:45, 27 September 2008 (UTC)

''My proposal for a lead paragraph for this article does not include the eptymology of the term (i.e., the latin meaning to flee from the center), because this applies to each and every one of the forked articles on centrifugal force, and yet it is not presented in any but this particular sub-article. It should either be repeated in each of the sub-articles (and more such sub-articles are needed, to cover for example the normal-tangential view of inertial centrifugal force)'' Fugal (talk) 17:55, 27 September 2008 (UTC)

In fact, the [etymology] is done in Centrifugal force (rotating reference frame) and in Centrifugal force (planar motion). It could be done in Reactive centrifugal force as well. On that page, already this subject is related to Centripetal force. As a reaction to centripetal force, the [etymology] is less helpful in this case in conveying the meaning, because the [etymology] does not refer to reaction. Brews ohare (talk) 18:45, 27 September 2008 (UTC)
 * I've substituted [etymology] for the earlier incorrect word choice "epistemology". Brews ohare (talk) 22:33, 27 September 2008 (UTC)

the present forking is just a tactic to evade the NPOV rules of Wikipedia by splitting off every POV other than the one Brews and Wolf favor into separate articles Fugal (talk) 17:55, 27 September 2008 (UTC)

Inflammatory accusations are counterproductive and counter to Wiki policy. Good reasons for the articles have been advanced: they cover different topics as is pointed out in the lead to each article and in the Centrifugal force (disambiguation) page. Brews ohare (talk) 18:45, 27 September 2008 (UTC)

Let me remind you of your objective:

At the moment, I'm just trying to get agreement on the correct description of this little sub-topic. Fugal (talk) 14:49, 26 September 2008 (UTC)

The present introduction to Centrifugal force (rotating reference frame) meets all your objectives. Brews ohare (talk) 19:07, 27 September 2008 (UTC)

Response to Brews
Brews claims that the following words "point out that more general meanings exist":

"In classical mechanics, centrifugal force is one of the three so-called inertial forces or fictitious forces that enter the equations of motion when Newton's laws are formulated in a non-inertial reference frame. The other two fictitious forces are the Coriolis force and the Euler force. This article discusses the important case of a reference frame rotating about a fixed axis."

Unfortunately, the words obviously do no such thing. It mentions nothing other than centrifugal, Coriolis, and Euler forces, which represents only the highly restricted context for centrifugal force that Brews prefers. In fact, the sentence is not just POV and inadequate to establish the context, it is flat-out FALSE, because in non-inertial reference frames the fictitious forces that appear (as acceleration terms) are NOT limited to just those three. A reference frame can be accelerating translationally as well as rotationally. So it's even worse than I've been saying. Of course, in addition to being FALSE, it also fails to adequately define the context, becasue (as explained repeatedly) it fails to distinguish this restricted context of frames from the more general and coherent context of coordinate systems, which is very prominently presented in the literature.
 * A reference frame can be accelerating translationally as well as rotationally.
 * If you wish, fictitious forces due to straight-line acceleration of a frame can be added to the list. However, the Euler force becomes such a force in the limit of a path with infinite radius of curvature. Brews ohare (talk) 22:24, 27 September 2008 (UTC)
 * it fails to distinguish this restricted context of frames from the more general and coherent context of coordinate systems, which is very prominently presented in the literature.
 * The subject of frames and coordinate systems has no place in the introduction to "centrifugal force". It requires a wider presentation. In part, that topic is covered in Frame of reference. Brews ohare (talk) 21:33, 27 September 2008 (UTC)

Brews' comments about epistemplogy are misplaced, because I was obviously referring here to etymology. (Perhaps he was misled by my regretable typo "p" in the word.) The point is that my comments obviously referred to the linguistic origin of the term. Hence Brews' comments are (as always) irrelevant non-sequiturs based on misunderstandings.
 * Sorry about that: "etymology" is the correct word, However, my comments are perfectly relevant if "etymology" is substituted for "epistemology". Your comments (as always) are unusually polite and civilized. Brews ohare (talk) 21:33, 27 September 2008 (UTC)

As to Brews' admonition about inflamatory comments, I can only say the comment in question was a simple statement of fact about the editorial condition of this article. Brews and Wolf have intentionally and self-admittedly fractured the subject into multiple sub-articles, for the expressed purpose of relegating all the other POVs on this subject to separate articles where they hope and expect them to be ignored. This is just a candid statement of fact. This fracturing/forking has been a conscious tactic adopted by Brews and Wolf to violate NPOV by moving all other POVs to separate articles. If Brews thinks this description of his behavior sounds disreputable, I would have to agree, but it's not the fault of the description, it's the fault of the behavior. He should stop trying to circumvent the NPOV policy of Wikipedia.Fugal (talk) 20:14, 27 September 2008 (UTC)
 * I'll let independent readers determine whether the statement "the present forking is just a tactic to evade the NPOV rules of Wikipedia by splitting off every POV other than the one Brews and Wolf favor into separate articles"  is a statement of fact or an assertion about motivation. The facts are that separate articles deal with separate topics, as stated in the disambiguation page and in the lead to the articles. Brews ohare (talk) 21:33, 27 September 2008 (UTC)

Let me remind you of your objective, as your mind is wandering:

At the moment, I'm just trying to get agreement on the correct description of this little sub-topic. Fugal (talk) 14:49, 26 September 2008 (UTC)

The present introduction to Centrifugal force (rotating reference frame) meets all your objectives. Brews ohare (talk) 21:33, 27 September 2008 (UTC)

Deletion of sentence
These frame-dependent terms are sometimes brought over to the force side of the equation (with reversed sign), and treated as fictitious forces. [Goodman and Warner, "Dynamics", Wadsworth Publishing, 1965, p 358]

I removed this sentence pending further examination. Brews ohare (talk) 23:56, 27 September 2008 (UTC)

New Intro
So much for discussion, eh? The new intro is pretty pale, and introduces the topic in terms of mathematical manipulation, not the most attractive or interesting way to go at it. The previous Intro was much better. It also uses the term "absolute acceleration", which I thought went out of use about 1905. It also uses the term "force in the Newtonian sense", which I'm sure means a lot to Newton, but nothing to me.


 * If you think "absolute acceleration" went out about 1905, you obviously have not the slightest understanding of relativity theory. And if you are unfamiliar with what a force in the Newtonian sense means, I suggest you read up on classical physics. I've included a reference in the article to Haliday and Resnik.Fugal (talk) 01:44, 28 September 2008 (UTC)
 * A quote:


 * Thanks for the civility. Pippard is pretty good company. Brews ohare (talk) 03:18, 28 September 2008 (UTC)

The statement is made: "Some authors object to the use of the word "force" to refer to these acceleration terms". The reference goes back to the first edition of a book now in its 3rd or 4rth edition. The authors in the newer editions use the term "centrifugal force", so I'd guess that if the reference once applied to support this statement, it does so no more. 01:38, 28 September 2008 (UTC)Brews ohare (talk)


 * The exact quotation from page 485 of the SECOND (not the first) edition is "Many people, therefore, object to the use of the word "force" when referring to the vector -ma ...". Are you saying this statement has been removed from subsequent editions? I will check and report back.Fugal (talk) 01:51, 28 September 2008 (UTC)
 * You did not provide the direct quote, so I could only look up "centrifugal force", which they do use themselves in their book. In fact this sentence you quote is made by them in the 1997 edition (not the latest), but only as unreferenced hearsay. It is not a policy they follow themselves, and they supply no references, reputable or otherwise, of those that support this viewpoint. Brews ohare (talk) 03:18, 28 September 2008 (UTC)


 * Brews' comment above is reprehensible. First he challenges the truthfulness of my direct quotation of a reputable published source on the subject, and then when he discovers that (as always) he was wrong, instead of apologizing, he responds by saying that this statement from a published reputable source of experts on this subject (7th edition!) does not cite any reputable source for their statement, and hence Brews suggests that it should be suppressed or, as much as he thinks he could get away with, presented in a POV form as "According to Beer...". Honestly, if direct quotes from reputable sources are to be selectively suppressed by Brews according to whether or not they support his (erroneous) POV, then this whole process is a shambles.


 * I've corrected the article now, by supplying another citation from Taylor, who explicitly stated that "In most introductory physics courses centrifugal force is regarded as an abomination to be avoided by all right thinking physicists." Note that he says not just "some" or even "many" (as I've worded it in the article), but "most".


 * Now, some may wonder how Brews could have such a distorted view of this subject. Well, it's fairly apparent that he simply acquired whatever information he possesses about the subject by going to Google books and searching on "centrifugal force". Needless to say, this is going to bring up preferentially books on dynamics that favor the introduction of that term. There are many books on Dynamics that never even introduce the term, because they regard it so disdainful. Then there are many others that mention it once, just to say to the reader "here is something that really stupid people do sometimes, but we will not follow this practice here". Obviously these books will not rank high in Google's hit list. This is a problem with editors who are not really educated on a subject, but who mistakenly think they are educated based on browsing the web. And this doesn't even touch on the fact that Brews invariably misunderstands even the limited selection of texts that he has accessed. There is a real systemic problem here in the editing of this article.Fugal (talk) 00:10, 5 October 2008 (UTC)

And if you are unfamiliar with what a force in the Newtonian sense means, I suggest you read up on classical physics Fugal (talk) 01:44, 28 September 2008 (UTC)
 * "force in the Newtonian sense" means only Newton's laws, which seems to mean in this intro that fictitious forces don't cause acceleration. That is really unhelpful, as the whole point of fictitious forces is to enable the calculation of accelerations in non-inertial frames. The useful distinction is between inertial forces and the forces studied in, for example, the Standard model. Brews ohare (talk) 03:43, 28 September 2008 (UTC)

Clarification of "observed" and "determined"
The opening sentence was worded as follows


 * "In classical mechanics, when an object is observed from a reference frame that is rotating about a fixed axis, the motion of the object can be determined from Newton's laws by introduction of fictitious forces..."

This a very vague and ambiguous, to the point of being meaningless. What does it mean to observe something from a particular reference frame? (
 * Of course, it simply means to record your observations in a frame, either inertial or non-inertial. Methinks you are being difficult. The language of "observers" appears all through classical mechanics. Brews ohare (talk)

For that matter, what does it mean to be "in" a reference frame? Being stationary with respect to the frame isn't sufficient, because the observer could be at a singularity of the frame, such as on the axis of rotation.) When people talk about "observing from a particular frame", this is just sloppy shorthand for "describing something in terms of a particular reference frame", bearing in mind that a reference frame is simply an equivalence class of coordinate systems. (Remember the discussion about how even Brews' source for the idea of the magical observer admits that it is a misleading concept and should be banished from our minds.) Also, what is the meaning of "can be determined from Newton's laws by the introduction of fictitious forces..."?
 * It means the same thing as the quote from Hand. Brews ohare (talk) 13:11, 28 September 2008 (UTC)

This makes it all sound very mysterious, by introducing these strange things without saying where they came from. It's perfectly simple. When we describe motions in terms of a rotating coordinate system, the expression for the acceleration includes terms involving the rotation rate of the coordinates, and if we feel like it, we can bring these terms over to the force side of the equations of motion (negating them), and call them fictitious forces. No mysterious magical alternate realities of observers. Simply treating acceleration terms as forces. And the majority of modern texts on Dynamics say "don't do this", but some texts describe it, if only so that the student will recognize this usage when they encounter it in the literature.Fugal (talk) 01:40, 28 September 2008 (UTC)
 * It's mysterious and it's simple. Very poetic. Brews ohare (talk) 13:11, 28 September 2008 (UTC)


 * Yes I agree, as I made clear (I hope!) before: also in Newtonian mechanics objects can be "observed from" a rotating reference frame that is however mapped to an inertial frame; thus without introducing any fictitius forces. Harald88 (talk) 11:51, 28 September 2008 (UTC)
 * Possible, but not necessary, and not done in most presentations today. Brews ohare (talk) 13:11, 28 September 2008 (UTC)
 * In addtion, IMHO the quotation by Bruce ": "Treat the fictitious forces like real forces, and pretend you are in an inertial frame" is perfect for the intro to this article. However, it should not falsely suggest that this is the "standard solution" of classical mechanics - that is out of context! See also my reply to Bruce a little higher in 23"Harald's views" which is now also about Bruce's views. Thus I moved the remaining banner (which I had placed) down to the first appropriate section (the current intro looks quite OK to me).
 * Harald88 (talk) 12:40, 28 September 2008 (UTC)
 * Take a look at the link to this book and read the whole section. If you still think the quote is out of context, say why with quotes of your own. I find the context of the quote describes the approach by return to an inertial frame as unnecessary.
 * It looks to me like the field of meteorology (for example) usually works directly in the rotating frame and invokes fictitious forces directly: no inertial frame. Brews ohare (talk) 13:11, 28 September 2008 (UTC)
 * I referred to the context that you provided: it is fine for when you want to use fictitious forces. I also gave you the reference to show that I as well as probably most people of my generation never had any need for fictitious forces for rotating frames, while that section wrongly suggests that the use of fictitious forces is necessary. Instead, for solving problems of mechanics in non-inertial reference frames, the advice given in textbooks is to map to an inertial frame as certainly still is done in the reprint of Alonso and Finn (5 stars) http://www.amazon.com/Physics-Marcelo-Alonso/dp/0201565188 Harald88 (talk) 14:05, 28 September 2008 (UTC)
 * I have altered the intro to the quote to indicate that other methods are possible, and fictitious forces are only one method. I also added a meteorology quote by Ryder further down that says the same thing. Brews ohare (talk) 14:50, 28 September 2008 (UTC)
 * With these additional changes, I believe your concerns have been met and suggest the banner be removed. Brews ohare (talk) 21:01, 29 September 2008 (UTC)

Note: It appears that Bruce cut up the text by Fugal. Please don't do that, as it makes the original less well readable for others (this is not like a discussion group whihc has headers etc.). Harald88 (talk) 14:02, 28 September 2008 (UTC)

Suggestions for Improvement
Following the lead/introduction, I think it would be good to go right ahead and give the precise mathematical derivation of "centrifugal force" in the sense of this article.

In the existing article, following the lead, there are a number of somewhat off-topic sections, most with little or nothing directly pertaining to "centrifugal force" in the sense of this article. In particular, I think the following sub-sections ought to be consolidated into the article on fictitious forces:

- Analysis using fictitious forces - Fictitious forces - Is the fictitious force ad hoc?

Also, I think the section entitled "Coriolis force" should be consolidated with the article on Coriolis force.Fugal (talk) 23:48, 28 September 2008 (UTC)


 * I'm interested to see the "precise mathematical derivation' and how it might compare to (for example) Rotating frame of reference.


 * The section "Analysis using fictitious forces" is not off-topic. It could be restricted to centrifugal forces, which might make it appear more on-topic, but why do that? This section explains how centrifugal force can be used just like any other force if one wishes to work in a rotating frame. That might seem like a simple idea, but it is a powerful one in practical work. It also seems to be a topic found controversial by many; hence the quotations to support this simple idea.


 * The section "Fictitious forces" could be shortened up. It seems a bit repetitious in places.


 * The section "Is the fictitious force ad hoc?" is an instance of the historically important rotating sphere example. It interpolates between the two particular cases presented for this example. Its logical value is to make connection with the general formula of Fictitious force, alleviating the impression that the particular cases require separate assessment. That is, a general approach is available: the other examples  are not just "cooked up".
 * As an additional point, the centrifugal force article undergoes periodic deconstruction (destruction?) involving lengthy arguments. This particular section proves invaluable in these discussions on occasion because it shows the other two cases (which have their separate explanations) actually are limiting cases of one explanation; this utility on the Talk page is another indication this section has useful content.


 * The justifications offered by Brews for retaining these three sections of the article all have a common thread: (1) "seems to be a topic found controversial by many", (2) show that "the other examples are not just cooked up", and (3) "this particular section proves invaluable... in lengthy arguments". These "justifications" prove my point, i.e., the sections were motivated primarily not by the requirements of a good NPOV Wikipedia article, but rather by the necessities of a silly and misguided polemical debate that had been waged here. I think Brews is too pessimistic about the situation going forward. One of the main causees of the endless arguments was the insistence of some editors on portraying this one specific and highly restricted mathematical definition of "centrifugal force" as THE only legitimate definition, and denigrating all others. Hence it was necessary to produce all these polemical asides in an effort to shore up the buttress the basic POV nature of the article and fight off all the critics. Now that the scope and context of the article has been clearly and correctly delineated, none of these polemics are needed. No one disputes (I trust) the simple facts abput this simply defined use of the term "centrifugal force". So all the polemics should be replaced with a simple and direct derivation of centrifugal force in the sense of this article. I think the resulting article will be much more readable and informative, and probably significantly shorter.Fugal (talk) 04:04, 30 September 2008 (UTC)


 * The section "Coriolis force" should be left alone. It is based on the same rotating sphere example as the two previous illustrations and so is in proper context. It is a treatment of a very natural case (that is, it answers a question that any reader would ask, "what happens when the spheres don't rotate?"). It just turns out that the answer involves the Coriolis force.
 * To move it to Coriolis force would weaken the example here, and require construction of the example all over again in Coriolis force. Isolated in Coriolis force, it would not be as readily understood as it is when all the cases are together. Brews ohare (talk) 16:15, 29 September 2008 (UTC)


 * This perhaps is an argument for consolidating the two (or three) simplistic fictitious forces associated with rotating coordinate systems into a single article. Something like "Fictitious Forces in Rotating Reference Frames".Fugal (talk) 04:04, 30 September 2008 (UTC)

Recap
I'm interested to see the "precise mathematical derivation' and how it might compare to (for example) Rotating frame of reference. Brews ohare (talk) 16:15, 29 September 2008 (UTC)
 * So all the polemics should be replaced with a simple and direct derivation of centrifugal force in the sense of this article. I think the resulting article will be much more readable and informative, and probably significantly shorter.Fugal (talk) 04:04, 30 September 2008 (UTC)
 * Please present this derivation. And, if possible, connect it with the derivation in Rotating frame of reference, which is supported by references to very reputable authors. Therefore, I anticipate your derivation to be consistent with, and not contrary to this cited work. Let's see what you got. Brews ohare (talk) 05:30, 30 September 2008 (UTC)

The section "Analysis using fictitious forces" is not off-topic. It could be restricted to centrifugal forces, which might make it appear more on-topic, but why do that? This section explains how centrifugal force can be used just like any other force if one wishes to work in a rotating frame. That might seem like a simple idea, but it is a powerful one in practical work. It also seems to be a topic found controversial by many; hence the quotations to support this simple idea. Brews ohare (talk) 16:15, 29 September 2008 (UTC)
 * [This section was] motivated primarily not by the requirements of a good NPOV Wikipedia article, but rather by the necessities of a silly and misguided polemical debate that had been waged here.Fugal (talk) 04:04, 30 September 2008 (UTC)
 * Your reply is not responsive to the stated purpose of this section, as outlined above. It's also nasty. Brews ohare (talk) 05:30, 30 September 2008 (UTC)

The section "Fictitious forces" could be shortened up. It seems a bit repetitious in places. Brews ohare (talk) 05:30, 30 September 2008 (UTC)
 * No response from Fugal. Brews ohare (talk) 05:30, 30 September 2008 (UTC)

The section "Is the fictitious force ad hoc?" is an instance of the historically important rotating sphere example. It interpolates between the two particular cases presented for this example. Its logical value is to make connection with the general formula of Fictitious force, alleviating the impression that the particular cases require separate assessment. That is, a general approach is available: the other examples are not just "cooked up".

As an additional point, the centrifugal force article undergoes periodic deconstruction (destruction?) involving lengthy arguments. This particular section proves invaluable in these discussions on occasion because it shows the other two cases (which have their separate explanations) actually are limiting cases of one explanation; this utility on the Talk page is another indication this section has useful content. Brews ohare (talk) 05:30, 30 September 2008 (UTC)
 * The justifications offered by Brews for retaining these three sections of the article all have a common thread: (1) "seems to be a topic found controversial by many", (2) show that "the other examples are not just cooked up", and (3) "this particular section proves invaluable... in lengthy arguments". These "justifications" prove my point, i.e., the sections were motivated primarily not by the requirements of a good NPOV Wikipedia article, but rather by the necessities of a silly and misguided polemical debate that had been waged here. Fugal (talk) 04:04, 30 September 2008 (UTC)
 * The second paragraph is just a little historical perspective: deal with it as you prefer. The first paragraph is very pertinent to the place this section plays in the overall presentation of the "rotating sphere" example. This role is simply one of completing the example. Your response has nothing to do with an assessment of its value. It's a rant, again. Brews ohare (talk) 05:30, 30 September 2008 (UTC)

The section "Coriolis force" should be left alone. It is based on the same rotating sphere example as the two previous illustrations and so is in proper context. It is a treatment of a very natural case (that is, it answers a question that any reader would ask, "what happens when the spheres don't rotate?"). It just turns out that the answer involves the Coriolis force.

To move it to Coriolis force would weaken the example here, and require construction of the example all over again in Coriolis force. Isolated in Coriolis force, it would not be as readily understood as it is when all the cases are together. Brews ohare (talk) 16:15, 29 September 2008 (UTC)
 * These "justifications" prove my point, i.e., the sections were motivated primarily not by the requirements of a good NPOV Wikipedia article, but rather by the necessities of a silly and misguided polemical debate that had been waged here. Fugal (talk) 04:04, 30 September 2008 (UTC)
 * Again, not responsive to the discussion put forward; just a rant. Brews ohare (talk) 05:30, 30 September 2008 (UTC)

Fugal, if you have interest in more than polemics, here are my suggestions:
 * 1) Propose your derivation that will be the magic cure.
 * 2) Respond to the concrete suggestions for retention of the articles you dislike in a serious manner.
 * 3) It may be that once you have presented your ultimate derivation the light cast on the rest of the article will require revisions. However, in advance of that perspective, it is hard to see what you are objecting to. Brews ohare (talk) 05:30, 30 September 2008 (UTC)


 * Since Brews has re-arranged my comments in his "recap", placing my response to one of his statements beneath a completely different statement, I think he has (one again) made it very difficult to account for his behavior on the assumption of good faith. Suffice it to say that, as always, his remarks are all non-sequiturs, based on his complete failure to grasp any of the issues involved in the discussion. Again, anyone who doesn't understand the meaning of absolute acceleration really ought not to be editing articles on classical dynamics.Fugal (talk) 16:15, 1 October 2008 (UTC)
 * I did my best to put something pertinent from Fugal's "comments" next to the original argument for each article under consideration. Apparently I missed something. If there is some pertinent remark from Fugal, perhaps he could put it under the relevant paragraph in this recap? Would that effort be too much?


 * And how about the proposed three steps:


 * 1) Propose your derivation that will be the magic cure.
 * 2) Respond to the concrete suggestions for retention of the articles you dislike in a serious manner.
 * 3) Once you have presented your ultimate derivation, indicate how the light it casts on the article requires some revisions.
 * Not too hard to do, eh Fugal?? Brews ohare (talk) 23:12, 1 October 2008 (UTC)

Contrasting views of centrifugal force
Fugal, you say that the centrifugal force in polar coordinates is the same centrifugal force that occurs in rotating frames of reference. And presumably likewise with the Coriolis force. But in the former case, the Coriolis force is always tangential. Is that so in the latter case? When the debate moves on to this point, you will realize that the previous debate was not silly and polemical. 217.43.10.119 (talk) 10:56, 30 September 2008 (UTC)


 * Thanks for your participation. Close examination will show Fugal uses the meaning of fictitious force based upon placing all but second time derivatives of the coordinates on the force side of the equation. That approach means there are always fictitious forces, even in a stationary frame of reference. Moreover, these "forces" change form, direction and magnitude depending upon which coordinate system is chosen (zero in Cartesian, non-zero in polar, different again in spherical), unlike the "standard" fictitious forces. (The "standard" fictitious forces behave like real forces for a rotating observer; they do not depend on what coordinate system they choose). Obviously these "second time-derivative" fictitious forces are not the same as the "standard" fictitious forces (including the Coriolis force) that are zero in a non-rotating situation. Brews ohare (talk) 14:36, 30 September 2008 (UTC)

Careful here now, "Moreover, these "forces" change form, direction and magnitude depending upon which coordinate system is chosen (zero in Cartesian, - - " Would same not also be so if the fictitious forces as viewed from rotating frames were to be measured in Cartesian coordinates? 217.43.10.118 (talk) 21:21, 30 September 2008 (UTC)
 * Here's how it works. In vector notation and therefore independent of coordinate system (subscript r for rotating) Newton's second law in a frame rotating at angular rate &Omega; according to Taylor, Arnol'd, Landau & Lifshitz, Lanczos etc., etc. is (See rotating frame of reference):
 * $$\mathbf{F_r} = \mathbf{F}_{\mathrm{imp}} +\mathbf{F}_{\mathrm{centrifugal}} +\mathbf{F}_{\mathrm{Coriolis}}+\mathbf{F}_{\mathrm{Euler}} = m\mathbf{a_r} \ . $$
 * with:


 * the Coriolis force

\mathbf{F}_{\mathrm{Coriolis}} = -2m \boldsymbol\Omega \times \mathbf{v}_{\mathrm{r}} $$
 * the centrifugal force

\mathbf{F}_{\mathrm{centrifugal}} = -m\boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{r}) $$
 * and the Euler force

\mathbf{F}_{\mathrm{Euler}} = -m\frac{d\boldsymbol\Omega}{dt} \times \mathbf{r} $$
 * and the total physical force in the inertial (non-rotating) frame (for example, force from physical interactions such as electromagnetic forces)

\mathbf{F}_{\mathrm{imp}} = m \mathbf{a}_{\mathrm{i}}\ , $$
 * with subscript i indicating the acceleration in an inertial (non-rotating) frame, and where $$m$$ is the mass of the object being acted upon.
 * All the forces above are physical forces in the rotating frame; they are vector entities. They refer to actual physical objects and are not coordinate system dependent. Whether you express them in Cartesian, polar or whatever coordinates, they have the same magnitudes and the same directions.


 * "So the short answer to your question is 'No, if the fictitious forces as viewed from rotating frames were to be measured in Cartesian coordinates (or any others) they would always point the same way and have the same size.'"


 * Next is a digression that describes in more detail the differences in the approaches. This may be a bore; it recapitulates things said elsewhere.
 * Notice first that all three fictitious forces vanish when the frame is not rotating, that is, when $$\boldsymbol{\Omega} = 0 \ . $$ That is what the references Taylor, Arnol'd, Landau & Lifshitz, Lanczos etc., etc. all say, and these formulas are explicitly provided in exactly this form in all these references. They do not exist in inertial coordinate systems. This property is not shared by the contrasting "coordinate " view explained next.


 * Let us now introduce coordinate systems into the picture. There is no mathematical issue with the terms on the right side of these equations. All camps agree on what form they take. This issue is with calling these terms by the names assigned.


 * What I will call the "coordinate" view says that applying these names to the forces on the right is valid only in Cartesian coordinates. That view is at variance with the references Taylor, Arnol'd, Landau & Lifshitz, Lanczos etc., etc., who call these terms by these names in every coordinate system.


 * The coordinate view is OK with these names in Cartesian coordinates because, in Cartesian coordinates, the acceleration involves only second-order time derivatives, which is the mantra of the coordinate view. That is,

\mathbf{a}_{\mathrm{r}} = \left(\ddot{x},\ \ddot{y}\ ,\ddot{z} \right)\. $$


 * In polar coordinates, on the other hand, second order time derivatives are not the only terms that exist. The true, physical vector that is the acceleration in the rotating frame is:
 * $$\frac{d^2\mathbf{r}}{dt^2} = (\ddot r - r\dot\theta^2)\hat{\mathbf{r}} + (r\ddot\theta + 2\dot r \dot\theta)\hat{\boldsymbol\theta} +\ddot{z}\hat{\boldsymbol{k}}$$
 * and the "coordinate" view is that all but the second-order time derivatives should be dragged over to the force side and added to the centrifugal, Coriolis and Euler forces.
 * This "coordinate" approach is not by any stretch of imagination the same as leaving these terms on the acceleration side where they started out and dealing with an actual physical vector acceleration $$\boldsymbol{a_r}$$ instead of the bastardized so-called "acceleration" $$\boldsymbol{\tilde{a}}=\left( \ddot{r},\ r\ddot{\theta},\ \ddot z \right) \ $$.
 * The terms carried over to the force side in the "coordinate" expressions involve $$\dot{\theta}$$ which has nothing to do with the angular rotation of the frame &Omega;. It is related to the motion of the observed object, not the frame. These extra terms dragged over to the force side of the equation are non-zero even in an inertial frame with &Omega; = 0.
 * Moreover, were I to choose yet another coordinate system, say hyperbolic coordinates, the real acceleration $$\frac{d^2\mathbf{r}}{dt^2}$$ in the rotating frame would have a different form (but exactly the same direction and magnitude). Dragging the terms that don't have double-time derivatives over to the force-side, in hyperbolic coordinates new terms, different in form from the polar terms, would become the "coordinate" fictitious forces. The so-called "acceleration" consisting of only the double time-derivative terms would not be the same as the previous bastardized acceleration $$\boldsymbol{\tilde{a}}=\left( \ddot{r},\ r\ddot{\theta},\ \ddot z \right) \ $$ of polar coordinates, neither in magnitude nor in direction. Thus, the so-called acceleration of the particle and the so-called fictitious forces both change with the coordinate system, unlike real physical vector quantities. Brews ohare (talk) 05:50, 1 October 2008 (UTC)