Talk:Centrifugal force/Archive 12

Choosing the redirect destination
(Copied from Talk:Centrifugal force (rotating reference frame)


 * I did a google on 'centrifugal force', ignoring the wikipedia I got:


 * - talks about rotating reference frames
 * rotating reference frames
 * rotating reference frames
 * [http://hyperphysics.phy-astr.gsu.edu/HBASE/corf.html[ rotating reference frames/mach principle
 * doesn't exist at all
 * rotating reference frame
 * copy of columbia encyclopedia reactive centrifugal force
 * dunno, vague "inertia"
 * rotating reference frame
 * spam
 * not specified, reactive?
 * fictitious doesn't really exist
 * rotating frames of reference

Feel free to check these to make sure I've classified them correctly, and do your own googles or other kinds of searches.- (User) WolfKeeper (Talk) 00:00, 10 August 2008 (UTC)


 * You say "3:2 isn't a consensus at all." Could you expand on that comment? Your views were in the minority, and yet you went ahead and made your change, so I pointed out that you couldn't justify your edit based on a clear consensus of the editors. Now your answer is to tell me that "3:2 isn't a consensus at all". I know it isn't a consensus, even less so for the 2 position than for the 3 position, and yet you implemented an edit based on the 2 position. How do you justify this?


 * As to your web search results, you unfortunately overlooked one or two, such as


 * http://math.ucr.edu/home/baez/classical/inverse_square.pdf
 * http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/CORIOLIS.PDF
 * http://www-math.mit.edu/~djk/18_022/chapter02/section04.html
 * http://www.phy.umist.ac.uk/~mikeb/lecture/pc167/gravity/central.html
 * http://www.cbu.edu/~jholmes/P380/CentralForce.doc
 * http://www.myoops.org/twocw/mit/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/1BEBB815-1441-4698-8D09-3C0E378291F3/0/spring_pendulum.pdf


 * This is just from about 60 seconds worth of browsing. All of these explicitly present as "centrifugal force" the term arising from the basis vectors changing in space, e.g., stationary spherical, cylindrical, polar, parabolic coordinates. I also found a cite that carefully stated centrifugal force appears only in rotating coordinates, and then proceded to derive the centrifugal force in terms of stationary polar coordinates, so one has to be careful to distinguish what people think they are doing from what they are actually doing.


 * Careful here. I just gave the top-hits from google, because it's the most unbiased way I know to quickly get a feel for what most people think on a subject (using multiple search engines would improve this further). Clearly there are a variety of views, but the majority are to do with rotating reference frames. Absolutely, absolutely you can come up with many references that talk about other ways of dealing with it, but rotating reference frames seems to be the most common, and this is compatible with the wikipedia's article layout. Your links above don't deal with the commonality angle at all.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

So based on this, the redirect is currently pointed at Centrifugal force (rotating reference frame)- (User) Wolfkeeper (Talk) 16:32, 25 September 2008 (UTC)

Centripetal Force?
Why is centripetal force listed here as a branch of centrifugal force? And why is the Leibniz approach to centrifugal force not listed? David Tombe (talk) 19:31, 6 May 2009 (UTC)


 * Centripetal force is listed as a "related concept", as are the other conceptions, because it's so closely related (like the IP editor on the talk page of the rotating frame article keeps insisting). Leibniz's isn't listed because I haven't seen a description of it that distinguishes it from the rotating reference frame concept; his equation, update to modern notation per sources, is exactly what the rotating reference frame approach comes up with, and the interpretation is also the same, at least in modern terms.
 * It would be good to add a section on the historical evolution of these concepts, which is where differences are likely to become apparent. We should probably start with Christiaan Huygens, who apparently coined the term.  Dicklyon (talk) 20:16, 6 May 2009 (UTC)

Dick, just because you haven't seen a description of the Leibniz approach which convinces you that it is different from the rotating frames of reference approach is not a reason to suppress references to the existence of the Leibniz approach. The reference which I supplied does not mention frames of reference and I have never seen planetary orbits dealt with using rotating frames of reference. Furthermore, in planetary orbits, the Coriolis force is always in the transverse direction whereas in rotating frames of reference, the Coriolis force swings around like a signpost in the wind that has come loose at the joints. I will now undo your reverts because they were totally out of order.

As for centripetal force, it is adequately mentioned in the reactive centrifugal force section. David Tombe (talk) 07:07, 8 May 2009 (UTC)

Technical
I'm going ahead and tagging this article as because I feel that it is especially important that this summary-style article remain accessible to the general reader. Those who want a highly technical in-depth analysis will go on to the branch articles. Specifically, I feel that the "Centrifugal force in planetary orbits" section needs some work to make it more readable. Please don't "dumb it down"; and I fully understand that this is not Simple WP; but it should be easily understood by the general public (think of an average high school student) with no technical background in Physics. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)

In further note, regarding my recent edit, I think I should state for the record that I am not a physicist. I am a linguist and a wikipedian. If I've made mush of any of the finer points of any of the highly technical material presented here in the process of my editing, feel free to correct me, but please do so in a way that avoids getting overly technical and encourages others to maintain civility. Thank you. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)


 * Looking to this edit by FyzixFighter, I think the passages referring to Bernoulli and Lagrange need a little more clarification. Thank you for the contribution, but please remember that these articles, particularly this one, need to be easily understood by the general reader. Wilhelm_meis (talk) 02:08, 9 May 2009 (UTC)


 * I'll see what I can do. It's the Meli article that refers specifically to Bernoulli and Lagrange. It mentions a few others, but article goes into quite a bit of detail on Bernoulli's contribution arguing that it is in his works where "the idea that the centrifugal force is fictitious emerges unmistakably." I'll see about distill it down to a non-technical but accurate summary, but another set of eyes that has access to the article would be appreciated. In the case of Lagrange, Meli doesn't go into great detail; he just says that Lagrange's work was the main text on mechanics in the second half of the 18th century and that Lagrange explicitly stated that the centrifugal force was dependent on the rotation of a system of perpendicular axes. To say any more on Lagrange would probably need another "history of mechanics"-type reliable source - I'll keep looking. --FyzixFighter (talk) 03:29, 9 May 2009 (UTC)
 * I know this can be frustrating, and I really don't mean to be tendentious, but I really think the Bernoulli passage is still a bit technical. Bernoulli, in seeking to describe the motion of an object relative to an arbitrary point, showed that the magnitude of the centrifugal force depended on which arbitrary point was chosen - so far so good (the average high school student could probably grasp it), but then, and not inherently determined by the properties of the problem. I'm not sure what the properties of the problem means exactly, and I'm sure most of our readers will be left wondering as well.  Sorry, but I really want to make sure we avoid jargon and highly technical explanations on this page, for the sake of those without any special background in physics. Wilhelm_meis (talk) 13:07, 9 May 2009 (UTC)


 * No problem. I don't mind the specific, constructive criticism. Let me think on it a bit to see if I can come up with a better wording. The idea from Meli that I'm trying to convey with properties of the problem are the inherent attributes of the bodies involved that all observers will agree on, such as mass, relative distance between bodies, charge, the elasticity of the bodies, etc. - at least that's my reading of Meli's statement. The values of these quantities don't depend on any of the observer's choices (at least in the classical sense) and so neither will the forces that result from these quantities, whereas the value for the centrifugal force does depend on the observer's choice of reference frame. Can you think of a concise but non-technical jargon-laced way to say this? --FyzixFighter (talk) 14:05, 9 May 2009 (UTC)

FyzixFighter, I'd be very surprised if Bernoulli had advocated that centrifugal force is fictitious. I have this quote from Whittaker 'A History of the Theories of Aether and Electricity; The Classical Theories (London; New York, American Institute of Physics, 1987) p.6'

''ET Whittaker writes “ - - - All space, according to the young [John] Bernoulli, is permeated by a fluid Aether, containing an immense number of excessively small whirlpools. The elasticity which the Aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools - - -''

It's within this context that I am particularly interested in centrifugal force. I had been aware of the Leibniz approach since 1979 but I didn't start questioning the conventional wisdom that centrifugal force is only fictitious until I tried to understand Maxwell's 1861 paper. I noticed that Maxwell was using the concept of centrifugal pressure between vortices in a similar sense to Bernoulli. I then extrapolated the Leibniz approach to the idea of two adjacent two body orbits and considered the centrifugal force term in relation to the mutual transverse speed as between objects criss-crossed between each system. It suggested that the two orbits would repel each other if the mutual transverse speeds were high enough, and that centrifugal force is indeed real.

You mentioned how Bernoulli had said that centrifugal force needs to be relative to a point origin. I would certainly agree with that, but that is not the same as saying that it needs to be associated with a rotating frame of reference. As regards the concept of rotating frames of reference, you will probably find that it began with rotating rigid bodies when they fixed a frame of reference inside those bodies to aid with the description of the motion. That'll be the Lagrange connection. I blame Coriolis (1835), for letting the concept become detached from physical reality. Gaspard-Gustave Coriolis was only interested in the physical forces associated with rotating water wheels, but he failed to see what was eventually called the Coriolis force in his first category of supplementary forces when considering the induced forces that oppose the dragging forces in a rotating frame. It seems that he didn't consider a constrained radial motion on a turntable, such as a marble running along a radial groove. Coriolis then took his 'compound centrifugal force' (Coriolis force) from the mathematical transformation equations (his second category of supplementary forces) and hence created a concept which had become totally detached from its physical context. It was a like a signpost that had become loose at the pole and allowed to blow in the wind. That is the disjointed basis for the modern science of rotating frames of reference.

I think that its time now to stand back and appraise this situation in a balanced way. You seem to be very keen to undermine all the physics edits which I make. Your record since I opened my account shows that you have only ever come to physics articles to undermine my edits. there are no exceptions to that rule. You are now trying too hard to package the Leibniz approach into the 'rotating frames' approach. If you were to fully consider the merits of the Leibniz approach, you might find that in a few days time you won't feel the need to bury it anymore.

Think about it this way. Could you fix a rotating frame of reference around two adjacent two body planetary orbits? David Tombe (talk) 11:43, 9 May 2009 (UTC)
 * David, please refrain from making any accusations. True or not, they serve only to perpetuate the edit warring.  If you really believe someone is hounding you, go to WP:ANI.  But please do not continue to post accusations on the talk pages.  It doesn't help us work together or build consensus. Wilhelm_meis (talk) 12:37, 9 May 2009 (UTC)

Models or examples
I think it would help the article, it would help the general reader and it would certainly help me, if we could provide some simple models or concrete examples of each of these scenarios and phenomena to illustrate some of the more difficult concepts in a more intuitive way. Of course (and here is perhaps the real challenge) even in this pursuit we must still stick to reliable sources, lest anyone become accused of inserting their own synthesis. Anybody got any good ones in the original sources? Wilhelm_meis (talk) 12:45, 9 May 2009 (UTC)


 * I just added (though I forgot to login) a physical example for the reactive centrifugal force. It's taken from the Roche source. It's a little technical in terms of engineering, but it gives it a real-world, oily physical machine touch . If other editors think it's too technical, then we can use the old object being spun around on a string example which Roche also uses. --FyzixFighter (talk) 17:47, 9 May 2009 (UTC)

FyzixFighter, Regarding the Bernoulli reference, I don't think that you can make the deduction which you did regarding the issue of frames of reference. Bernoulli clearly points out that centrifugal force varies according to which point of reference that we choose. That is a fact of which I am well aware, and I have made my own conclusions about it. I don't intend to insert my own conclusions in the article. But you saw from my edit above that one of the Bernoulli's believed that space is filled with tiny vortices that press against each other due to centrifugal force. I have a theory that these vortices are rotating electric dipoles. It's an established fact that an electric dipole is surrouded by an inverse cube law force field. Hence if a body moves through a sea of such dipoles, it will experience an inverse cube law repulsive force relative to any arbitrarily chosen point, providing that the effect is induced by transverse motion relative to that point. That would mean that centrifugal force is built into Euclidean geometry and it would explain why centrifugal force does not show up in Cartesian coordinates. Centrifugal force hence becomes a property of absolute space and not a property of any frame of reference. That's what Newton's Bucket argument showed. But that is only my own interpretation of the situation. I don't intend to insert it. Likewise, you are entitled to deduce that Bernoulli's statement regarding centrifugal force varying according to the point of origin implies that Bernoulli was thinking in terms of frames of reference. But you are not entitled to insert that opinion into the main article.David Tombe (talk) 18:41, 9 May 2009 (UTC)


 * I'm not making any deduction about what Bernoulli (note this is Daniel Bernoulli, Johann Bernoulli's son) meant in his memoir. That would be original synthesis from a primary source. What I am doing is reporting what a published author says about Daniel Bernoulli's memoir in a reliable source. Your recent edit to that sentence now bears little resemblance to the statement found in that reliable source. I will make the sentence in line with the reference cited. --FyzixFighter (talk) 19:50, 9 May 2009 (UTC)

FyzixFighter, before you do so, can you not balance it out with what I wrote regarding Coriolis's role in the field of rotating frames of reference? Coriolis is much more relevant than anything that Bernoulli ever had to say on the issue of rotating frames of reference and fictitious forces. Why are you so keen to insert a quote by a man in the year 1990? It spoils the whole flow of the section. David Tombe (talk) 19:57, 9 May 2009 (UTC)


 * I have two sources (that I've listed) that place the paradigm shift from real force to fictitious force in the late 18th century. I've also got one more that I need to hunt down that Roche refers to: Dugas (1958) "Mechanics in the Seventeenth Century" (Neuchˆatel: Editions du Griffon). The references I've found to this source would indicate that it too places the paradigm shift in the late 18th century, but since I haven't gotten my hands on it yet, I'll wait to confirm before including it. I fail to see how this text spoils the flow of the section. The section is on the history of the centrifugal force concept, and the source is a mainstream journal on the history of science and technology. I'm keen to include it because it's from a reliable secondary source and is relevant to the topic.
 * I'll see if I can work in Coriolis, but to say that he is the pivot point where the paradigm shifted would require a reliable source saying as such. At most we can say that Coriolis derived all the fictitious forces in his work and gave the name compound centrifugal force to the combined outward radial components of those forces. --FyzixFighter (talk) 20:30, 9 May 2009 (UTC)

This is what I mean about sticking close to the sources and treading lightly with our models. If we move even one step away from the source it may look like we're inserting synthesis, and yet we have to make the article accessible as well. My solution to this is that we give the information as it appears in the source (i.e. either a direct quote or a close paraphrasing), and then give a parenthetical explanation in layman's terms where needed, and then give a model or concrete example that is taken directly from a source, and provide inline citations for everything. Regarding sources, I don't see a problem with using whatever sources we have available (provided that they satisfy WP:RS and WP:COI). I know it's a fine line to walk, but this group of editors is more than equal to the task, and it will help the article thrive and help us all work together. Regarding inline citations, it may sometimes be necessary to provide a note for each element of a passage (1. quote, 2. paraphrasing for clarification, 3. model) even if they came from the same source, just for the sake of clarity. Thank you all for your efforts to come together and improve this article. Wilhelm_meis (talk) 02:16, 10 May 2009 (UTC)

Experts, debates, competing, etc.
Let's don't put stuff into the article to portray the various conceptions as something involved in controversy, debates, argument among experts, etc., unless we have sources to that effect and identify the players. From all that I've read, the concepts and experts seem to co-exist peacefully, though sometimes a clarification is needed as to what technical on non-technical concept of centrifugal force is meant in a given situation. Dicklyon (talk) 16:12, 8 May 2009 (UTC)

I added some sources on the historical debates about absolute and relative motion; these can obviously stay. Brews is pretty keen on this idea, and it should expanded somewhere if it's not already; there's not much in Mach's principle. Dicklyon (talk) 17:08, 8 May 2009 (UTC)


 * Dick, your edits are within the basic framework for a new settlement to this long running edit war. I like the historical introduction, but there is one line which I wish to question you about. I have just left a note on Wilhelm's talk page and I mentioned that very point. I don't anticipate any further edit wars providing that the supporters of the 'rotating frames/fictitious' approach don't try to subsume the Leibniz approach.


 * Was there any need to mention that the planetary orbital equation (The Kepler problem) can be treated within the context of a rotating frame of reference? I did that topic in detail in 1979 at university using Williams's 'Dynamics'. I saw quite a number of methods for solving the radial second order differential equation in question. But I never saw any attempt to solve that problem using rotating frames of reference. The next year, I used Goldstein to do Lagrangian and rotating rigid body motion. As you can see, Goldstein does not use rotating frames of reference in connection with planetary orbits. Leibniz does not use rotating frames of reference either. So why the need to mention rotating frames in this context?


 * Let's recap what the edit war was all about. It was all about everybody but myself making sure that the Leibniz approach was kept off the page. At first I was accused of introducing original research. It took me a while to get my act together and dig up a Goldstein. But when I did, the Leibniz method was still rejected. You can look at how my first attempts to introduce the planetary orbital equation were reverted last July 2008. It indirectly led to me getting a nearly permanent block.


 * And now when finally the Leibniz method has been recognized due to the arrival of more sources, it seems that you are trying to subsume it into the rotating frames approach. Let's be quite clear about this. The two approaches differ in three important respects.


 * (1) In the rotating frames approach, centrifugal force is fictitious. In the Leibniz approach, centrifugal force is real.


 * (2) In the rotating frames approach, great significance is attached to the actual rotating frames themselves. In the Leibniz approach, there are no rotating frames.


 * (3) In the rotating frames approach, the Coriolis force swivels as like a weather cock on a pole. In the Leibniz approach, the Coriolis force is firmly fixed in the transverse direction.


 * So we cannot subsume the Leibniz approach into the rotating frames approach. On the centrifugal force (rotating frames of reference) page, I could see that you were all desperately trying to tangle the planetary orbital problem up with rotating frames. You were doing this as a result of momentum from the edit war. This needs to stop. Each approach now needs to be dealt with separately and in isolation, and that is the best way to ensure that there will be no return to an edit war.


 * So I intend to remove that sentence in the introduction which drags rotating frames of reference into the Kepler problem. There are no rotating frames of reference in the Kepler problem. David Tombe (talk) 17:13, 8 May 2009 (UTC)


 * I think you're fooling yourself when you say it was "all about everybody but myself making sure that the Leibniz approach was kept off the page." I introduced the Leibniz approach, and have never tried to keep it or the Goldstein approach suppressed.  On the other hand, it's true that it's pretty much everyone else against you.  Maybe some thoughtful self-examination is in order. Dicklyon (talk) 17:20, 8 May 2009 (UTC)

Dick, you brought it to my attention that it was the Leibniz approach and I'm grateful to you for that. I didn't realize that that approach originated with Leibniz until you showed me that link last week. But nevertheless it was that approach that I had known for 28 years when I began to try and insert it into wikipedia in early 2007. I had always known that it wasn't a Newtonian approach, and it had been my intention for years to study Newton's Principiae to try and find out exactly how Newton solved the Kepler problem. I knew that Newton got as far as the inverse square law of gravity and that he also invented calculus. On the other hand, I knew how to use Newton's law of gravity, calculus, and the inverse cube law centrifugal force to solve the Kepler problem, but I knew that it wasn't Newton's method. By producing that Leibniz reference, you have solved a long standing mystery for me. It all ties in perfectly with the notorious animosity between Newton and Leibniz. Now that I have it all clear, I can better discuss the reactive centrifugal force which I still disagree with. We're all now beginning to see how it all fits together. The initial days of the edit war in 2007 involved some editors who have long disappeared. But the thrust of it was always that they were dug into the 'rotating frames/fictitious' concept whereas I wanted a real outward centrifugal force.

On a point of curiosity, have you ever considered two × two body problems side by side in their mutual equatorial planes? If you adopt the Leibniz approach, you will be able to criss-cross a centrifugal repulsion between any pair amongst the four, providing the angular speeds are high enough. The two orbits will repel. That's how Maxwell explained magnetic repulsion. He used a sea of tiny vortices aligned solenoidally. David Tombe (talk) 20:07, 8 May 2009 (UTC)


 * No, I really don't know much about this stuff. Just going by what I find in books. Dicklyon (talk) 04:50, 9 May 2009 (UTC)

Physics and engineering dichotomy
Dick, I think I can live with not stating the dichotomy in the intro. But just to clarify where that came from, the Roche 2001 article is the one that casts the fictitious vs. reactive as a physics vs. engineering dichotomy. In it he states, "I have identified at least three interpretations of centrifugal force in the literature: a valid meaning in physics, an entirely different but equally valid meaning in engineering, and a cluster of false meanings." The two distinct concepts he goes on to talk about are the fictitious and reactive centrifugal forces. Since the physics/engineering dichotomy is touched on in the "reactive" section, that can be sufficient for me. Anyways, Cheers. --FyzixFighter (talk) 05:12, 9 May 2009 (UTC)


 * OK, thanks; no problem with it if it comes with a citation. It's funny though, as I was just discussing this with an engineering prof who assures me it's common to use the rotating-frame approach in Mech. Eng. and robotics. Dicklyon (talk) 05:39, 9 May 2009 (UTC)

Dick and FyzixFighter, It might help to calm down the edit war if everybody were to openly admit their preference. I have openly admitted that I am only in favour of the Leibniz approach. But I will not be trying to obliterate or hide the other approaches. I am not particularly interested in the 'rotating frames' approach since, in my opinion, it contains some serious errors, particularly in relation to where it has allowed the Coriolis force to swing freely like a weather cock.

It would seem to me that you are clearly committed to the 'rotating frames' approach. That's fair enough. But try not to loose sight of the contexts within which that approach is used in the textbooks. It is used mainly in relation to Coriolis problems in meteorology and missiles being fired on rotating platforms etc. In my days, it was never used in connection with the Kepler problem. You would have a hard job inserting a co-rotating frame of reference around a three body problem.

As regards the Newtonian 'reactive centrifugal force', I think that we all disagree with it and at any rate it has disappeared from the textbooks in recent years. But we can still write about it and explain its historical origins in connection with Newton's animosity towards Leibniz. The reactive approach still appears to be of interest to engineers.

As regards the issue of preferences, I have explained fully why I prefer the Leibniz approach. It is an 'all in one' approach which can explain any scenario. Start with a weak gravity hyperbolic two body problem. Then attach a string between the two bodies. The centrifugal force will pull the string taut. The induced tension in the string will then cause an inward centripetal force on top of gravity and change the orbit to circular.

Can you and FyzixFighter give me any reasons why you are so keen to promote the 'rotating frames' approach? David Tombe (talk) 12:02, 9 May 2009 (UTC)


 * David, thank you for asking. I came to this article with no preconceptions, not have studied how CF is treated in sources.  My participation was to try to help resolve the ongoing arguments, by understanding what is in Goldstein that you kept saying others were suppressing (which was partially true), and why the topic had been split into two against the will of many editors.  It was a mess.  So I did what I could to move it toward an article based on sources, respecting all verifiable sourced points of view.  I found that the Goldstein analysis is perfectly sensible, and not different in any significant respect from the analysis by Taylor and others that end up with the same results.  I've done my best to find and cite sources, unify the treatment of the different valid points of view, etc.  I found and added the Leibniz point of view and the flip that Newton had done.  All good stuff, don't you agree?  Dicklyon (talk) 20:41, 9 May 2009 (UTC)

Dick, I certainly think that we have all learned something new from the arguments. Originally I was only focused on getting recognition of the centrifugal force as it arose in planetary orbital theory. I only learned from you last week that that was actually Leibniz's method. I have been fascinated by that analysis for many years. I didn't do it until my second year at university and I did it over in the applied maths department. In my first year I did a classical mechanics course in the physics department and it only dealt with circular motion, and of course we were taught that centrifugal force didn't exist. Having been sold on the idea of the singular role of centripetal force in circular motion, I just couldn't figure out how to rationalize with elliptical orbits. (I was doing astronomy that year too). The next year, I did the orbital mechanics course and learned the Leibniz method. I was fascinated with the power of calculus to resolve such a difficult problem so concisely. The hyperbolic, parabolic, and elliptical solutions simply fell out of the second order differential equation. Most physics students in my time didn't do that applied maths course and I feel that they missed out on something very important. Having said that, the main thrust of that applied maths course was more on solving tricky problems centred around that theme rather than the actual theme itself, and that really was maths as opposed to physics. I remember asking my lecturer about the (Leibniz) method method and he told me that it wasn't Newton's method. I always wondered whose method it was. My specific interest in centrifugal force came many years later when I was studying Maxwell. I re-examined the Leibniz approach and realized that Maxwell was right about the fact that vortices would repel each other due to centrifugal force. We just criss-cross the centrifugal force across any permutation of pairs of particles. David Tombe (talk) 21:43, 9 May 2009 (UTC)

The connection between rotating frames and the Kepler problem?
Regarding this line in the main article,

In modern science based on Newtonian mechanics, Leibniz's centrifugal force is a subset of this conception and is a result of his viewing the motion of a planet from the standpoint of a special reference frame co-rotating with the planet.[6]

I have never seen the planetary orbital problem dealt with using a rotating frame of reference, and I have seen it done many ways using both force and energy equations. The modern science of rotating frames of reference never writes centrifugal force in its inverse cube law form, and indeed it is generally more interested in the Coriolis force. It would be impossible to insert a co-rotating frame of reference around a three body problem. So I cannot see how Leibniz's real centrifugal force can possibly be considered to be a subset of anything to do with rotating frames of reference. I don't doubt that in recent years some scientists have tried to deal with the Kepler problem using rotating frames of reference. But it definitely isn't necessary to do so and it would be a most cumbersome thing to do considering that the rate of rotation is varying. We would we bother and why do we need to have this sentence in the article? What is the exact line in the quoted reference which clarifies the reasons for this point? David Tombe (talk) 19:19, 9 May 2009 (UTC)


 * Some quick references that I have close at hand:
 * Whiting, J.S.S. (November 1983). "Motion in a central-force field". Physics Education 18 (6): pp. 256–257
 * Jeremy B. Tatum Celestial Mechanics Chapter 16 (bottom of page 1, top of page 1 - the radial equation with an inverse cube centrifugal force and Tatum explicitly states that the equation describes the motion "relative to a co-rotating frame".
 * And from the Aiton reference:
 * "Leibniz viewed the motion of the planet from the standpoint of a frame of reference moving with the planet. planet. The planet experienced a centrifugal force in the same way that one experiences a centrifugal force when turning a corner in a vehicle. From the standpoint of an observer outside the vehicle the centrifugal force appears as an illusion arising from the failure of the traveller to take account of his acceleration towards the centre. Although both standpoints are valid, Newton, in the Principia, always used a fixed frame of reference." (p. 32)
 * "Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference." (p 34)
 * I believe that I haven't strayed to far afield from the secondary sources and that I'm not synthesizing new conclusions from them. Do we have any reliable secondary sources that contradict this source on the question of Leibniz? You and the other editors are welcome to double-check the sources and my edits to see if I've been dishonest or remiss in reporting what they say. --FyzixFighter (talk) 20:15, 9 May 2009 (UTC)

FyzixFighter, You cannot use a co-rotating frame for the three body problem. As regards the two body problem, I didn't say that you couldn't analyze it using a rotating frame of reference. I was pointing out that it is not necessary to do so, and it was never done that way when I was studying the Kepler problem in 1979. All those references above merely tell me that some people in recent times have tried to incorporate the Leibniz approach into the modern fictitious concept. I could show references which counteract those modern opinions, but we shouldn't have to go down the road of a reference war. If you are serious about this topic, you will be able to judge the broader picture over a wider base of references. As it is, you need to ask yourself why you are so keen to promote the rotating frames approach. You have stated yourself that you don't form opinions and that you only copy from reliable sources. If you don't form opinions on this topic why are you so keen to edit on this page in particular and promote a particular point of view to the extent of trying to eclipse the Leibniz point of view? David Tombe (talk) 20:33, 9 May 2009 (UTC)


 * I fail to see how the reference you give contradicts the references I provided. Also note that the Aiton reference is from 1962 - not exactly what I would call recent times. Your reference does explain Leibniz's theory, but does not say anything about whether or not Leibniz approach can be incorporated into the modern rotating frames understanding of the centrifugal force. Interestingly, a search of your reference does yield this statement (p. 264):
 * "...Newton had realized crucially that it was much simpler to consider things from a frame of reference in which the point of attraction was fixed rather than from the point of view of the body in motion. In this way, centrifugal forces - which were not forces at all in Newton's new dynamics - were replaced by forces that acted continually toward a fixed point."
 * and this (p. 413, discussing eq. 11.7):
 * "The second term on the right-hand side is referred to as the "centrifugal force" and is due simply to the rotation of the coordinate system."
 * But perhaps I missed the part you're keying off of. What sentences in that text do see as contradicting the sentences from the Aiton reference?
 * I also fail to see where, when, or why the three-body problem entered into this discussion. I know that was one of Leibniz's biggest beefs with Newton's Principia (it didn't have a closed form solution for the 3-body problem). Does Leibniz's theory handle it, and do you have a reliable source I can look at to see how it handles it? --FyzixFighter (talk) 03:59, 10 May 2009 (UTC)

David, it's not at all clear to me what the Leibniz approach was, really; it doesn't seem to connect to dynamics as we know it. Your source says he got the equation (which is correct) from consideration of the equal areas law of Kepler among other ideas; sounds plausible. You've characterized modern sources as trying "to incorporate the Leibniz approach into the modern fictitious concept" (I presume you mean fictitious-force concept); I don't see that so much; most sources say it's consistent, if anything. I haven't seen the Aiton ref, to which the idea that the Leibniz approach is a "subset of the conception" of the rotating frame approach is attributed. I'd have to see it; I agree it sounds a bit like modern revisionism. I don't think Leibniz really treated r-double-dot as "acceleration", and probably didn't know about F=ma; Goldstein certainly did, and the only way r-double-dot can be interpreted as an acceleration is in a co-rotating frame, which he clearly did know about, and was what his "equivalent one-dimensional system" was that allowed him to go from eq 3-12 to 3-22 with the centripetal acceleration term moved over to become a centrifugal force term, just like in Taylor. I'd be surprised if Leibniz went through any analogous process in getting to the equivalent equation. Dicklyon (talk) 04:36, 10 May 2009 (UTC)


 * Dick, the whole thing comes down to two equations. There is a transverse equation which is essentially the law of conservation of angular momentum (Kepler's second law of planetary motion). From this equation, we can establish a constant, normally written by the symbol L. This constant L when substituted into the radial equation converts the radial equation into an equation in one variable (r) and the centrifugal force term shows up as an inverse cube law force. We then have a second order differential equation in r and it solves to yield either a hyperbola, a parabola, or an ellipse. That is the whole subject in a nutshell. Ever case scenario in this entire topic can be understood in terms of the radial equation.


 * What I want you to do now is to ask yourself why everybody has been so obstinate about accepting this simplistic approach to the problem. I have my own theory on that. If a person attends a course and is taught that centrifugal force does not exist, or that centrifugal force is only a fictitious force that is observed from a rotating frame of reference, you will find that they will dig into that viewpoint forever more. Recently, I checked out a local university science library. I couldn't find any physics textbooks going back earlier than the 1960's. I was told that all the old physics books had been moved away to storage in another building. The only book in that library that dealt with the Leibniz approach was the 2002 revision of Goldstein (although problem 8-23 in Taylor (2005) is the Leibniz approach without saying it). The vast majority of the books there treated centrifugal force as a fictitious force in rotating frames of reference. The more modern the books got, the more they tried to laugh off centrifugal force. One recent book published in California in the last ten years (with a picture of the Golden Gate Bridge on the cover) actually went out of its way to counteract any arguments that might be put up in favour of centrifugal force, and they did it so boldly and with such confidence. Clearly, we are in an age in which centrifugal force is not popular. It is not politically correct. My own view is that this is because the implications of it in relation to absolute motion, such as the Bucket argument do not sit comfortably with modern relativity. In relativity, frames of reference have almost taken on a physical reality in their own right.


 * I suspect that the instant ganging up which I encountered two years ago when I first tried to insert the Leibniz approach was because the editors involved had never heard of the Leibniz approach before and they saw that it didn't sit nicely with the rotating frames approach in the case of non-co-rotating situations. I had clearly interrupted a group that had come to a consensus and they were very keen on promoting the rotating frames approach in the special case when it is extrapolated to its ludicrous conclusions. That of course is the notion that centrifugal force even acts on a stationary object when it is observed from a rotating frame of reference, and that the Coriolis force swings into the radial direction and overrides it to cause an apparent circular motion. In my opinion, that is total nonsense and it represents the inevitable conclusion of a nonsense theory. But the editors here liked that concept too much to have it threatened by something like Leibniz's theory on planetary orbits. Hence the edit war.


 * You say above that you don't fully understand the Leibniz approach. I think that you do. And I think that the more it sinks in, the more you will loose any desire to promote the rotating frames approach or to search around for references that try to subsume the Leibniz approach into the rotating frames approach. Such references are clearly written by men who fear the reality of centrifugal force that is implicit in the Leibniz approach. David Tombe (talk) 13:11, 10 May 2009 (UTC)

Bernoulli
FyzixFighter, regarding this line which you inserted in the main article,

In a 1746 memoir by Daniel Bernoulli, the "idea that the centrifugal force is fictitious emerges unmistakably."[5]

who exactly made that quote regarding centrifugal force being unmistakably fictitious? David Tombe (talk) 19:44, 9 May 2009 (UTC)


 * The author of the reliable source that is cited following that statement. --FyzixFighter (talk) 19:53, 9 May 2009 (UTC)

FyzixFighter, As I said above, that author wrote that in 1990. Bernoulli did not have any significant role to play in the development of the modern conception of rotating frames of reference. It was Coriolis. Your stuff on Bernoulli spoils the flow of the section. Bernoulli merely pointed out the interesting fact that centrifugal force depends on the point of origin. He didn't say anything about frames of reference. You cannot base an encyclopaedia on one opinion like that. David Tombe (talk) 20:01, 9 May 2009 (UTC)


 * It's called a WP:secondary source, which is what wikipedia is supposed to mainly rely on. Dicklyon (talk) 20:43, 9 May 2009 (UTC)

Dick, Yes I do have to accept that fact. It's a secondary source as preferred by wikipedia's rules. But I can't help thinking that more effort should be made to examine a wider range of sources to build a higher picture. It's a pity to let the opinion of one man in recent times spoil the flow of a historical evolution simply because he has had his opinion published in a journal or a book. In this case, the author makes his opinion that Bernoulli was alluding to frames of reference when it is clear that Bernoulli was alluding to the mysterious property of centrifugal force whereby it changes its value according to the chosen point of origin. It's not the same thing. That's why I would like everybody to explain more about their own personal interest in this topic, because if we all appreciate each others points of view more, then it will be easier to apply sources in a more balanced fashion. We would be able to question each other on the motive for introducing sources and we would have less responses of the kind such as 'I have no opinions, I am only reading from a source'. If they have no opinions, then why are they bothering at all? David Tombe (talk) 21:56, 9 May 2009 (UTC)

Compound Centrifugal Force
FyzixFighter, you got all that so badly wrong. Compound centrifugal force in Coriolis's paper is the Coriolis force. It takes on the mathematical form of centrifugal force but acts in any direction, and it's multiplied by 2. You tried this kind of thing out on the other page when you tried to tell us all that the centrifugal force in the radial equation was the centripetal force. You are continuing to distort the facts. I personally don't even agree with Coriolis's idea that it can act in any direction. I think that it can only act in the transverse direction. But I didn't write my opinion in. One thing is sure and that is that it is definitely not restricted to the radial direction as you have claimed. David Tombe (talk) 22:04, 9 May 2009 (UTC)


 * Thanks for the catch on that. I see that I misread the source. Just for everyone to see, here's the sentence I was looking at:
 * "The centrifugal force can therefore be decomposed into one radial centrifugal force, $$m\omega^2r$$, and another, $$-2m\omega v$$, the “Coriolis force.” It is worth noting that Coriolis called the two components “forces centrifuges composées” and was interested in “his” force only in combination with the radial centrifugal force to be able to compute the total centrifugal force."
 * I'll adjust my previous edit and reinsert it. I do feel that the reference I'm using is superior to the one you provided since it goes into details like his focus on the waterwheel that your source did not. Neither source contains some of the details from your edit, neither do they state that Coriolis is the source of the paradigm shift that resulted in today's classical understanding of the centrifugal force and rotating reference frames. --FyzixFighter (talk) 02:10, 10 May 2009 (UTC)

FyzixFighter, what you ideally need is to have an opinion on this topic. If you have an opinion, then we can discuss that opinion. If it's simply a case of stating that you don't have any opinions but that you only quote from reliable sources, then we're not going to be able to write a coherent article. Coherent articles don't arise out of a patchwork of contradictory quotes from modern textbooks that have been written in an age when centrifugal force is not politically correct. I don't want to play a silly game of textbook whist. As regards Coriolis, your alterations of my edit and your removal of my reliable source were totally pointless. But I don't really care too much because I don't actually agree with Coriolis's idea that the 'compound centrifugal force' is free to act in any direction according to the expression 2mv×ω. Coriolis's work was a highly relevant landmark in the development of the concept of rotating frames of reference and so I thought that I'd add in a bit about him and explain his position. It was sad to watch you change it to something that was quite wrong. And then when the error was pointed out, you still proceeded to alter my edit and clip it down in size and remove the source. If you want to play all those details about Coriolis's attitude down, then so be it. I got those ideas from a secondary reliable source and you have degenerated this into kicking out one set of sources and replacing them with another set, and under your own admission you don't even have any opinions on this topic.

I really suggest that you examine the Leibniz approach and consider the merits of it. When you have realized that it contains all that is needed to cover the entire topic of centrifugal force then maybe you'll lose your enthusiasm about trying to view the Leibniz approach as a subset of the modern rotating frames of reference approach. The two are not the same. The Leibniz approach can be extrapolated to the three body problem, but you'd have a hard job strapping a co-rotating frame around three bodies. And by the way, I'm the one that is introducing the three body problem, and I'm doing it to make the very point that I've just made. And furthermore, equation 3-11 in Goldstein gives a zero value for r double dot for circular motion when the centripetal force is equal and opposite to the centrifugal force. I don't care if we have to call r double dot 'Harry' and I'm not going to waste my time getting into anymore pointless arguments about whether or not r double dot rightfully bears the name 'radial acceleration'. In the rotating frames approach, a stationary particle as observed from a rotating frame, traces out a circle. In that case, according to the rotating frames approach, the centripetal force will be twice the centrifugal force in magnitude. So the two approaches are not compatible, and in my opinion, the rotating frames approach is a nonsense. David Tombe (talk) 17:39, 10 May 2009 (UTC)


 * I'd just like to say, that I completely agree!- (User) Wolfkeeper (Talk) 18:20, 10 May 2009 (UTC)


 * I completely agree that in your opinion the rotating frames approach is nonsense. That is why we cannot let your opinion affect the text of the wikipedia, because we are knee deep in reliable sources that do not agree with you. So, even if you're right, we don't care; because we don't have to. The wikipedia is about verifiability over truth.- (User) Wolfkeeper (Talk) 18:20, 10 May 2009 (UTC)


 * FWIW wrapping a rotating frame about 3 bodies is trivial to do with numerical integration. The fact that it may or may not have a closed form analytical solution (depending on the exact scenario being examined) doesn't change the physics, nor does it change the fact that you can get a predictive solution that will match reality that way. Sure, it will diverge eventually due to rounding errors, but in the real world orbits are chaotic, so are not predictable.- (User) Wolfkeeper (Talk) 18:20, 10 May 2009 (UTC)

Wolfkeeper, I was not inserting my opinion on that matter into the main article. So I'm not sure what point you are making. I related Coriolis's approach exactly as it was in the secondary source which I supplied. I do not agree with Coriolis's conclusion, but I didn't say that in the main article. FyzixFighter altered it to something that was wrong in every respect. He now acknowledges that error. He then proceeded to make a pointless re-wording and clipping down of my edit. David Tombe (talk) 18:47, 10 May 2009 (UTC)


 * David I trimmed the edit for two reasons. First, in my opinion in went into a more detail than was necessary and was relevant to the material. Second, I could not find support for many of those statements from the source you provided. This was the source you provided:
 * A Treatise on Infinitesimal Calculus
 * And these are the statements that I could not find support for:
 * Coriolis was interested in water wheels and he was trying to work out what forces were acting in rotating systems.
 * He divided these supplementary forces into two categories. The first category was that of the induced forces that oppose the applied forces that would be needed to drag an object in a rotating frame of reference.
 * Coriolis also considered a second category of supplemenatry forces based on the mathematical transformation equations.
 * He saw a term which looked like the expression for centrifugal force, except that it was multiplied by a factor of two.
 * Coriolis's concept of 'compound centrifugal force' was named in his honour many years later and is now known as the Coriolis force.
 * Now some of these I've been able to find in other references, such as #1 and #5. If you have references for the other statements, or can direct us to page number or sentences in the given source, that would be helpful. --FyzixFighter (talk) 22:35, 10 May 2009 (UTC)

FyzixFighter, I do alot of these edits from memory. Have a look at this reference here and you will see numbers 2,3,and 4 explained exactly as I have described. It's all in one single paragraph beginning at line 8 on page 377. David Tombe (talk) 01:18, 11 May 2009 (UTC)


 * So are you saying that you were wrong to accuse me of removing sourced material in this instance? --FyzixFighter (talk) 02:55, 11 May 2009 (UTC)

FyzixFighter, you removed sourced material. If you had had any genuine query about my synthesis, you should have asked me on the talk page and I would have dug up a better source, such as the one that I have now provided. But instead you just reverted without discussion. David Tombe (talk) 16:33, 11 May 2009 (UTC)

Reactive Centrifugal Force
Brews, I saw your edit about the Earth exerting a force of gravity on the Moon and the Moon exerting a reactive centrifugal force on the Earth. What happens in situations in which objects are falling radially without angular momentum? How can gravity be balanced by an equal and opposite centrifugal force?

For action-reaction, you have to consider gravity separately from centrifugal force. There will be an action-reaction pair with gravity across the Earth and Moon and there will also be an action-reaction pair for centrifugal force across the Earth and Moon. Centrifugal force and gravity will not in general be equal in magnitude.

The problem is that Newton was actually referring to an action-reaction pair in relation to centripetal force and centrifugal force acting on the same body in the planetary orbit. It doesn't make any sense, but he was only being twisted to spite Leibniz. Have a look at this interesting article, David Tombe (talk) 01:27, 11 May 2009 (UTC)


 * I'd suppose when two objects are falling toward each other radially that body A is pulled by the gravity of body B and therefore exerts a reaction force on body B. And vice versa. So the force acting upon B may viewed two ways: as the gravity of A acting upon B or as the reaction upon B due to its pull on A. Brews ohare (talk) 06:22, 11 May 2009 (UTC)

Brews, we need to be quite clear about this. As regards gravity in isolation, there is indeed an action-reaction pair across two bodies. And so also as regards centrifugal force across two bodies. But for the purposes of action-reaction pair, you do not criss-cross between the two types of force, because centrifugal force and centripetal force are not an action-reaction pair, even in the special case when the two are equal in magnitude as is the case in circular motion.

As regards the section on reactive centrifugal force, although I don't agree with the concept, it is not even written up correctly in the main article according to the sources. I have in front of me right now the 1961 edition of Nelkon & Parker 'Advanced level Physics'. This book is quite clear on the fact that the centripetal force and the centrifugal force are acting on the same object. (the section was completely purged by 1971). The fact that we are only looking at one body may not make any sense in light of the Newton's third law upon which the centrifugal force is here justified, but that is neverthelss what the books are saying. And as you can see from that other reference which I gave you, this very point was raised against Newton in relation to the dispute with Leibniz. Newton's approach does not make sense. But if you are going to report it, you should report it accurately. What you have done is altered that approach in order to try and make some sense out of it. You have tried to correct the dilemma regarding the third law by making the issue straddle over two bodies. Hence you have shifted the emphasis from the actual centrifugal force itself to the effect which that centrifugal force transmits to the other body. In other words, you are applying the action-reaction pair as per centrifugal force in isolation to a false concept of action-reaction across a reactive centrifugal force and a centripetal force. The reactive centrifugal force in a circular motion will of course be equal in magnitude to the centripetal force, but that is why I have always urged that we look at elliptical scenarios so that the true facts can emerge from behind the inequality.

Your biggest problem is that when you come across a dilemma in the literature, your tendency is to split it up into different topics. What you should really be doing is trying to work out which approach is correct. David Tombe (talk) 10:35, 11 May 2009 (UTC)


 * Hi David: Well, as you know, we don't agree on this, as I believe the topics really are different. Brews ohare (talk) 03:52, 12 May 2009 (UTC)

Centripetal force without a reaction force
It appears that FyzixFighter does not think Newton's third law applies to the Earth-Moon system. That is a shocker. Of course, transforming to a center of mass coordinate system eliminates the physical origin of the forces, replacing it with the origin of coordinates. The reaction force of the reduced mass then is exerted upon the origin, which is a bit of a fiction, but one could say that such a reaction force does occur - it's just not going to have any effect upon the origin because it is pinned. Brews ohare (talk) 06:13, 11 May 2009 (UTC)


 * Brews, Ironically I actually agree with FyzixFighter on this point. The situation regarding 'reactive centrifugal force' is a bit of a mess and I have tried to explain it to you in the section above. I don't think that FyzixFighter is denying Newton's third law. He is trying to make better sense out of a nonsense concept, and even right now his reversions of your edits did not completely cure the problem. Newton's third law holds for sure. It acts over two bodies. But centrifugal force is never a reaction to centripetal force no matter what it says in those older textbooks.


 * Reactive centrifugal force needs to be carefully written up accurately within its historical context and the dispute with Leibniz, and with regard to the fact that it has been dropped in recent years from the textbooks. The real centrifugal force which engineers feel in circular motion situations is the one an only centrifugal force which appears as an inverse cube law in equation 3-12 of Goldstein. It's the centrifugal force of Leibniz which you guys have now subtley relegated to the history section. David Tombe (talk) 10:42, 11 May 2009 (UTC)


 * Brews, you've misread FyzixFighter. He didn't say that there no reaction force, he merely pointed out that since the force on the Earth is toward the center of gravity, it's not a great example of the reactive force being "centrifugal".  If you make it clear that the forces toward the CM are equal and opposite, and that with respect to the Moon the reaction force on the Earth is "outward", you could use this example.  Dicklyon (talk) 14:48, 11 May 2009 (UTC)


 * (after ec with Dick) Brews, you misunderstand my reasoning. Newton's third law does apply to the Earth-Moon system. The Moon exerts a gravitational force equal and in the opposite direction as the gravitational force of the Earth on the Moon. However, in the sources that I've found, the reactive centrifugal force is always "centrifugal" with respect to the axis of rotation, ie the point about which an inertial observer will say the object or objects are rotating. With respect to this axis, both forces in the reaction-action pair are centripetal.
 * There was a request to use examples/models from reliable sources. If you can find a RS that uses that example and calls it something along the lines of a reactive centrifugal force, then there's little I can do to oppose it's inclusion. At best I try find another RS that supports the other POV. Does my explanation make sense, or is there still some misunderstanding between us? --FyzixFighter (talk) 14:58, 11 May 2009 (UTC)

The Comparison table
The bottom three rows in the comparison table need to be re-examined. The top two rows point out key differences in the two concepts with the important point covered that the so-called reactive centrifugal force is purely a circular motion concept, since the centripetal force is equal in magnititude to the centrifugal force.

The bottom two rows are rather pointless since we know that centrifugal force is always radial. The third row seems to be wrong. The third row contains somebody else's attempt to make sense of a wrong concept. An action-reaction pair does indeed act over two bodies, but Newton' reactive centrifugal force acts on the same body as the centripetal force. It may not make any sense, but that is the reality. I intend to remove the bottom three rows of that table. David Tombe (talk) 19:30, 11 May 2009 (UTC)


 * All the rows in the table make perfect sense and contribute to the comparison. I object strenuously to their deletion. Brews ohare (talk) 03:49, 12 May 2009 (UTC)

Brews, one of the rows is somebody's attempt to rationalize with Newton's third law of motion in connection with his concept of reactive centrifugal force. The reality is that the two are not compatible. We hence have nonsense on top of nonsense. It would be best to quietly drop that row. The other two rows that I mentioned are rather trivial and I can't see the importance of them. But if you want to leave them there, then so be it. David Tombe (talk) 11:18, 12 May 2009 (UTC)

The Introduction
Centrifugal force exists also in relation to straight line motion relative to any chosen point in space. It is not restricted to curved path motion. That's why it's better to use the term 'in connection with rotation' in the introduction because rotation extends to the transverse motion of a straight line path relative to a point origin. David Tombe (talk) 19:46, 11 May 2009 (UTC)


 * This viewpoint need considerable elaboration, as on the surface it appears to conflict with modern mechanics. Having read D. Tombe's more extensive writings on this topic, I do not expect any agreement to be reached. Brews ohare (talk) 03:51, 12 May 2009 (UTC)

Brews, centrifugal force has a different value according which arbitrary point in space we choose to measure it relative to. This is a somewhat mysterious characteristic of centrifugal force and it was pointed out by Dan Bernoulli. It is a characteristic of centrifugal force which is not shared by forces such as gravity, or electrostatics etc. This mysterious characteristic is what causes people to debate whether or not it is real. It can show up real when you try to interfere with it, yet when you leave it alone, it appears to blend in with Euclidean geometry and an object simply follows the inertial path.

But putting all that aside, the reality is that centrifugal force is an inverse cube law repulsive force relative to any chosen point in space. And it will exist, even if the object is moving in a straight line past that point. The radial vector connecting the object and the point will be accelerating and rotating. Hence we need to generalize the introduction to cater for rotation in general, and not just curved path motion. David Tombe (talk) 11:25, 12 May 2009 (UTC)

Reactive force section
This section no longer serves the purpose of introducing the topic, but is entirely an historical discussion that should go into the history section. There is no point reviewing all the missteps of history and evolving conceptions in this section. We need a clear, simple, modern statement of what it is. Brews ohare (talk) 03:47, 12 May 2009 (UTC)


 * Brews, this is only a summary article for the topic in general. The detailed treatments have been devolved to two separate articles. I am hoping that there are no plans to greatly expand any of the different approaches that are detailed in this summary article. I catered for your preferred approach to centrifugal force by stating that it is the approcah which is most commonly promoted in the literature nowadays. David Tombe (talk) 11:33, 12 May 2009 (UTC)


 * I think I'm going to have to agree with Brews here, and the changes he made today. It's the very essence of a summary article, that we succinctly state what "centrifugal force" is in the lead section, and then just as succinctly state each of its various applications in the appropriate sections below. As to the history of the concept of centrifugal force, that can (and probably should) have its own section too.  I think it's a good idea for this article that we keep the summary sections from getting too bogged down in historical analysis.  I just want to say thanks to everybody here, David, Brews, FyzixFighter, all of you, for your work on making this technical information more accessible to the general readers and providing good citations where needed.  It's good to see everybody working together as a group!  Wilhelm_meis (talk) 14:44, 12 May 2009 (UTC)

Wilhelm, OK, but that then brings us back to the very first introductory section. I am advocating that the reference to 'curved path motion' should be changed to 'rotation'. That will then give the widest general summary possible. Curved path motion only occurs in the special case when centripetal force also becomes involved on top of centrifugal force. In isolation, centrifugal force will arise in connection with a straight line 'fly-by' motion relative to any arbitrarily chosen point in space. This is the extreme case of the hyperbola in Leibniz's equation, when the centripetal force (gravity) is zero. The inducing factor is the rate of rotation (circulation) of the radial line that connects the object to that chosen point.

Hence, if we introduce an equal and opposite centripetal force relative to that chosen point, that will maintain the radial distance at a fixed value, and we will have circular motion. In a circular motion, we will have an equal and opposite centrifugal force and centripetal force. But they will not constitute an action-reaction pair. David Tombe (talk) 15:39, 12 May 2009 (UTC)
 * What's wrong with saying "rotation or curved path motion"? That would be the best reflection of the situation and would indicate to the reader that we are looking at CF applied to different circumstances. Wilhelm_meis (talk) 23:37, 12 May 2009 (UTC)

Wilhelm, the significance of the curved path relates to centripetal force and not to centrifugal force. A centripetal force causes a curved path. Centrifugal force on the other hand is a product of angular velocity of the radial vector relative to a point origin. The most general and accurate way for summarizing centrifugal force is "an outward radial force that arises in connection with rotation". David Tombe (talk) 00:09, 13 May 2009 (UTC)

Misunderstandings surrounding reactive centrifugal force
Brews, I want you to carefully consider this case scenario,

(1) Two planets in mutual orbit. The gravitational force of attraction is so negligible that the orbit is an infinitely eccentric hyperbola. In other words, the two planets have done a straight line fly-by of each other. According to Leibniz's equation, and equation 3-12 in Goldstein, and the equation at problem 8-23 in Taylor, this straight line motion will be the sole product of the inverse cube law centrifugal force.

(2) Now attach a string between the two planets. The outward centrifugal force will pull the string taut.

(3) When the string is taut, there will be a tension in the string.

(4) If the string does not snap, the tension in the string will then cause an inward centripetal force to act on the planets on top of the negligible gravity and the outward centrifugal force.

(5) The centripetal force, in conjunction with the centrifugal force, will now cause a circular motion.

Where do you see centrifugal force as being reactive in any way to centripetal force? There is no such thing as reactive centrifugal force. Newton's concept was wrong. But you have made it even more wrong by trying to apply it across two bodies in order to rationalize it with Newton's 3rd law of motion.

We both wish to report Newton's concept of reactive centrifugal force on the main article even if we don't agree with it. But it should at least be reported accurately. At the moment, it is not being reported accurately. Instead, we have a revisionist reporting of a nonsense concept. It might help if you were to read near the bottom of page 268 in this link David Tombe (talk) 16:09, 12 May 2009 (UTC)


 * One thing that has been on my mind, and I guess this is as good a time as any to mention it (though I don't mean to single anyone out), is that we may be venturing dangerously close to text book material in some aspects of our approach. We want to report the material appropriately and accurately, but we don't want to rewrite the material as if we were producing our own text book. Remember, WP is here to inform, not instruct. Wilhelm_meis (talk) 23:46, 12 May 2009 (UTC)

Wilhelm, The above excercise is not intended to go in the main article in that form. The point of that excercise was to demonstrate that centrifugal force is never reactive to centripetal force, and also to clearly explain what exactly centrifugal force is.

You were asking for examples to demonstrate centrifugal force. The above scenario would serve as the ultimate example that would involve all aspects of the topic. In the main article it would simply be described step by step. The key points are that a centrifugal force acts outwards between two bodies that are in mutual transverse motion (as per Leibniz's inverse cube law/equation 3-12 in Goldstein). If a string is connected between them, that centrifugal force will pull the string taut. The ensuing tension in the string will then give rise to an inward centripetal force which will pull the two bodies into a curved path, and more specifically into a circular motion.

Do you follow those points through from (1) to (5)? Do you need any clarification? David Tombe (talk) 00:22, 13 May 2009 (UTC)
 * David, I understand the scenario described above perfectly well, and again, I did not mean to single you out, but I have reserved this critique because just about anywhere I put it on this talk page, someone would think I meant them specifically. My comment above was intended as a general message to all the editors here.  My only question about the scenario above is, is it found in a reliable source, or is it a synthesis?  I do think real-world examples or simple hypothetical scenarios can do a lot to help the reader understand the material, but in creating our own scenarios we risk venturing into synthesis and textbook territory, so I think we should stick to those examples we can find in reliable sources and make sure we don't misapply them in any way.  If we tread lightly here, we can make a great article with strong verifiability, neutrality, and accessibility.  So please understand, I was not singling you out for criticism, just offering a general word of caution that everyone here would do well to heed. Wilhelm_meis (talk) 07:57, 13 May 2009 (UTC)

Wilhelm, the purpose of it was to try to explain to Brews exactly what centrifugal force is. I'm sure I could dig up an example for the main article, but we are not at that stage yet. So long as Brews continues to hold some misinformed views about the topic, there is no point in getting involved on the main page. We need to get a comprehension of the topic on the talk page first. As regards sources, I should remind you that there is only one equation which caters for all case scenarios in centrifugal force, and it is equation 3-12 in Goldstein, or the equation 8-23 in the Kepler's law problems in Taylor, which is in fact Leibniz's equation.

If we drop the centripetal force term from that equation, we will be left with a centrifugal force in isolation, and that will lead to a fly-by straight line motion (infinitely eccentric hyperbola). The centrifugal force is dependent on the rate of rotation of the radial vector. So if two bodies are moving past each other (with neglible gravity), they will go in a straight line. You hardly need a source to prove that. The line connecting the two bodies will be rotating and it will be changing in length as a function of time, according to the inverse cube law in Leibniz's equation. If we try to restrain the outward expansion we will need to apply an inward centripetal force, and that will lead to a curved path motion. In the special case of attaching an unbreakable string between the two bodies, it will lead to a circular motion. I'm glad that you can understand this simple case scenario, but unfortunately the two year edit war has been caused because of the fact that few others appear to have been able to understand it. David Tombe (talk) 10:32, 13 May 2009 (UTC)

The reverts by RRacecarr
Rracecarr, the passage which you deleted was quite clear about the fact that the 1961 Nelkon & Parker was referring to the Newtonian concept of centrifugal force in the sense that it is an action-reaction pair with centripetal force. I personally don't subscribe to that approach and abviously neither do the modern textbooks. But that's exactly why that was written into the history section. Why did you feel the need to delete this passaage, as it gave important information regarding modern changing attitudes to centrifugal force? Both the Newtonian approach and the Leibniz approach are clearly being phased out in favour of the rotating frames of reference approach, which is your preferred approach. But this is a history section and there is no need to delete history to try and create a make believe that the Newtonian and the Leibniz approaches never existed. David Tombe (talk) 15:50, 13 May 2009 (UTC)

Rotation v. curved path motion in the introduction
We need to make it clear that it is angular speed which is the determining factor in centrifugal force. That is the angular speed of the radial vector relative to any arbitrarily chosen point origin. It has got nothing to do with whether or not the path of motion is curved. Curvature of the path of motion is a feature of any inward centripetal force which may or may not be acting. David Tombe (talk) 23:52, 13 May 2009 (UTC)


 * David: It may be your wording is very unclear, but I don't think we agree. I believe we do agree that the centripetal force depends upon the path curvature.


 * I'd say that for any observer, the real force on the body has to provide the centripetal acceleration calculated by an inertial observer in order that the path be followed. For example, if the inertial observer sees uniform circular motion (a ball on a string, say), he requires v^2/R from the string. The co-rotating observer sees equilibrium, but to balance the ever-present centrifugal force, still needs to apply v^2/R from the string.


 * So I'd guess the point of disagreement is this: Because the required centripetal acceleration depends upon the path curvature, so must the centrifugal force.


 * That means centrifugal force has a lot to do with the path curvature.


 * Here's another example. The inertial observer sees a plane do a steep dip. At the bottom of the dip he determines a centripetal force of v^2/ρ is needed to turn the plane around. (ρ is the instantaneous curvature.) That force is provided by the lift on the plane. To the pilot the plane is stationary. He needs to maintain equilibrium at the bottom of the dive. However, he feels a downward centrifugal force of v^2/ρ at the bottom of the dive, and must provide a lift of v^2/ρ to maintain equilibrium just as predicted by the inertial observer. (I neglected gravity.)


 * Other examples are in the other centrifugal force article.Brews ohare (talk) 01:19, 14 May 2009 (UTC)

In this case David has it more correct. For the centripetal force (and corresponding reactive centrigual force), path curvature is what matters. But in the case of the other centrifugal force (of course David would never call it fictitious), it's just the angular speed (frame rotation rate) and distance that matter, independent of path curvature. Even a particle moving in a straight line in an inertial frame has a centrifugal force in the co-rotating, or any rotating, frame. But I'm having a nice wikibreak, so don't know why I looked at this... Dicklyon (talk) 03:27, 14 May 2009 (UTC)


 * Dick, it's good that we agree on this aspect in isolation, even if we can't agree on the need to deem the centrifugal force to be fictitious. David Tombe (talk) 10:43, 14 May 2009 (UTC)


 * It's not a "need to deem"; it's just what it's called; a defined technical term. Our job is as reporters.  Dicklyon (talk) 15:42, 14 May 2009 (UTC)


 * A bit of a semantic debate, inasmuch as the "center of rotation" might be inferred to be the instantaneous center of rotation. Of course, any such "center of rotation" implies a curved path, with the straight line being the degenerate case of infinite radius of curvature. Brews ohare (talk) 05:50, 14 May 2009 (UTC)


 * If the degenerate case of zero curvature still have nonzero centrifugal force, then you can't say the centrifugal force is due to the path curvature; what it's due to is the rotating frame of reference; the "center of rotation" is a propert of the reference frame, not of the path, as you've pointed out in your comparison table. Semantics is important. Dicklyon (talk) 15:42, 14 May 2009 (UTC)


 * I am a victim of adopting the local frame of reference, the one attached to the object, in which the centrifugal force is the only fictitious force and always matches the centripetal force. Brews ohare (talk) 17:23, 14 May 2009 (UTC)


 * So in the planetary orbit case, you'd take the center of the osculating circle, instead of the center of the system, as the point to rotate about? Then the centripetal force would be something other than the gravitational force?  Seems highly impractical, if possible at all. Dicklyon (talk) 04:19, 17 May 2009 (UTC)


 * I was confessing to a mistaken viewpoint, nothing else. Brews ohare (talk) 14:48, 17 May 2009 (UTC)

Brews, think of it this way. Take any arbitrary point in space. Then apply Goldstein's equation 3-12 (or 3-11). Take out the centripetal force. You will be left with only the centrifugal force term. The solution to the second order differential equation will therefore be a hyperbola with infinite eccentricity. That means a straight line fly-by motion. The centrifugal force can be observed as the second time derivative of the magnitude of the rotating radial vector which connects the fly-by object with the arbitrarily chosen point origin.

If we then introduce a centripetal force, the path will become curved. The greater the centripetal force, the greater the curvature. When the centripetal force becomes equal in magnititude to the centrifugal force, we will have a circular motion.

This should help you to understand every case scenario in this topic. Always just apply the Leibniz equation, which is Taylor's problem 8-23 equation and Goldstein's 3-11/3-12 equation. David Tombe (talk) 10:43, 14 May 2009 (UTC)

Brews's recent edits and centrifugal potential energy
Brews, I looked at your substantial edits to the absolute rotation section. I am quite happy with the way that you condensed the rotating bucket argument. That section needed condensed and it is now good.

I did notice however that opinions were inserted. I will not be reverting however because I think that you have presented it in a way that will make people think about the issue. Having said that, it would not have been exactly the way that I would have worded the conclusions. Newton concluded, as I do in this situation that rotation is absolute. The experiment clearly points to the fact that there is one frame of reference in particular, marked out by the background stars, in which rotation is absolute and in which rotation generates centrifugal force. Your alternative opinion is rather strange. It's like as if you are trying to mask out that reality by playing with words.

Anyway, have you thought about putting in a short note about how transverse kinetic energy can act as a potential energy function for centrifugal force? 1/2mv^2 equals 1/2mr^2ω^2 for transverse kinetic energy. Differentiate that with respect to r and you get centrifugal force. David Tombe (talk) 10:55, 14 May 2009 (UTC)

Removing sentence
I removed the sentence "This article summarizes the several ideas surrounding the concept of centrifugal force." because you're not supposed to be talking about a wikipedia article like "this page" or something... Right? —Preceding unsigned comment added by 84.202.236.123 (talk) 13:30, 16 May 2009 (UTC)


 * I don't know of any guideline of that sort. Dicklyon (talk) 01:35, 17 May 2009 (UTC)

I do think the lead section of this article needs some attention in general. I would encourage everyone here to consult WP:LEAD and WP:BETTER and contribute accordingly. Writing a good lead section can be one of the best ways to improve an article, because when a reader encounters a great article with a poorly written lead section, they may not even proceed to the article's better content. Wilhelm_meis (talk) 04:11, 17 May 2009 (UTC)

Centrifugal force and absolute rotation
Why is this section with four sub-sections in this article? It's interesting, but rather a sideline on the topic. How about splitting it out to its own article, and leaving a summary, as this is a summary-style article? Dicklyon (talk) 01:43, 17 May 2009 (UTC)


 * That raises the same issues as arise over the introduction: what are the objectives of this article? The introduction is a great place to spell them out.
 * David introduced the absolute rotation topic; I reorganized it and added two figures. I do believe it is illuminating as to one role of centrifugal force and connects to the idea of fictitious force. It is an introduction to the topic, which is gone into in much more detail in other articles. Maybe one purpose of this article is to provide a guide to the many topics found in more detail elsewhere? Brews ohare (talk) 07:18, 17 May 2009 (UTC)

Dick, The 'absolute rotation' controversy is one of the most interesting aspects of the subject. Once again it split Newton and Leibniz, and on this particular issue I side with Newton. Leibniz believed in relative motion, which in my opinion seems to actually contradict his planetary orbital equation. My overall assessment of the situation is that Newton was working along the right tracks in his early days but that Leibniz beat him to the planetary orbital equation. Newton had only managed to get as far as the inward inverse square law part of the equation for gravity. But Leibniz beat him to the outward inverse cube law for centrifugal force. Newton was highly jealous of Leibniz's equation and so he corrupted the topic by introducing his 3rd law of motion into it.

I am overall happy enough with this section as it stands because the issue has been raised and it is written in a way that clearly exposes the controversy. Brews does go a wee bit over the top in his attempts to undermine Newton's opinion, but I don't consider that to be a major problem.

As regards Leibniz, there are suggestions that Boscovich took the best of Newton and Leibniz, and that a blended form of the two outlooks prevailed until the early 20th century. When relativity came along, Leibniz and Newton were deliberatley split in the literature so as to contrast Newtonian mechanics against special relativity. Leibniz was then phased out, but in later years it has been speculated that Einstein's work on the unified field theory was closely related to Leibniz. Hence you will find that people who are interested in Einstein's general theory of relativity will be very keen to promote the concept of centrifugal force in curvilinear coordinates relative to the inertal frame of reference.

In my days, planetary orbital theory was done with an emphasis on the fact that Newton derived the inverse square law force of gravity. The inverse cube law centrifugal force was then usually wheeled in quietly through the back door and joined up. The method used was polar coordinates relative to the inertial frame with the centrifugal force quietly sitting alongside the second time derivative of the radial distance, and the two of them collectively referred to as radial acceleration. The name centrifugal force was very much played down, but not absolutely played down. David Tombe (talk) 10:56, 17 May 2009 (UTC)

Putting the edit war behind us
I think this article is on the right track, but what will ultimately drive consensus and produce a good article is if everyone plays by the rules, specifically: 1. Report but do not promote (or refute) a particular point of view expressed in the sources (WP:NPOV and WP:SOAP); 2. Explain what is known about CF without instructing the reader (WP:NOTTEXTBOOK); 3. Always assume good faith in others' edits and assume the other editors are intelligent, well-intended people with a valid misunderstanding (WP:AGF and WP:CIVIL); 4. Always take discussion to the talk page BEFORE reverting an edit (unless it has already been thoroughly discussed - then be sure to indicate that discussion in your edit summary); 5. Stick close to the sources and avoid synthesis (WP:Verifiability, WP:RS, WP:SYNTHESIS); 6. Provide ample in-line citations for maximum clarity and verifiability (WP:Verifiability, WP:CITE); 7. Always be sure to identify the common ground where you do agree with the editor(s) with whom you find yourself in disagreement, and spread a little wikilove to those who have done something innovative or commendable, even if you often disagree with the same editor ("Love thy enemies...", what better way to bring someone out of their shell?). If you have held a long-standing disagreement with an editor about one thing, and they do something else which you agree with, leave them a pleasant note about it on their talk page. It will mean a lot to them and can help deescalate the disagreement. The whole thing boils down to this: show me an edit war and I will show you a group of editors that are ignoring the rules to pursue their own agendas. So when these things flare up, just keep cool and be specific and factual in your counterarguments, and cut a wide berth around any sort of personal attacks. We are all just editors, and our egos [should be] meaningless; our very raison d'etre is to produce a better article for the reader, and everything we do should serve that purpose. If we maintain this frame of reference, there is never any need to make personal attacks, nor to take any criticism personally. When personal attacks are made, they say much more about the attacker than the target. One might think a group of physicists would be particularly well-suited to the sort of objectivity and emotional detachment from the material that is required to produce a good article and avoid edit warring. In the end, of course, we are all people, and all our work is subject to all the flaws and vulnerabilities that go along with that. I'll keep this article on my watchlist and try to help out with it from time to time, but I think we have the basis of a good article here already (in what must be some kind of record time). Thank you all for helping to put the edit war behind us. It took all of you to make this progress, so my thanks go out to each and every one. Wilhelm_meis (talk) 04:01, 17 May 2009 (UTC)


 * Wilhelm, thanks for your intervention. It took the intervention of a neutral arbitrator to break the deadlock. I think that it would now be beneficial to actually try and analyze the cause of the edit war. Had it simply been an open clash of differing opinions on the topic, with everybody openly admitting their prejudices, then I'm sure a compromise could have been found a long time ago. But unfortunately that was not the nature of the edit war. The edit war began because a certain group did not want to believe that there could possibly exist other opinions on the topic beyond that which had formed a part of their education.


 * Unfortunately, at the beginning, I wasn't very persuasive and I didn't have any sources immediately at hand. But by the time I started to introduce sources, the opposition were so dug in and re-inforced that it simply became a childish game of sniping from behind screens. It all came down to the issue of superior numbers.


 * While Dick doesn't appear to favour my point of view, at least he was honest enough to present to me with the historical origins of my point of view, which I had previously been unaware of. We have all learned alot from this edit war. I hope that the last stage is done more maturely and in such a way that we can all learn more about the topic in the process. I think that we should all openly declare our prejudices on the topic. My future contributions will now be to highlight the historical sources of the differing and changing attitudes to the topic. David Tombe (talk) 11:14, 17 May 2009 (UTC)
 * No one gets to point fingers here. As they say, it takes two to tango.  If the minority opinion had been squashed altogether, there would not have been much of an edit war.  Of course that doesn't mean it would be a better article - it would have NPOV problems and lacunae in its coverage of the topic, but not much of an edit war.  If you really want to get to the cause of the edit war, it wasn't that people were dishonest about their opinions or that anyone was obfuscating their motives; it's that people were too emotionally invested in the material.  They weren't just reporting what was said by whom in what source, they were defending their own views.  This was an edit war on par with those in the histories of articles on abortion and evolution, because people were approaching it in the same way.  It all comes down to this: dispassionate objectivity is the key to maintaining neutrality, and without it edit wars are inevitable.  We cannot write our own dearly held views into the articles we edit.  Remember, this is an encyclopedia, not a textbook.  You don't get to write whatever you want here.  We report on what is written in the most reliable sources available.  That's what an encyclopedia is.  And that's where these articles fell short for so long.  People forgot they were editing an encyclopedia and thought they were writing a textbook.  People were defending their own views, rather than reporting the views of the experts.  No one here is an expert, we are just editors, and we would all do well to remember that.  That is what caused this edit war, and it is the very same thing that has caused a good many other edit wars elsewhere on WP.  Everyone involved in any edit war shares in it, not just the person making "tendentious" edits, and not just the people "trying to squash" the minority opinion.  We're all in the same mud here, and if we're to get out of it, it will be together.  Wilhelm_meis (talk) 02:29, 18 May 2009 (UTC)


 * The problem is that David spent a year arguing without sources, except for one where his interpretion was pretty much contradicted in the source, and aliening everyone who tried to reason with him. But since I found him some sources, we're making progress. Dicklyon (talk) 04:32, 18 May 2009 (UTC)

Dick, I appreciate your honesty in bringing forth sources that have backed up my opinion. It makes it easier for me to reciprocate the gesture by acknowledging that the opposition viewpoint dominates the modern textbooks. On that basis, we can move forward. We can put the opposition viewpoint first place in the article and state that it is the most common approach nowadays. But we will also now have room to describe the Leibniz approach further down and mention the muted manner in which it is dealt with by Goldstein, along with some modern efforts to treat the planetary orbital problem within the context of rotating frames of reference. But we cannot suppress the fact that 29 years ago, I did planetary orbital theory without involving rotating frames of reference, and that I saw many different approaches to planetary orbital theory which didn't use rotating frames of reference. And those texbooks are still floating about in the stacks somewhere.

On that point I call into question the line in the introduction (The Roche reference) which talks about two distinct but equally valid approaches to centrifugal force. I don't know what he has in mind for those two approaches. But if he is talking about the rotating frames approach and the Newtonian approach then that sentence needs to be removed, because it effectively denies the existence of a third approach. This is were the issue of references can become tricky unless discrepancies can be brushed over in a mature fashion. If we have references that show that there are three approaches, and then we have a reference which states the opinion of a man that there are only two approaches, we cannot allow that latter reference to dominate the article. We need to talk broadly about the several approaches. That is why I inserted the line about 'several approaches'. An anonymous from Norway removed my line. Despite a large number of edits by Brews, this anonymous honed in and deleted my edit in particular. I'm very glad that you stepped in and reverted it. But we now need to remove the clause which narrows it down to 'two approaches'. The truth is that there are at least three approaches to this topic. Besides, it is quite ridiculous to state that there are two approaches that are different but both equally valid. If the two approaches are different, then they cannot both be equally valid. One of them must be wrong, and so we shouldn't be making statements such as to paper over cracks, even if it is the quote from some man who wrote a textbook in 1991. Do you agree with me that the Roche reference should be taken out as a beginning for a slightly expanded introduction? David Tombe (talk) 12:40, 18 May 2009 (UTC)


 * David, the two approaches can indeed be equally valid; they are just different definitions of what centrifugal force is. The Liebniz approach is problematic, as a third approach, as it doesn't connect to F=ma as we know it.  I still think you are mistaken to say that Goldstein used that approach, or that you did planetary orbits without rotating frames of reference.  If you work out the accelerations in polar coordinates, under the force of gravity, th term you care about appears on the acceleration side as a centripetal acceleration.  Only by taking r-double-dot as an acceleration can you interpret that term as a centrifugal force.  The only frame in which r-double-dot is a acceleration is the one that co-rotates with the planet.  So by doing the algebra, without knowing it, you moved to a co-rotating frame.  This is consistent with one of the two definitions of centrifugal force (not the reaction force, but the fictitious force, where fictitious means it's zero in a special non-rotating frame).  So, while you have a different "approach", it's the same definitioin and results, and a special application of, the usual dominant method.  I agree that Liebniz and Graneau don't conceptualize it this way; Liebniz because he didn't understand F = ma yet, and Graneaux because he has an axe to grind, like you.  So you need to find a way to report this stuff without saying there's a third way, I think; the history of conceptions section is the place. Dicklyon (talk) 14:41, 18 May 2009 (UTC)

Dick, the facts are that there are three approaches, and that only one of them can be correct. The planetary orbital equation is a central force equation. All forces in that equation are radial forces. There is an inward inverse square law force of gravity and an outward inverse cube law centrifugal force. The equation can be found at 3-12 in Goldstein without any mention of rotating frames of reference. The Leibniz equation, which is the same as equation 3-12 in Goldstein covers for every possible scenario which you could possibly encounter involving centrifugal force. The Newtonian approach is wrong because it restricts centrifugal force to being equal and opposite to centripetal force, and the rotating frames approach involves an unnecessary encumbrance which becomes completely wrong when it allows the Coriolis force to swing into the radial direction.

Let's sort that latter business out once and for all. Equation 3-12 tells us that in the special case of circular motion, the centrifugal force must be equal and opposite to the centripetal force. In the rotating frames scenario in which a stationary object is observed to trace out a circle as when observed from a rotating frame, I would say that there is no centrifugal force acting at all. You say that there is, but that it it counteracted by a centripetal force that is twice as large and which is supplied from the Coriolis force. Well if the centripetal force is twice as large as the centrifugal force, then we cannot have a circular motion under the terms of equation 3-12. David Tombe (talk) 15:25, 18 May 2009 (UTC)


 * In general the centrifugal and centripetal are not equal and opposite in Newtonian mechanics, that's only true for circular orbits. Newton thought that they must be equal for a while, but that's all; at the end of the the day he knew perfectly well that that doesn't hold for elliptical orbits.- (User) Wolfkeeper (Talk) 14:24, 19 May 2009 (UTC)

Wolfkeeper, You are misrepresenting what I said. I said that centripetal force and centrifugal force are not in general equal and opposite. They are only equal and opposite in the special case of circular motion. Hence in the scenario where you guys try to justify centrifugal force on non-rotating objects by using an oppositely acting Coriolis force to act as the centripetal force, you have got it all wrong, because you are claiming to have an apparent circular motion in which the centripetal force is twice as large as the centrifugal force. David Tombe (talk) 11:43, 20 May 2009 (UTC)


 * If I may butt in for a minute, as I recall the "two approaches" referred to 1) Physics and 2) Engineering, but then someone objected to the Physics v. Engineering dichotomy (see above discussion). I don't think the original edit was in reference to Newton v. Rotating Frames at all.  Wilhelm_meis (talk) 02:23, 21 May 2009 (UTC)


 * I objected, since I know the fictitious force approach is widely used in engineering, e.g. in robotics, where the joint torques needed depend on whether the member carrying the joint is rotating due to a previous joint; if some author draws this dichotomy, it's OK to attribute that idea, but it's by no means universally viewed that way. Dicklyon (talk) 03:22, 21 May 2009 (UTC)

The bottom line is that it's wrong to make an unequivocal statement in the introduction to the extent that there are specifically two approaches to centrifugal force when in fact the literature points to at least three approaches. The problem would be solved by removing that sentence altogther as it is not necessary. It is only misleading. David Tombe (talk) 09:45, 21 May 2009 (UTC)

Tombe revisions
Hi David:

I disagree with almost all your recent changes on this page.

One issue is the prominence given to what you call Leibniz position, which prominence is not justified based upon the present day view of matters, as you have frequently complained. The present article as you have re-written it does not adequately warn the reader.

Your view of centrifugal force also is very tightly tied to the problem of planetary motion, which is only one very specific problem, and one tightly admixed with gravitational attraction. That specific example is not a paradigm for all of centrifugal force.

I vote to revert all your recent edits. As proposed by someone earlier, these Leibniz opinions should be in the history section. The table should be restored to its original form, with all the rows and no Leibniz column. Brews ohare (talk) 12:24, 19 May 2009 (UTC)


 * Brews, I didn't give any prominence to the Leibniz position. I added it as an alternative position alongside the other two positions. You on the other hand appear to want to consign it to history even though it appears in Goldstein's 'Classical mechanics'. David Tombe (talk) 12:23, 20 May 2009 (UTC)


 * I've reverted the massive undue weight. Leibniz was never able to come up with a consistent theory; he thought the planets were pushed around by a solar vortex around the Sun, but if that was so, the radial motion you need for elliptical orbits would have damped right out; ultimately his theory doesn't work.- (User) Wolfkeeper (Talk) 14:27, 19 May 2009 (UTC)


 * Wolfkeeper, I certainly don't support a solar vortex concept. I oppose Descartes on the grounds that one large vortex would consign all orbits to the same direction. But that doesn't really matter too much here. The point is that Leibniz produced the radial planetary orbital equation as it still stands in modern textbooks. It doesn't matter what Leibniz thought the physical explanation is. David Tombe (talk) 12:27, 20 May 2009 (UTC)

Here's the strange table per David, so we can discuss it here (my line breaks added): Dicklyon (talk) 00:16, 20 May 2009 (UTC)

The table below compares various facets of the concepts of centrifugal force.

So, David, I have to ask for some clarification of your thinking. If the Leibniz method works in "any" reference frame, what is meant by the "rotation axis"? And where it says "induced by absolute rotation", rotation of what? Didn't you already agree that it depends on the viewpoint? Isn't it rotation about a chosen viewpoint, giving rise to an acceleration in the r dimension that you're talking about? And does it, or does it not, give rise to a force that can be used in Newton's laws of motion? Dicklyon (talk) 00:19, 20 May 2009 (UTC)


 * Also, no basis laid in this article to understand the items in the table: for example, where did the inverse cube of radius come from? Answer: another article.
 * Also, this table uses Isaac Newton as a column heading as though Newton is associated only with the reactive form of centrifugal force, and doesn't explain that.
 * However, the main point is that we don't need to introduce Leibniz outside of the historical section.Brews ohare (talk) 01:47, 20 May 2009 (UTC)


 * Plus it's a gross mischaracterization. The Liebniz method, as far as we know, is only for the case of a radial aligned with the gravity vector; that is, it's not "any" frame, but only the frame centered at a center of a one-body problem and co-rotating with that body; at least, that's all that I've seen attributed to Leibniz, and is what Goldstein did.  Dicklyon (talk) 02:25, 20 May 2009 (UTC)

Yes Dick, I realized that mistake later. That bit alone could have been changed. There was no need to delete all my edits because of it. The Leibniz equation is identical to equation 3-12 in Goldstein. The frame of reference involved is the inertial frame of reference. The angular velocity is measured relative to the inertial frame of reference. It is not a historical issue. This is a question of an inability of you guys to accomodate a perfectly legitimate approach to centrifugal force. Brews seems to think that the planetary orbital approach is only one facet of centrifugal force. It is in fact the most general approach which covers every case scenario. I am afraid that we are dealing with a situation here in which the article is being controlled by a group who do not fully comprehend this topic. Wolfkeeper was completely wrong in his assessment of the situation. The outward inverse cube law centrifugal force acts in tandem with the inward inverse square law force of gravity. The two power laws lead to stable equilibrium nodes and orbits which are hyperbolic, parabolic, or elliptical. That was Leibniz's approach and it is the approach which I learned at university and which appears in modern textbooks. You are insisting on restricting this article to the most common modern approach and placing it alongside a redundant Newtonian approach. You are falsifying the situation by promoting your own preferred point of view in conjunction with an acceptable face of opposition, and deliberately suppressing the third way.

And one final point. You were very quick to spot that error. That proves that deep down, you fully understand the issue. Why are you so keen to consign the radial planetary orbital equation, relative to the inertial frame, to the history books?David Tombe (talk) 11:36, 20 May 2009 (UTC)


 * That set of errors was not the reason for reverting your strange table. If you can provide a meaningful improvement to the table we have, or somehow manage to make a coherent interpretation of Liebniz's POV on CF (based on sources, that is), that might be interesting; but present it here first, instead of messing up the article with it.  As far as any of us can tell, the Liebniz approach is still just a special case of the rotating frame approach, for the frame centered at the center of the one-body problem and co-rotating with that body.  Check for example the Meli 1990 paper (ask me if you need a copy) where it says the Leibniz approach was "close" to Daniel Bernoulli's views; but the situation back then was very complicated, and essentially impossible to coherently relate to modern physics except via the concept of pseudo forces. Dicklyon (talk) 05:16, 21 May 2009 (UTC)

Dick, 'That set of errors'? There was one error. I should have written 'inertial frame' where I wrote 'any frame'. As regards a coherent interpretation of Leibniz's equation/equation 3-12 in Goldstein/problem 8-23 in Taylor, a coherent interpretation should not be difficult. The problem here is that you don't want it on the page at all, so you will argue that any attempt to describe it without involving rotating frames of reference is incoherent.

Leibniz's equation does not need to be interpreted in terms of rotating frames of reference. The fact that you can produce a few references that attempt to do so does not mean that it has to be done so. Goldstein does not use rotating frames of reference.

Your tactic here is to consign the Leibniz equation to the history section because it conflicts with the rotating frames approach. And you are using the specious argument that it is one and the same approach and hence doesn't need to be mentioned. All three approaches share a common element. The Leibniz approach shares a common element with the rotating frames approach and the Newtonian approach but that doesn't mean that it is the same approach. You are deliberately trying to suppress an approach which you don't like because it was not the approach that you were first taught.

I thought that you were interested in compromise here, but now it seems not. You are trying to falsify the picture by emphasizing that there are only two approaches to the topic. David Tombe (talk) 09:56, 21 May 2009 (UTC)


 * The errors are in not noting that it's only in a co-rotating frame, and not saying what's meant by "rotation axis", etc. Generally, it's not a good characterization.  In an inertial frame, the accelerations are completely described by the real forces, with no need for the centrifugal force term, so it's not clear why you would claim inertial frame there.  There are only two modern and consistent approaches that I'm aware of.  The historical approaches were complex and inconsistent, as the cited refs make clear.  From a modern perspective, the Leibniz approach is just the rotating frames approach, as Taylor's derivation, and Goldstein's, make clear.  And it's not necessary to impute negative motives to my edits; I've been doing all I can to settle the edit wars around the polarized fights that you and the others carried on for over a year before I came here; I found you sources that you can use to correctly position the approach historically and technically; I can't help it if you can't get over your hangups. Dicklyon (talk) 17:23, 21 May 2009 (UTC)

Dick, Goldstein does not use rotating frames of reference for the planetary orbital equation at 3-12. You keep saying that he does. But he doesn't, and so you are deliberately trying to distort the facts. I never used rotating frames of reference when I did orbital mechanics. It doesn't matter that you happen to have found a few references involving attempts to strap a co-rotating frame around the Kepler problem. If the Kepler problem can be dealt with without using rotating frames of reference, then we do not need to use rotating frames of reference. Goldstein deals with equation 3-12 using plane polar coordinates with all displacements measured relative to the inertial frame. Absolute rotation induces an absolute outward expansion pressure. That is what centrifugal force is all about, and that is what you are trying to hide.

You have to ask yourself why you are trying to block such a simple exposure of the concept from appearing in the article. It is not original research and there is no problem as regards reliable sources. But you are determined to either subsume it into the fictitious rotating frames of reference approach, which it doesn't match in every respect, or to consign it to the history section.David Tombe (talk) 18:48, 21 May 2009 (UTC)


 * Goldstein's section "equivalent one-dimensional system" is where he converts the centripetal acceleration term in eq 3-12 to a centrifugal force term in 3-22, corresponding to a rotating 1D system along the radial. Any system in which r-double-dot is an acceleration is necessarily rotating.  I don't understand what you're saying about eq. 3-12; absolute rotation of what?  It's just F = ma in polar coordinates in an inertial frame; do you see centrifugal force in 3-12?  The only term on the force side is f(r), which represents gravity.  The acceleration side has a centripetal acceleration term. Goldstein's approach is standard; Liebniz's is historical; feel free to describe them both, correctly, based on what sources say about them.  Dicklyon (talk) 23:06, 21 May 2009 (UTC)

Dick, you are hopelessly confused. There is no need to mention the equation for the 1-D problem. We are talking here about the 2-D problem at equation 3-12 in which the outward radial inverse cube law term is the centrifugal force. It's the same as Leibniz's equation. Centrifugal force is an outward inverse cube law force, providing that angular momentum is conserved. It's as simple as that. By not seeing this simplicity, and by blocking it from the article, you are not helping the readers. David Tombe (talk) 11:43, 22 May 2009 (UTC)


 * So the question comes down to what the literature calls the second term in equation 3-12? Well, Goldstein calls it the "centripetal acceleration term" on page 25 (or page 27 in the 3rd edition), which makes sense since the inverse cube term in 3-12 looks like a radially inward contribution to the acceleration side of the equation. He only calls it the centrifugal force after moving it over to the force side of the equation and after introducing the 1D problem. He also refers to it as the "reversed effective force" of the centripetal acceleration. --FyzixFighter (talk) 14:50, 22 May 2009 (UTC)

FyzixFighter, you are hopelessly confused. The inverse cube law term in equation 3-12 can be nothing other than the centrifugal force. Let's not play silly games with the endless confusion in the literature. David Tombe (talk) 18:53, 22 May 2009 (UTC)


 * From Goldstein, Ch 1 (pg 27 in the 3rd edition) using the same Lagrangian formalism he uses in chapter 3 to get equations 3-11 and 3-12:
 * The derivatives occurring in the r equation are
 * {|style="width:75%"


 * $$\frac{\partial T}{\partial r}=mr\dot\theta^2$$,
 * $$\frac{\partial T}{\partial \dot r}=m\dot r$$,
 * $$\frac{d}{dt}\left(\frac{\partial T}{\partial \dot r}\right)=m\ddot r$$
 * }
 * and the equation itself is
 * $$m\ddot r-mr\dot\theta^2=F_r$$,
 * the second term being the centripetal acceleration term.
 * So if I'm confused, so is Goldstein. --FyzixFighter (talk) 21:17, 22 May 2009 (UTC)

FyzixFighter, go on ahead and ruin the article with your twisted use of confused references. The administrators are on your side. Goldstein was clearly wrong on this point. A force can never change its direction simply by being placed on the other side of an equation. That term is the centrifugal force. It couldn't possibly be the centripetal force. The centripetal force only takes on that mathematical form in the special case of circular motion. Centrifugal force will of course get a negative sign if we bring it across to the left hand side of the equation, but that doesn't make it into a centripetal force. And I know that you must know that fine well. You are thriving on the confusion which you can stir up by sifting through the literature to fish out the endless inconsistencies and errors which exist. I on the other hand was trying to bring a coherent order to the mess for the benefit of the readers. But the administrators want to do it your way.

Goldstein uses the term 'centrifugal force' for the inverse cube law term in 3-12, and that is all that is important. And it shouldn't even have to come down to what Goldstein says, because we all know that it has to be the centrifugal force. It is the exact same planetry orbital equation that Leibniz produced. And furthermore, you didn't revert that edit a few days ago for the good of the reader. You reverted it because it drew attention to the fact that all is not straightforward in the literature as regards centrifugal force. You are playing a silly game here in which the literature is gospel, despite the inconsistencies and errors which you are clearly aware of, and you are doing this deliberately to undermine my attempts to bring order and understanding to the subject. I'm very sorry that the administrators are totally incapable of seeing right through you. David Tombe (talk) 10:15, 23 May 2009 (UTC)

Technical
I'm going ahead and tagging this article as because I feel that it is especially important that this summary-style article remain accessible to the general reader. Those who want a highly technical in-depth analysis will go on to the branch articles. Specifically, I feel that the "Centrifugal force in planetary orbits" section needs some work to make it more readable. Please don't "dumb it down"; and I fully understand that this is not Simple WP; but it should be easily understood by the general public (think of an average high school student) with no technical background in Physics. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)

In further note, regarding my recent edit, I think I should state for the record that I am not a physicist. I am a linguist and a wikipedian. If I've made mush of any of the finer points of any of the highly technical material presented here in the process of my editing, feel free to correct me, but please do so in a way that avoids getting overly technical and encourages others to maintain civility. Thank you. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)


 * Looking to this edit by FyzixFighter, I think the passages referring to Bernoulli and Lagrange need a little more clarification. Thank you for the contribution, but please remember that these articles, particularly this one, need to be easily understood by the general reader. Wilhelm_meis (talk) 02:08, 9 May 2009 (UTC)


 * I'll see what I can do. It's the Meli article that refers specifically to Bernoulli and Lagrange. It mentions a few others, but article goes into quite a bit of detail on Bernoulli's contribution arguing that it is in his works where "the idea that the centrifugal force is fictitious emerges unmistakably." I'll see about distill it down to a non-technical but accurate summary, but another set of eyes that has access to the article would be appreciated. In the case of Lagrange, Meli doesn't go into great detail; he just says that Lagrange's work was the main text on mechanics in the second half of the 18th century and that Lagrange explicitly stated that the centrifugal force was dependent on the rotation of a system of perpendicular axes. To say any more on Lagrange would probably need another "history of mechanics"-type reliable source - I'll keep looking. --FyzixFighter (talk) 03:29, 9 May 2009 (UTC)
 * I know this can be frustrating, and I really don't mean to be tendentious, but I really think the Bernoulli passage is still a bit technical. Bernoulli, in seeking to describe the motion of an object relative to an arbitrary point, showed that the magnitude of the centrifugal force depended on which arbitrary point was chosen - so far so good (the average high school student could probably grasp it), but then, and not inherently determined by the properties of the problem. I'm not sure what the properties of the problem means exactly, and I'm sure most of our readers will be left wondering as well.  Sorry, but I really want to make sure we avoid jargon and highly technical explanations on this page, for the sake of those without any special background in physics. Wilhelm_meis (talk) 13:07, 9 May 2009 (UTC)


 * No problem. I don't mind the specific, constructive criticism. Let me think on it a bit to see if I can come up with a better wording. The idea from Meli that I'm trying to convey with properties of the problem are the inherent attributes of the bodies involved that all observers will agree on, such as mass, relative distance between bodies, charge, the elasticity of the bodies, etc. - at least that's my reading of Meli's statement. The values of these quantities don't depend on any of the observer's choices (at least in the classical sense) and so neither will the forces that result from these quantities, whereas the value for the centrifugal force does depend on the observer's choice of reference frame. Can you think of a concise but non-technical jargon-laced way to say this? --FyzixFighter (talk) 14:05, 9 May 2009 (UTC)

Models or examples
I think it would help the article, it would help the general reader and it would certainly help me, if we could provide some simple models or concrete examples of each of these scenarios and phenomena to illustrate some of the more difficult concepts in a more intuitive way. Of course (and here is perhaps the real challenge) even in this pursuit we must still stick to reliable sources, lest anyone become accused of inserting their own synthesis. Anybody got any good ones in the original sources? Wilhelm_meis (talk) 12:45, 9 May 2009 (UTC)


 * I just added (though I forgot to login) a physical example for the reactive centrifugal force. It's taken from the Roche source. It's a little technical in terms of engineering, but it gives it a real-world, oily physical machine touch . If other editors think it's too technical, then we can use the old object being spun around on a string example which Roche also uses. --FyzixFighter (talk) 17:47, 9 May 2009 (UTC)

FyzixFighter, Regarding the Bernoulli reference, I don't think that you can make the deduction which you did regarding the issue of frames of reference. Bernoulli clearly points out that centrifugal force varies according to which point of reference that we choose. That is a fact of which I am well aware, and I have made my own conclusions about it. I don't intend to insert my own conclusions in the article. But you saw from my edit above that one of the Bernoulli's believed that space is filled with tiny vortices that press against each other due to centrifugal force. I have a theory that these vortices are rotating electric dipoles. It's an established fact that an electric dipole is surrouded by an inverse cube law force field. Hence if a body moves through a sea of such dipoles, it will experience an inverse cube law repulsive force relative to any arbitrarily chosen point, providing that the effect is induced by transverse motion relative to that point. That would mean that centrifugal force is built into Euclidean geometry and it would explain why centrifugal force does not show up in Cartesian coordinates. Centrifugal force hence becomes a property of absolute space and not a property of any frame of reference. That's what Newton's Bucket argument showed. But that is only my own interpretation of the situation. I don't intend to insert it. Likewise, you are entitled to deduce that Bernoulli's statement regarding centrifugal force varying according to the point of origin implies that Bernoulli was thinking in terms of frames of reference. But you are not entitled to insert that opinion into the main article.David Tombe (talk) 18:41, 9 May 2009 (UTC)


 * I'm not making any deduction about what Bernoulli (note this is Daniel Bernoulli, Johann Bernoulli's son) meant in his memoir. That would be original synthesis from a primary source. What I am doing is reporting what a published author says about Daniel Bernoulli's memoir in a reliable source. Your recent edit to that sentence now bears little resemblance to the statement found in that reliable source. I will make the sentence in line with the reference cited. --FyzixFighter (talk) 19:50, 9 May 2009 (UTC)

FyzixFighter, before you do so, can you not balance it out with what I wrote regarding Coriolis's role in the field of rotating frames of reference? Coriolis is much more relevant than anything that Bernoulli ever had to say on the issue of rotating frames of reference and fictitious forces. Why are you so keen to insert a quote by a man in the year 1990? It spoils the whole flow of the section. David Tombe (talk) 19:57, 9 May 2009 (UTC)


 * I have two sources (that I've listed) that place the paradigm shift from real force to fictitious force in the late 18th century. I've also got one more that I need to hunt down that Roche refers to: Dugas (1958) "Mechanics in the Seventeenth Century" (Neuchˆatel: Editions du Griffon). The references I've found to this source would indicate that it too places the paradigm shift in the late 18th century, but since I haven't gotten my hands on it yet, I'll wait to confirm before including it. I fail to see how this text spoils the flow of the section. The section is on the history of the centrifugal force concept, and the source is a mainstream journal on the history of science and technology. I'm keen to include it because it's from a reliable secondary source and is relevant to the topic.
 * I'll see if I can work in Coriolis, but to say that he is the pivot point where the paradigm shifted would require a reliable source saying as such. At most we can say that Coriolis derived all the fictitious forces in his work and gave the name compound centrifugal force to the combined outward radial components of those forces. --FyzixFighter (talk) 20:30, 9 May 2009 (UTC)

This is what I mean about sticking close to the sources and treading lightly with our models. If we move even one step away from the source it may look like we're inserting synthesis, and yet we have to make the article accessible as well. My solution to this is that we give the information as it appears in the source (i.e. either a direct quote or a close paraphrasing), and then give a parenthetical explanation in layman's terms where needed, and then give a model or concrete example that is taken directly from a source, and provide inline citations for everything. Regarding sources, I don't see a problem with using whatever sources we have available (provided that they satisfy WP:RS and WP:COI). I know it's a fine line to walk, but this group of editors is more than equal to the task, and it will help the article thrive and help us all work together. Regarding inline citations, it may sometimes be necessary to provide a note for each element of a passage (1. quote, 2. paraphrasing for clarification, 3. model) even if they came from the same source, just for the sake of clarity. Thank you all for your efforts to come together and improve this article. Wilhelm_meis (talk) 02:16, 10 May 2009 (UTC)

Putting the edit war behind us
I think this article is on the right track, but what will ultimately drive consensus and produce a good article is if everyone plays by the rules, specifically: 1. Report but do not promote (or refute) a particular point of view expressed in the sources (WP:NPOV and WP:SOAP); 2. Explain what is known about CF without instructing the reader (WP:NOTTEXTBOOK); 3. Always assume good faith in others' edits and assume the other editors are intelligent, well-intended people with a valid misunderstanding (WP:AGF and WP:CIVIL); 4. Always take discussion to the talk page BEFORE reverting an edit (unless it has already been thoroughly discussed - then be sure to indicate that discussion in your edit summary); 5. Stick close to the sources and avoid synthesis (WP:Verifiability, WP:RS, WP:SYNTHESIS); 6. Provide ample in-line citations for maximum clarity and verifiability (WP:Verifiability, WP:CITE); 7. Always be sure to identify the common ground where you do agree with the editor(s) with whom you find yourself in disagreement, and spread a little wikilove to those who have done something innovative or commendable, even if you often disagree with the same editor ("Love thy enemies...", what better way to bring someone out of their shell?). If you have held a long-standing disagreement with an editor about one thing, and they do something else which you agree with, leave them a pleasant note about it on their talk page. It will mean a lot to them and can help deescalate the disagreement. The whole thing boils down to this: show me an edit war and I will show you a group of editors that are ignoring the rules to pursue their own agendas. So when these things flare up, just keep cool and be specific and factual in your counterarguments, and cut a wide berth around any sort of personal attacks. We are all just editors, and our egos [should be] meaningless; our very raison d'etre is to produce a better article for the reader, and everything we do should serve that purpose. If we maintain this frame of reference, there is never any need to make personal attacks, nor to take any criticism personally. When personal attacks are made, they say much more about the attacker than the target. One might think a group of physicists would be particularly well-suited to the sort of objectivity and emotional detachment from the material that is required to produce a good article and avoid edit warring. In the end, of course, we are all people, and all our work is subject to all the flaws and vulnerabilities that go along with that. I'll keep this article on my watchlist and try to help out with it from time to time, but I think we have the basis of a good article here already (in what must be some kind of record time). Thank you all for helping to put the edit war behind us. It took all of you to make this progress, so my thanks go out to each and every one. Wilhelm_meis (talk) 04:01, 17 May 2009 (UTC)


 * Wilhelm, thanks for your intervention. It took the intervention of a neutral arbitrator to break the deadlock. I think that it would now be beneficial to actually try and analyze the cause of the edit war. Had it simply been an open clash of differing opinions on the topic, with everybody openly admitting their prejudices, then I'm sure a compromise could have been found a long time ago. But unfortunately that was not the nature of the edit war. The edit war began because a certain group did not want to believe that there could possibly exist other opinions on the topic beyond that which had formed a part of their education.


 * Unfortunately, at the beginning, I wasn't very persuasive and I didn't have any sources immediately at hand. But by the time I started to introduce sources, the opposition were so dug in and re-inforced that it simply became a childish game of sniping from behind screens. It all came down to the issue of superior numbers.


 * While Dick doesn't appear to favour my point of view, at least he was honest enough to present to me with the historical origins of my point of view, which I had previously been unaware of. We have all learned alot from this edit war. I hope that the last stage is done more maturely and in such a way that we can all learn more about the topic in the process. I think that we should all openly declare our prejudices on the topic. My future contributions will now be to highlight the historical sources of the differing and changing attitudes to the topic. David Tombe (talk) 11:14, 17 May 2009 (UTC)
 * No one gets to point fingers here. As they say, it takes two to tango.  If the minority opinion had been squashed altogether, there would not have been much of an edit war.  Of course that doesn't mean it would be a better article - it would have NPOV problems and lacunae in its coverage of the topic, but not much of an edit war.  If you really want to get to the cause of the edit war, it wasn't that people were dishonest about their opinions or that anyone was obfuscating their motives; it's that people were too emotionally invested in the material.  They weren't just reporting what was said by whom in what source, they were defending their own views.  This was an edit war on par with those in the histories of articles on abortion and evolution, because people were approaching it in the same way.  It all comes down to this: dispassionate objectivity is the key to maintaining neutrality, and without it edit wars are inevitable.  We cannot write our own dearly held views into the articles we edit.  Remember, this is an encyclopedia, not a textbook.  You don't get to write whatever you want here.  We report on what is written in the most reliable sources available.  That's what an encyclopedia is.  And that's where these articles fell short for so long.  People forgot they were editing an encyclopedia and thought they were writing a textbook.  People were defending their own views, rather than reporting the views of the experts.  No one here is an expert, we are just editors, and we would all do well to remember that.  That is what caused this edit war, and it is the very same thing that has caused a good many other edit wars elsewhere on WP.  Everyone involved in any edit war shares in it, not just the person making "tendentious" edits, and not just the people "trying to squash" the minority opinion.  We're all in the same mud here, and if we're to get out of it, it will be together.  Wilhelm_meis (talk) 02:29, 18 May 2009 (UTC)


 * The problem is that David spent a year arguing without sources, except for one where his interpretion was pretty much contradicted in the source, and aliening everyone who tried to reason with him. But since I found him some sources, we're making progress. Dicklyon (talk) 04:32, 18 May 2009 (UTC)

Dick, I appreciate your honesty in bringing forth sources that have backed up my opinion. It makes it easier for me to reciprocate the gesture by acknowledging that the opposition viewpoint dominates the modern textbooks. On that basis, we can move forward. We can put the opposition viewpoint first place in the article and state that it is the most common approach nowadays. But we will also now have room to describe the Leibniz approach further down and mention the muted manner in which it is dealt with by Goldstein, along with some modern efforts to treat the planetary orbital problem within the context of rotating frames of reference. But we cannot suppress the fact that 29 years ago, I did planetary orbital theory without involving rotating frames of reference, and that I saw many different approaches to planetary orbital theory which didn't use rotating frames of reference. And those texbooks are still floating about in the stacks somewhere.

On that point I call into question the line in the introduction (The Roche reference) which talks about two distinct but equally valid approaches to centrifugal force. I don't know what he has in mind for those two approaches. But if he is talking about the rotating frames approach and the Newtonian approach then that sentence needs to be removed, because it effectively denies the existence of a third approach. This is were the issue of references can become tricky unless discrepancies can be brushed over in a mature fashion. If we have references that show that there are three approaches, and then we have a reference which states the opinion of a man that there are only two approaches, we cannot allow that latter reference to dominate the article. We need to talk broadly about the several approaches. That is why I inserted the line about 'several approaches'. An anonymous from Norway removed my line. Despite a large number of edits by Brews, this anonymous honed in and deleted my edit in particular. I'm very glad that you stepped in and reverted it. But we now need to remove the clause which narrows it down to 'two approaches'. The truth is that there are at least three approaches to this topic. Besides, it is quite ridiculous to state that there are two approaches that are different but both equally valid. If the two approaches are different, then they cannot both be equally valid. One of them must be wrong, and so we shouldn't be making statements such as to paper over cracks, even if it is the quote from some man who wrote a textbook in 1991. Do you agree with me that the Roche reference should be taken out as a beginning for a slightly expanded introduction? David Tombe (talk) 12:40, 18 May 2009 (UTC)


 * David, the two approaches can indeed be equally valid; they are just different definitions of what centrifugal force is. The Liebniz approach is problematic, as a third approach, as it doesn't connect to F=ma as we know it.  I still think you are mistaken to say that Goldstein used that approach, or that you did planetary orbits without rotating frames of reference.  If you work out the accelerations in polar coordinates, under the force of gravity, th term you care about appears on the acceleration side as a centripetal acceleration.  Only by taking r-double-dot as an acceleration can you interpret that term as a centrifugal force.  The only frame in which r-double-dot is a acceleration is the one that co-rotates with the planet.  So by doing the algebra, without knowing it, you moved to a co-rotating frame.  This is consistent with one of the two definitions of centrifugal force (not the reaction force, but the fictitious force, where fictitious means it's zero in a special non-rotating frame).  So, while you have a different "approach", it's the same definitioin and results, and a special application of, the usual dominant method.  I agree that Liebniz and Graneau don't conceptualize it this way; Liebniz because he didn't understand F = ma yet, and Graneaux because he has an axe to grind, like you.  So you need to find a way to report this stuff without saying there's a third way, I think; the history of conceptions section is the place. Dicklyon (talk) 14:41, 18 May 2009 (UTC)

Dick, the facts are that there are three approaches, and that only one of them can be correct. The planetary orbital equation is a central force equation. All forces in that equation are radial forces. There is an inward inverse square law force of gravity and an outward inverse cube law centrifugal force. The equation can be found at 3-12 in Goldstein without any mention of rotating frames of reference. The Leibniz equation, which is the same as equation 3-12 in Goldstein covers for every possible scenario which you could possibly encounter involving centrifugal force. The Newtonian approach is wrong because it restricts centrifugal force to being equal and opposite to centripetal force, and the rotating frames approach involves an unnecessary encumbrance which becomes completely wrong when it allows the Coriolis force to swing into the radial direction.

Let's sort that latter business out once and for all. Equation 3-12 tells us that in the special case of circular motion, the centrifugal force must be equal and opposite to the centripetal force. In the rotating frames scenario in which a stationary object is observed to trace out a circle as when observed from a rotating frame, I would say that there is no centrifugal force acting at all. You say that there is, but that it it counteracted by a centripetal force that is twice as large and which is supplied from the Coriolis force. Well if the centripetal force is twice as large as the centrifugal force, then we cannot have a circular motion under the terms of equation 3-12. David Tombe (talk) 15:25, 18 May 2009 (UTC)


 * In general the centrifugal and centripetal are not equal and opposite in Newtonian mechanics, that's only true for circular orbits. Newton thought that they must be equal for a while, but that's all; at the end of the the day he knew perfectly well that that doesn't hold for elliptical orbits.- (User) Wolfkeeper (Talk) 14:24, 19 May 2009 (UTC)

Wolfkeeper, You are misrepresenting what I said. I said that centripetal force and centrifugal force are not in general equal and opposite. They are only equal and opposite in the special case of circular motion. Hence in the scenario where you guys try to justify centrifugal force on non-rotating objects by using an oppositely acting Coriolis force to act as the centripetal force, you have got it all wrong, because you are claiming to have an apparent circular motion in which the centripetal force is twice as large as the centrifugal force. David Tombe (talk) 11:43, 20 May 2009 (UTC)


 * If I may butt in for a minute, as I recall the "two approaches" referred to 1) Physics and 2) Engineering, but then someone objected to the Physics v. Engineering dichotomy (see above discussion). I don't think the original edit was in reference to Newton v. Rotating Frames at all.  Wilhelm_meis (talk) 02:23, 21 May 2009 (UTC)


 * I objected, since I know the fictitious force approach is widely used in engineering, e.g. in robotics, where the joint torques needed depend on whether the member carrying the joint is rotating due to a previous joint; if some author draws this dichotomy, it's OK to attribute that idea, but it's by no means universally viewed that way. Dicklyon (talk) 03:22, 21 May 2009 (UTC)

The bottom line is that it's wrong to make an unequivocal statement in the introduction to the extent that there are specifically two approaches to centrifugal force when in fact the literature points to at least three approaches. The problem would be solved by removing that sentence altogther as it is not necessary. It is only misleading. David Tombe (talk) 09:45, 21 May 2009 (UTC)

In the Grip...
The book In the Grip of the Distant Universe] by Neal Graneau should be a good source for representing David's viewpoint that the typical way modern physics deal with inertia and centrifugal force using "fictitious" forces is a travesty. I don't happen to agree with that assessment, but there is a good reasoned argument here for a point of view based on Mach's principle, which I like. The author thinks the way it's taught now is "shameful", but it also seems clear that he just doesn't accept the the term "fictitious", saying "Presumably, this means they do not really exist." This is the same nonsense that David pulls -- instead of looking at what fictitious means, he makes up a strawman interpretation to criticize. Anyway, it's a source, so if we attribute such a POV to that author, it should be fine. Dicklyon (talk) 01:40, 17 May 2009 (UTC)


 * Dick, I never tried too hard to figure out what the word 'fictitious' means in the context of centrifugal force. The word is misleading at the best. As far as I am concerned, centrifugal force is a radial force without the need for any further qualifying adjectives. I've just looked at the reference which you have provided and I can see that this guy Neal Graneau has got his head totally screwed on. He is saying the exact same as what I have been saying all along. David Tombe (talk) 01:04, 18 May 2009 (UTC)


 * Ironically, fictitious forces are characterised by not obeying Newton's third law.


 * Tell me again, does centrifugal force in your polar coordinate equation obey the third law or not?- (User) Wolfkeeper (Talk) 21:52, 27 May 2009 (UTC)

So, I've been reading this book while traveling. It's quite strange really, but also it turns out not at all like David's POV. The authors Graneau and Graneau are seeking to explain the "ma" in F = ma as a "force" of inertia, pushing back in the opposite direction, such that there's a "dynamic equilibrium" in which all forces sum to zero, for any acceleration. It's exactly the "reaction force" or "Newton's thrid law" approach (they do say as much) plus a few different words to reinterpret F = ma, but its really mostly about trying to get at where this reaction force comes from, using Mach's principle, that it must be an interaction with all the distant matter in the universe, with instantaneous communication. I don't buy the argument that it has to instaneous, as others formulate similar theories with speed-of-light advanced and retarded wave functions, but that's not really relevant here. Want's interest though is the extent to which they don't understand, and vehemently criticize the other use of centrifugal force to describe a pseudo force in a rotating system. They don't realize that these different conceptions are in no way in conflict with each other, they're just using the same term for different concepts. It's really quite bizaree that they would right a book displaying such strong feelings about a simple misunderstanding.

As to the Leibniz approach, I suppose that if you took the r-double-dot in the co-rotating 1D or 2D system, and converting it to a corresponding inertial force and put it on the force side, there would still also be a centrifugal force term that in combination with it would make a total inertial force equal to the gravitational force; yes, that would work. Then the sum of accelerating forces balances the applied gravitational force, so it's just Newton's third law stuff again, resolved into two parts. But that's a stretch, as they don't go near anything that looks like the Leibniz approach. Dicklyon (talk) 20:19, 24 May 2009 (UTC)

Fictitious force equation
The standard one is derived in the Wiki article of the same name:



\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} - m \boldsymbol\Omega  \times (\boldsymbol\Omega \times \mathbf{x}_B ) $$&ensp;$$\ - m \frac{d \boldsymbol\Omega  }{dt} \times \mathbf{x}_B \. $$

The first term is Coriolus (depends on velocity vB of the test object in the rotating frame), the second term is the centrifugal force (depends on the radius XB only), and the third is the Euler force, which depends on how the rotational speed omega = d(theta)/dt changing, which means the value of d(omega)/dt. Here it is again, with the x replaced by r, and the subscript B's removed.



\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\Omega \times \mathbf{v} - m \boldsymbol\Omega  \times (\boldsymbol\Omega \times \mathbf{r}) $$&ensp;$$\ - m \frac{d \boldsymbol\Omega  }{dt} \times \mathbf{r} \. $$

That's it. We can reduce it only a bit more for circular motion so that all the cross products come out simple products, and I can replace the omega capital with the lower case:



\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\omega \mathbf{v} - m \boldsymbol\omega  (\boldsymbol\omega \mathbf{r}) $$&ensp;$$\ - m \frac{d \boldsymbol\omega  }{dt} \mathbf{r} \. $$



\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\omega \mathbf{v} - m \boldsymbol\omega^2 \mathbf{r} $$&ensp;$$\ - m \frac{d \boldsymbol\omega  }{dt} \mathbf{r} \. $$

That looks a lot like your equation, except your Coriolus term is missing entirely, as though it didn't exist as a fictitous force. My dw/dt is your d^2(theta)/dt^2, so that's your centrifugal term. But you have an dr^2/dt^2 where I have an r(dw/dt). That cannot be right. I have no idea what your term there is meant to be. It's wrong for Euler, and it's wrong for Coliolus.

Anyway, you can see how it works for uniform circular motion. dw/dt = 0, so the Euler term drops out. Because of the way I dropped out the cross products, the v left in the equation above is tangential v ONLY, as seen in the rotating frame, which means it's omega * r = -wr. (You don't even have a Coriolus term, which I think assumes that you can't even consider the case where you see a tangential v, as you would with an object you see moving in a circle around you). Note the sign for v in that direction is negative. Putting -wr for v, I get:



\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\omega^2 \mathbf{r} + m \boldsymbol\omega^2 \mathbf{r} $$&ensp;$$\. $$



\mathbf{F}_{\mathrm{fict}} = - m \boldsymbol\omega^2 \mathbf{r} $$&ensp;$$\. $$

And there we are. If I see an object circling me for no good reason (simply because I choose to pirouette), then in that rotating frame I must see a fictious force which appears to make it do that. But if I have a rope attached to it and am rotating with it, then I see it stationary. In that case, the exact same fictious force is calculated, but that is not the only force on the object. I am also exerting a centripetal force on the object via my rope, and it is m w^2 r also, but now positive because in the opposite direction. The two forces (net fictious as a result of both radial Coriolus and centrifugal forces), and the centripetal force from my rope, all add to zero. Which is good, because the object is stationary with regard to me, so can have no net force act on it from my frame. But if I don't rotate with the object but simply swing it about, all the fictious terms go to zero, and the centripetal force from my rope remains: F = m w^2 r. And that's also good, because I need a force again here to explain why this object is circling me, instead of flying off in a straight line, or sitting out there at rest (as appears when I rotate with it). S B Harris 02:53, 27 May 2009 (UTC)


 * In the co-rotating case, the Coriolis and Euler forces cancel each other; that is the acceleration of the frame rotation rate matches that of the theta to the planet, as it must by definition of co-rotating. The equation with difference of reciprocal r square and cube terms also depends on assuming conservation of angular momentum; in other words, only central forces.  It's an elegant simplification, but not a different approach. Dicklyon (talk) 03:49, 27 May 2009 (UTC)

SBharris, I didn't miss out on the Coriolis force. There are two equations in planetary orbital theory, which is what we are talking about here. There is a transverse equation and a radial equation. Equation 3-11/3-12 is only the radial equation. It contains the centripetal force and the centrifugal force. There is not supposed to be a Coriolis force in that equation.


 * Yes, there is. The Coriolis force is defined by


 * $$\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\omega  \times \mathbf{v}_{B} \ .$$


 * That cross product gives the force both radial and transverse components, depending on radial and transverse velocities of the object. A tangential velocity will result in a radial Coriolus force, and that's quite relevant here. (Radial velocities cause tangential Coriolus forces, and velocities in the spin axis direction produce no forces). So your equation for radial forces needs the transverse velocity. If it doesn't have a place for it, it's wrong. S B Harris 20:58, 27 May 2009 (UTC)

The Coriolis force and the Euler force are in the transverse equation. The two transverse terms are mathematically equal and opposite, and that leads to the conservation of angular momentum, as you already know.
 * Yes, but you can't just leave out one component of the Coriolis force. Do you know what a cross product is? S  B Harris 20:58, 27 May 2009 (UTC)

The argument between myself and Dick is whether or not the 'rotating frames of reference' approach to centrifugal force is the same as the planetary orbital approach. I agree with Dick that in the special case of co-rotation, they are the same, although I personally don't believe that we need to bother with the rotating frames of reference. I can see what is happening perfectly well without having to strap rotating frames of reference around the problem. At any rate, I am satisfied now that Dick understands the basic principles of the planetary orbit.


 * You already brought in and "strapped on" a rotating frame of reference when you started to talk about centrifugal force. Since it ONLY appears in rotating frames. Otherwise, like the Euler and Coriolus force, it vanishes. If the frame doesn't rotate (which you can easily tell by whether or not the fixed stars are rotating), all that appears is centripetal force. If the stars don't rotate, just ONE arrow points at every ONE object. And which is provided by gravity in planetary motion. Or mechanically by the floor in spacestations, centrifuges and the like. That one arrow, plus the object's inertia, makes it move in a curve and that's it. No other forces enter at all. S B Harris 21:20, 27 May 2009 (UTC)

But I am not satisfied that you understand this topic at all. While I have been trying to expose the difference between planetary orbital theory and 'rotating frames' theory to Dick, you have now arrived on the scenes and attempted to undermine the planetary orbital theory by pointing out where it differs from the 'rotating frame' theory which you have copied above, as if to imply that the planetary orbital theory is wrong because of this difference. The difference which you have highlighted is in the fact that in the 'rotating frame' approach, the Coriolis force has become free to swing into the radial direction. (I don't know how that affects the conservation of angular momentum!).

Dick will of course correctly point out that this difference only applies in the non-co-rotating situation. So we are once again back to looking at the ludicrous extrapolation of rotating frame transformation equations to objects that are stationary in the inertial frame. I have told you on a number of occasions why this is nonsense, but you have completely ignored it, simply because it appears in some sources.


 * No, I have ignored it because what you want makes no sense. Seen in a rotating frame (or a linearly accelerating frame, for that matter), an inertial object is SEEN to travel as though it has a mysterious force applied to it! That's the whole point of introducing these "fictious forces" to begin with. S  B Harris 21:20, 27 May 2009 (UTC)

So as regards Dick, I have been showing him that equation 3-12 means that centrifugal force counterbalances the centripetal force in circular motion. Dick knows that that is true.


 * No! It is neither "true" nor "false." It depends on what frame you choose. Only in a rotating frame (hint: the stars move) does a centrifugal force "appear" which counterbalances the centripetal force. If you think you see "centrifugal force" you've put yourself mentally into a frame where the stars go round and round! In the non-rotating intertial frame, there is no need for a centrifugal force, and it doesn't appear, so all we're left with is the centripetal force. Which is fine, because we always need a net force on an object, to explain why the object is moving in a circle! S B Harris 21:21, 27 May 2009 (UTC)

But in the ludicrous extrapolation scenario in which we observe an apparent circular motion, you are introducing nonsense on top of nonsense. First of all, you are taking a term from the transverse equation and putting it into the radial equation 3-11/3-12. That's the first piece of nonsense. The second piece of nonsense is when you then have a circular motion with a net inward centripetal force.


 * The last is not nonsense at all. All circular motion is caused by net centripetal force, so long as you view the motion from a non-rotating frame (so that you do indeed SEE a circular motion). Objects don't move circularly without a force. See Newton's first law. S  B Harris 21:20, 27 May 2009 (UTC)

It's nonsense, but it's in some sources, and I have conceded that it is in some sources, and we were no longer arguing about that issue. My argument with Dick is that the planetary orbital approach to centrifugal force is a different approach than the rotating frames approach for the specific reason that in the planetary orbital approach, the Coriolis force is firmly fixed in the transverse direction and relates to conservation of angular momentum. In the rotating frames approach, the Coriolis force can swing like a weather cock and it is used to undermine the reality of the outward expansion effect of centrifugal force. The Coriolis force in 'rotating frames' theory is being used as a buckled spoke on a wheel to corrupt the whole picture.

The argument at the moment is that Wolfkeeper will not entertain any mention of Leibniz's approach to planetary orbital theory to appear outside the history section of the article, despite the fact that Goldstein's method is in fact Leibniz's method. Dick will entertain it but he is determined to mix it all up with rotating frames of reference and act as if it's all one and the same topic. He has also shown tendencies to want to name the centrifugal force 'the centripetal force', despite the fact that it is clear that he understands the topic sufficiently well to know that this is wrong. David Tombe (talk) 06:59, 27 May 2009 (UTC)

Technical
I'm going ahead and tagging this article as because I feel that it is especially important that this summary-style article remain accessible to the general reader. Those who want a highly technical in-depth analysis will go on to the branch articles. Specifically, I feel that the "Centrifugal force in planetary orbits" section needs some work to make it more readable. Please don't "dumb it down"; and I fully understand that this is not Simple WP; but it should be easily understood by the general public (think of an average high school student) with no technical background in Physics. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)

In further note, regarding my recent edit, I think I should state for the record that I am not a physicist. I am a linguist and a wikipedian. If I've made mush of any of the finer points of any of the highly technical material presented here in the process of my editing, feel free to correct me, but please do so in a way that avoids getting overly technical and encourages others to maintain civility. Thank you. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)


 * Looking to this edit by FyzixFighter, I think the passages referring to Bernoulli and Lagrange need a little more clarification. Thank you for the contribution, but please remember that these articles, particularly this one, need to be easily understood by the general reader. Wilhelm_meis (talk) 02:08, 9 May 2009 (UTC)


 * I'll see what I can do. It's the Meli article that refers specifically to Bernoulli and Lagrange. It mentions a few others, but article goes into quite a bit of detail on Bernoulli's contribution arguing that it is in his works where "the idea that the centrifugal force is fictitious emerges unmistakably." I'll see about distill it down to a non-technical but accurate summary, but another set of eyes that has access to the article would be appreciated. In the case of Lagrange, Meli doesn't go into great detail; he just says that Lagrange's work was the main text on mechanics in the second half of the 18th century and that Lagrange explicitly stated that the centrifugal force was dependent on the rotation of a system of perpendicular axes. To say any more on Lagrange would probably need another "history of mechanics"-type reliable source - I'll keep looking. --FyzixFighter (talk) 03:29, 9 May 2009 (UTC)
 * I know this can be frustrating, and I really don't mean to be tendentious, but I really think the Bernoulli passage is still a bit technical. Bernoulli, in seeking to describe the motion of an object relative to an arbitrary point, showed that the magnitude of the centrifugal force depended on which arbitrary point was chosen - so far so good (the average high school student could probably grasp it), but then, and not inherently determined by the properties of the problem. I'm not sure what the properties of the problem means exactly, and I'm sure most of our readers will be left wondering as well.  Sorry, but I really want to make sure we avoid jargon and highly technical explanations on this page, for the sake of those without any special background in physics. Wilhelm_meis (talk) 13:07, 9 May 2009 (UTC)


 * No problem. I don't mind the specific, constructive criticism. Let me think on it a bit to see if I can come up with a better wording. The idea from Meli that I'm trying to convey with properties of the problem are the inherent attributes of the bodies involved that all observers will agree on, such as mass, relative distance between bodies, charge, the elasticity of the bodies, etc. - at least that's my reading of Meli's statement. The values of these quantities don't depend on any of the observer's choices (at least in the classical sense) and so neither will the forces that result from these quantities, whereas the value for the centrifugal force does depend on the observer's choice of reference frame. Can you think of a concise but non-technical jargon-laced way to say this? --FyzixFighter (talk) 14:05, 9 May 2009 (UTC)

Models or examples
I think it would help the article, it would help the general reader and it would certainly help me, if we could provide some simple models or concrete examples of each of these scenarios and phenomena to illustrate some of the more difficult concepts in a more intuitive way. Of course (and here is perhaps the real challenge) even in this pursuit we must still stick to reliable sources, lest anyone become accused of inserting their own synthesis. Anybody got any good ones in the original sources? Wilhelm_meis (talk) 12:45, 9 May 2009 (UTC)


 * I just added (though I forgot to login) a physical example for the reactive centrifugal force. It's taken from the Roche source. It's a little technical in terms of engineering, but it gives it a real-world, oily physical machine touch . If other editors think it's too technical, then we can use the old object being spun around on a string example which Roche also uses. --FyzixFighter (talk) 17:47, 9 May 2009 (UTC)

FyzixFighter, Regarding the Bernoulli reference, I don't think that you can make the deduction which you did regarding the issue of frames of reference. Bernoulli clearly points out that centrifugal force varies according to which point of reference that we choose. That is a fact of which I am well aware, and I have made my own conclusions about it. I don't intend to insert my own conclusions in the article. But you saw from my edit above that one of the Bernoulli's believed that space is filled with tiny vortices that press against each other due to centrifugal force. I have a theory that these vortices are rotating electric dipoles. It's an established fact that an electric dipole is surrouded by an inverse cube law force field. Hence if a body moves through a sea of such dipoles, it will experience an inverse cube law repulsive force relative to any arbitrarily chosen point, providing that the effect is induced by transverse motion relative to that point. That would mean that centrifugal force is built into Euclidean geometry and it would explain why centrifugal force does not show up in Cartesian coordinates. Centrifugal force hence becomes a property of absolute space and not a property of any frame of reference. That's what Newton's Bucket argument showed. But that is only my own interpretation of the situation. I don't intend to insert it. Likewise, you are entitled to deduce that Bernoulli's statement regarding centrifugal force varying according to the point of origin implies that Bernoulli was thinking in terms of frames of reference. But you are not entitled to insert that opinion into the main article.David Tombe (talk) 18:41, 9 May 2009 (UTC)


 * I'm not making any deduction about what Bernoulli (note this is Daniel Bernoulli, Johann Bernoulli's son) meant in his memoir. That would be original synthesis from a primary source. What I am doing is reporting what a published author says about Daniel Bernoulli's memoir in a reliable source. Your recent edit to that sentence now bears little resemblance to the statement found in that reliable source. I will make the sentence in line with the reference cited. --FyzixFighter (talk) 19:50, 9 May 2009 (UTC)

FyzixFighter, before you do so, can you not balance it out with what I wrote regarding Coriolis's role in the field of rotating frames of reference? Coriolis is much more relevant than anything that Bernoulli ever had to say on the issue of rotating frames of reference and fictitious forces. Why are you so keen to insert a quote by a man in the year 1990? It spoils the whole flow of the section. David Tombe (talk) 19:57, 9 May 2009 (UTC)


 * I have two sources (that I've listed) that place the paradigm shift from real force to fictitious force in the late 18th century. I've also got one more that I need to hunt down that Roche refers to: Dugas (1958) "Mechanics in the Seventeenth Century" (Neuchˆatel: Editions du Griffon). The references I've found to this source would indicate that it too places the paradigm shift in the late 18th century, but since I haven't gotten my hands on it yet, I'll wait to confirm before including it. I fail to see how this text spoils the flow of the section. The section is on the history of the centrifugal force concept, and the source is a mainstream journal on the history of science and technology. I'm keen to include it because it's from a reliable secondary source and is relevant to the topic.
 * I'll see if I can work in Coriolis, but to say that he is the pivot point where the paradigm shifted would require a reliable source saying as such. At most we can say that Coriolis derived all the fictitious forces in his work and gave the name compound centrifugal force to the combined outward radial components of those forces. --FyzixFighter (talk) 20:30, 9 May 2009 (UTC)

This is what I mean about sticking close to the sources and treading lightly with our models. If we move even one step away from the source it may look like we're inserting synthesis, and yet we have to make the article accessible as well. My solution to this is that we give the information as it appears in the source (i.e. either a direct quote or a close paraphrasing), and then give a parenthetical explanation in layman's terms where needed, and then give a model or concrete example that is taken directly from a source, and provide inline citations for everything. Regarding sources, I don't see a problem with using whatever sources we have available (provided that they satisfy WP:RS and WP:COI). I know it's a fine line to walk, but this group of editors is more than equal to the task, and it will help the article thrive and help us all work together. Regarding inline citations, it may sometimes be necessary to provide a note for each element of a passage (1. quote, 2. paraphrasing for clarification, 3. model) even if they came from the same source, just for the sake of clarity. Thank you all for your efforts to come together and improve this article. Wilhelm_meis (talk) 02:16, 10 May 2009 (UTC)

Putting the edit war behind us
I think this article is on the right track, but what will ultimately drive consensus and produce a good article is if everyone plays by the rules, specifically: 1. Report but do not promote (or refute) a particular point of view expressed in the sources (WP:NPOV and WP:SOAP); 2. Explain what is known about CF without instructing the reader (WP:NOTTEXTBOOK); 3. Always assume good faith in others' edits and assume the other editors are intelligent, well-intended people with a valid misunderstanding (WP:AGF and WP:CIVIL); 4. Always take discussion to the talk page BEFORE reverting an edit (unless it has already been thoroughly discussed - then be sure to indicate that discussion in your edit summary); 5. Stick close to the sources and avoid synthesis (WP:Verifiability, WP:RS, WP:SYNTHESIS); 6. Provide ample in-line citations for maximum clarity and verifiability (WP:Verifiability, WP:CITE); 7. Always be sure to identify the common ground where you do agree with the editor(s) with whom you find yourself in disagreement, and spread a little wikilove to those who have done something innovative or commendable, even if you often disagree with the same editor ("Love thy enemies...", what better way to bring someone out of their shell?). If you have held a long-standing disagreement with an editor about one thing, and they do something else which you agree with, leave them a pleasant note about it on their talk page. It will mean a lot to them and can help deescalate the disagreement. The whole thing boils down to this: show me an edit war and I will show you a group of editors that are ignoring the rules to pursue their own agendas. So when these things flare up, just keep cool and be specific and factual in your counterarguments, and cut a wide berth around any sort of personal attacks. We are all just editors, and our egos [should be] meaningless; our very raison d'etre is to produce a better article for the reader, and everything we do should serve that purpose. If we maintain this frame of reference, there is never any need to make personal attacks, nor to take any criticism personally. When personal attacks are made, they say much more about the attacker than the target. One might think a group of physicists would be particularly well-suited to the sort of objectivity and emotional detachment from the material that is required to produce a good article and avoid edit warring. In the end, of course, we are all people, and all our work is subject to all the flaws and vulnerabilities that go along with that. I'll keep this article on my watchlist and try to help out with it from time to time, but I think we have the basis of a good article here already (in what must be some kind of record time). Thank you all for helping to put the edit war behind us. It took all of you to make this progress, so my thanks go out to each and every one. Wilhelm_meis (talk) 04:01, 17 May 2009 (UTC)


 * Wilhelm, thanks for your intervention. It took the intervention of a neutral arbitrator to break the deadlock. I think that it would now be beneficial to actually try and analyze the cause of the edit war. Had it simply been an open clash of differing opinions on the topic, with everybody openly admitting their prejudices, then I'm sure a compromise could have been found a long time ago. But unfortunately that was not the nature of the edit war. The edit war began because a certain group did not want to believe that there could possibly exist other opinions on the topic beyond that which had formed a part of their education.


 * Unfortunately, at the beginning, I wasn't very persuasive and I didn't have any sources immediately at hand. But by the time I started to introduce sources, the opposition were so dug in and re-inforced that it simply became a childish game of sniping from behind screens. It all came down to the issue of superior numbers.


 * While Dick doesn't appear to favour my point of view, at least he was honest enough to present to me with the historical origins of my point of view, which I had previously been unaware of. We have all learned alot from this edit war. I hope that the last stage is done more maturely and in such a way that we can all learn more about the topic in the process. I think that we should all openly declare our prejudices on the topic. My future contributions will now be to highlight the historical sources of the differing and changing attitudes to the topic. David Tombe (talk) 11:14, 17 May 2009 (UTC)
 * No one gets to point fingers here. As they say, it takes two to tango.  If the minority opinion had been squashed altogether, there would not have been much of an edit war.  Of course that doesn't mean it would be a better article - it would have NPOV problems and lacunae in its coverage of the topic, but not much of an edit war.  If you really want to get to the cause of the edit war, it wasn't that people were dishonest about their opinions or that anyone was obfuscating their motives; it's that people were too emotionally invested in the material.  They weren't just reporting what was said by whom in what source, they were defending their own views.  This was an edit war on par with those in the histories of articles on abortion and evolution, because people were approaching it in the same way.  It all comes down to this: dispassionate objectivity is the key to maintaining neutrality, and without it edit wars are inevitable.  We cannot write our own dearly held views into the articles we edit.  Remember, this is an encyclopedia, not a textbook.  You don't get to write whatever you want here.  We report on what is written in the most reliable sources available.  That's what an encyclopedia is.  And that's where these articles fell short for so long.  People forgot they were editing an encyclopedia and thought they were writing a textbook.  People were defending their own views, rather than reporting the views of the experts.  No one here is an expert, we are just editors, and we would all do well to remember that.  That is what caused this edit war, and it is the very same thing that has caused a good many other edit wars elsewhere on WP.  Everyone involved in any edit war shares in it, not just the person making "tendentious" edits, and not just the people "trying to squash" the minority opinion.  We're all in the same mud here, and if we're to get out of it, it will be together.  Wilhelm_meis (talk) 02:29, 18 May 2009 (UTC)


 * The problem is that David spent a year arguing without sources, except for one where his interpretion was pretty much contradicted in the source, and aliening everyone who tried to reason with him. But since I found him some sources, we're making progress. Dicklyon (talk) 04:32, 18 May 2009 (UTC)

Dick, I appreciate your honesty in bringing forth sources that have backed up my opinion. It makes it easier for me to reciprocate the gesture by acknowledging that the opposition viewpoint dominates the modern textbooks. On that basis, we can move forward. We can put the opposition viewpoint first place in the article and state that it is the most common approach nowadays. But we will also now have room to describe the Leibniz approach further down and mention the muted manner in which it is dealt with by Goldstein, along with some modern efforts to treat the planetary orbital problem within the context of rotating frames of reference. But we cannot suppress the fact that 29 years ago, I did planetary orbital theory without involving rotating frames of reference, and that I saw many different approaches to planetary orbital theory which didn't use rotating frames of reference. And those texbooks are still floating about in the stacks somewhere.

On that point I call into question the line in the introduction (The Roche reference) which talks about two distinct but equally valid approaches to centrifugal force. I don't know what he has in mind for those two approaches. But if he is talking about the rotating frames approach and the Newtonian approach then that sentence needs to be removed, because it effectively denies the existence of a third approach. This is were the issue of references can become tricky unless discrepancies can be brushed over in a mature fashion. If we have references that show that there are three approaches, and then we have a reference which states the opinion of a man that there are only two approaches, we cannot allow that latter reference to dominate the article. We need to talk broadly about the several approaches. That is why I inserted the line about 'several approaches'. An anonymous from Norway removed my line. Despite a large number of edits by Brews, this anonymous honed in and deleted my edit in particular. I'm very glad that you stepped in and reverted it. But we now need to remove the clause which narrows it down to 'two approaches'. The truth is that there are at least three approaches to this topic. Besides, it is quite ridiculous to state that there are two approaches that are different but both equally valid. If the two approaches are different, then they cannot both be equally valid. One of them must be wrong, and so we shouldn't be making statements such as to paper over cracks, even if it is the quote from some man who wrote a textbook in 1991. Do you agree with me that the Roche reference should be taken out as a beginning for a slightly expanded introduction? David Tombe (talk) 12:40, 18 May 2009 (UTC)


 * David, the two approaches can indeed be equally valid; they are just different definitions of what centrifugal force is. The Liebniz approach is problematic, as a third approach, as it doesn't connect to F=ma as we know it.  I still think you are mistaken to say that Goldstein used that approach, or that you did planetary orbits without rotating frames of reference.  If you work out the accelerations in polar coordinates, under the force of gravity, th term you care about appears on the acceleration side as a centripetal acceleration.  Only by taking r-double-dot as an acceleration can you interpret that term as a centrifugal force.  The only frame in which r-double-dot is a acceleration is the one that co-rotates with the planet.  So by doing the algebra, without knowing it, you moved to a co-rotating frame.  This is consistent with one of the two definitions of centrifugal force (not the reaction force, but the fictitious force, where fictitious means it's zero in a special non-rotating frame).  So, while you have a different "approach", it's the same definitioin and results, and a special application of, the usual dominant method.  I agree that Liebniz and Graneau don't conceptualize it this way; Liebniz because he didn't understand F = ma yet, and Graneaux because he has an axe to grind, like you.  So you need to find a way to report this stuff without saying there's a third way, I think; the history of conceptions section is the place. Dicklyon (talk) 14:41, 18 May 2009 (UTC)

Dick, the facts are that there are three approaches, and that only one of them can be correct. The planetary orbital equation is a central force equation. All forces in that equation are radial forces. There is an inward inverse square law force of gravity and an outward inverse cube law centrifugal force. The equation can be found at 3-12 in Goldstein without any mention of rotating frames of reference. The Leibniz equation, which is the same as equation 3-12 in Goldstein covers for every possible scenario which you could possibly encounter involving centrifugal force. The Newtonian approach is wrong because it restricts centrifugal force to being equal and opposite to centripetal force, and the rotating frames approach involves an unnecessary encumbrance which becomes completely wrong when it allows the Coriolis force to swing into the radial direction.

Let's sort that latter business out once and for all. Equation 3-12 tells us that in the special case of circular motion, the centrifugal force must be equal and opposite to the centripetal force. In the rotating frames scenario in which a stationary object is observed to trace out a circle as when observed from a rotating frame, I would say that there is no centrifugal force acting at all. You say that there is, but that it it counteracted by a centripetal force that is twice as large and which is supplied from the Coriolis force. Well if the centripetal force is twice as large as the centrifugal force, then we cannot have a circular motion under the terms of equation 3-12. David Tombe (talk) 15:25, 18 May 2009 (UTC)


 * In general the centrifugal and centripetal are not equal and opposite in Newtonian mechanics, that's only true for circular orbits. Newton thought that they must be equal for a while, but that's all; at the end of the the day he knew perfectly well that that doesn't hold for elliptical orbits.- (User) Wolfkeeper (Talk) 14:24, 19 May 2009 (UTC)

Wolfkeeper, You are misrepresenting what I said. I said that centripetal force and centrifugal force are not in general equal and opposite. They are only equal and opposite in the special case of circular motion. Hence in the scenario where you guys try to justify centrifugal force on non-rotating objects by using an oppositely acting Coriolis force to act as the centripetal force, you have got it all wrong, because you are claiming to have an apparent circular motion in which the centripetal force is twice as large as the centrifugal force. David Tombe (talk) 11:43, 20 May 2009 (UTC)


 * If I may butt in for a minute, as I recall the "two approaches" referred to 1) Physics and 2) Engineering, but then someone objected to the Physics v. Engineering dichotomy (see above discussion). I don't think the original edit was in reference to Newton v. Rotating Frames at all.  Wilhelm_meis (talk) 02:23, 21 May 2009 (UTC)


 * I objected, since I know the fictitious force approach is widely used in engineering, e.g. in robotics, where the joint torques needed depend on whether the member carrying the joint is rotating due to a previous joint; if some author draws this dichotomy, it's OK to attribute that idea, but it's by no means universally viewed that way. Dicklyon (talk) 03:22, 21 May 2009 (UTC)

The bottom line is that it's wrong to make an unequivocal statement in the introduction to the extent that there are specifically two approaches to centrifugal force when in fact the literature points to at least three approaches. The problem would be solved by removing that sentence altogther as it is not necessary. It is only misleading. David Tombe (talk) 09:45, 21 May 2009 (UTC)

Equation 3-12 in Goldstein
Dick, you asked me where Goldstein mentioned 'centrifugal force' in relation to equation 3-12. Page 76 in the second edition, beginning on the fourth paragraph down. He says,

"The equation of motion in r, with θ(dot) expressed in terms of l, Eq. (3-12), involves only r and its derivatives. It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force

f' = f + l^2/mr^3                             (3-22)

The significance of the additional term is clear if it is written as mr[θ(dot)]^2 = mv^2/r, which is the familiar centrifugal force."

The form mr[θ(dot)]^2 of course appears at equation 3-11. You have been trying to insinuate that Goldstein only uses the term 'centrifugal force' in relation to the fictitious one-dimensional problem. But that is hardly likely, because we cannot possibly write it in the familiar centrifugal force format (mr[θ(dot)]^2) with an angular speed in a one-dimensional problem. You have been playing a clever game of word association. You saw the opportunity with the word 'fictitious' which bears no relationaship in the context with the fictitious force concept in rotating frames of reference.

On page 179 in the same edition, Goldstein writes,

"Incidentally, the centrifugal force on a particle arising from the earth's revolution around the Sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the Sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun."

There is no mention of rotating frames of reference in either the first edition (1950) or the second edition (1980). However in the 2002 edition, the new editors have added an extra bit in about rotating frames of reference to justify their own prejudices. They are obviously from that generation that have been brainwashed into thinking that you can't have a centrifugal force unless you strap a rotating frame of reference around the problem.

Also on page 78 in the second edition, beginning sixth line down on discussing planetary orbits, Goldstein writes,

"A particle will come in from infinity, strike the "repulsive centrifugal barrier", be repelled, and travel back out to infinite".

In problem 8-23 on Keplerian orbits at the end of chapter 8 in the 2005 edition of Taylor, Taylor draws attention to the Leibniz equation without actually explicitly saying so. He cites the radial force equation in which the outward term is an inverse cube law force and the inward term is an inverse square law force. He then tasks the reader to show that this equation solves to yield, elliptical, hyperbolic, or parabolic orbits.

You have been trying far too hard to deny this well known topic in applied mathematics because it exposes centrifugal force as a real outward inverse cube law force, and that this conflicts with what is being taught on physics courses and in other courses in applied maths regarding rotating frames of reference. Because it was not part of your own education and because you have only just discovered it during this edit war, you are trying to distort it to fit in with your previous view of the matter, and you are not being fair to the readers. Your attitude is something along the lines of 'since I didn't know it, nobody is allowed to know it'. David Tombe (talk) 00:03, 25 May 2009 (UTC)


 * Thanks; in my first edition it's the same, but eq 3-12 is on page 61 and the quote about centrifugal force after eq. 3-22 on p. 64, in the section "Equivalent one-dimensional problem". The bit you quoted has the mention of "centrifugal force" a sentence or two later than the reference to eq. 3=12, and it specifically refers to a term in 3-22, on the just-introduced "fictitious one-dimensional problem".


 * This one-dimensional system obviously rotates its r axis to align with the planet, and the equation 3-22 is where he shows a net "effective force" in this system by adding the centrifugal force on the force side to make the "effective force" work in F = ma in that system. He calls it "the equation of motion in r", which clearly means in a system that rotates such that r-double-dot can be interpreted as acceleration in F = ma.  This is all completely conventional, and there's no suggest anywhere that he refers to the centripetal acceleration term in 3-11 as centrifugal force; he's in an inertial system at that point, so he has it on the acceleration side; when he rewrites it as an equation in r only in 3-12, it's still on the acceleration side, he's just one step away from writing the F = ma in the rotating 1D system as he does in 3-22.  But he's not calling it centrifugal force until after he does that; after he puts it on the force side, where he can say "The significance of the additional term is clear if it is written as mr[θ(dot)]^2 = mv^2/r, which is the familiar centrifugal force." – the reason it's clear is that it's now part of the force in F = ma, and the system in which this equation applies is the 1D system, the "fictitious one-dimensional problem" as he calls it.


 * There is absolutely no evidence, or reason to think, that he means centrifugal force to mean anything different from what other modern physicists interpret, which is a pseudo-force in a rotating system. Would he have called the system in whose equation of motion it appears a "fictitious one-dimensional problem" if he meant to distinguish it from the usual fictitious-force approach?  I think not.


 * I've argued for the inclusion of this approach, sourced to both Goldstein and Taylor, and with historical roots with Leibniz. If there's a well-known topic that you think I'm denying, show us some sources.  If you believe it is somehow a "third way", as opposed to a special case of the usual rotating frame analysis, show us some sources that support that interpretation. Dicklyon (talk) 17:50, 25 May 2009 (UTC)

Dick, here is equation 3-11 exactly,


 * $$m\ddot r-mr\dot\theta^2=f(r)$$

Equation 3-12 replaces the second term on the left hand side with the inverse cube law term by substituting the angular momentum to reduce it to one variable. You are trying to tell me that the second term on the left hand side is not the centrifugal force. Can you then please name the three terms in this equation. Do bear in mind that it is the radial planetary orbital equation and it is solved to yield Keplerian orbits. And do bear in mind that Leibniz had both an inverse square law force of gravity and an inverse cube law centrifugal force in this equation. David Tombe (talk) 20:13, 25 May 2009 (UTC)


 * In the usual intepretation, that equation 3-11 is ma = F. The left hand side is the mass times the total centripetal acceleration, and the right hand side is the force of gravity.  I'm not trying to tell you that it can't be rearranged and interpreted as just the first term being acceleration, and the second term moved to the force side and called centrifugal force – it can be; in the system that co-rotates with the planet, the fictitious 1D system as Goldstein calls it, the first term with r-double-dot is the entire mass*acceleration, and the second term is the usual pseudo force known as centrifugal force, as Goldstein points out after he does that in 3-22.  Dicklyon (talk) 22:08, 25 May 2009 (UTC)

OK Dick, It's time to get to the point. Let's call the $$mr\dot\theta^2$$ term 'Harry Lime'. In order to have circular motion, Harry Lime needs to be equal and opposite to the centripetal force $$f(r)$$ in order for $$m\ddot r$$ to be zero.

In the rotating frames of reference approach to centrifugal force, circular motion arises from a net centripetal force. That is a fundamental difference between the two approaches. In the rotating frames of reference approach $$m\ddot r$$ is zero in circular motion, yet balanced in the equation with a net inward centripetal force. Something is seriously wrong there. Yet you are saying that these two approaches are the same. You are quite wrong on this point. The two approaches are not the same at all, and one is badly wrong. The latter approach has made Harry Lime mysteriously disappear from the equation. David Tombe (talk) 22:23, 25 May 2009 (UTC)


 * I haven't seen any Harry Lime in any analysis, and your attempt to introduce a new name is in no way instructive or helpful, so not clear what point you are trying to get to. In all approaches, $$\ddot r$$ is zero in circular motion, by definition of a circle.  It's not clear to me what you're saying is different between the approaches.  All of the rotating-frame approaches, including Goldstein's, have $$\ddot r$$ equal to zero due to a cancellation of a gravity term and a centrifugal force term when the orbit is circular, and not quite zero for other shapes.  Any analysis in an inertial frame also has the same $$\ddot r$$ if you calculate it, e.g. by solving for it in Goldstein's 3-11, which is essentially equivalent to converting to the 1d rotating frame and looking at the acceleration (in the inertial frame, $$\ddot r$$ is not acceleration, as I'm sure you'll acknowledge).  The fact that inertial-frame approaches do not need a centrifugal force is why such forces are called pseudo forces – they arise when making F=ma work in a rotating frame, and not otherwise.  Dicklyon (talk) 00:41, 26 May 2009 (UTC)


 * He's not exactly doing his equation in inertial frames. Tombe is using polar coordinates and in polar coordinates the axes rotate with the body rather than at constant speed. So a 'centrifugal force' and a 'coriolis force' appear; but they're mathematically different to rotating reference frames. Tombe does not have a clue about rotating reference frames, he is apparently incapable of understanding them, but nevertheless makes sweeping claims about them; like he thinks coriolis force is always tangential to the radius vector. That's where his maths ends and crankiness starts.- (User) Wolfkeeper (Talk) 17:54, 27 May 2009 (UTC)

Dick, Equation 3-11 is,

$$m\ddot r-mr\dot\theta^2=f(r)$$

Conservation of angular momentum converts the $$mr\dot\theta^2$$ term into $$l^2/mr^3$$. Hence, equation 3-11 becomes,

$$m\ddot r-l^2/mr^3=f(r)$$

which is equation 3-12.

Goldstein says that equation 3-12 is the same equation as that which occurs in the fictitious one-dimensional problem because it is an equation in one variable ,r. He also points out that the significance of the inverse cube law term in the one-dimensional problem becomes clear when it is written in the form $$mr\dot\theta^2$$ which is the 'familiar centrifugal force'. So I can't see any basis at all for your attempts to deny that centrifugal force is in either equation 3-11 or 3-12. It is there as either $$mr\dot\theta^2$$, or as the inverse cube law term, and that fact is backed up by Leibniz's equation in which the inverse cube law term is the centrifugal force.

You are absolutely correct when you say that the special case of circular motion requires that $$m\ddot r$$ be equal to zero. But in order for it to be equal to zero we need the other two terms to be equal and opposite. Those other two terms are of course the centripetal force term and the centrifugal force term. To start with, you are engaged right now in a specious attempt to deny that one of those terms is in fact the centrifugal force term. And secondly, in your favoured 'rotating frames approach', one of your key arguments that is used to back up the extrapolation of centrifugal force to situations where a stationary object is observed in a rotating frame, involves a specious argument in which the centrifugal force is overridden by a radial Coriolis force which is twice as large, hence leading to a net inward centripetal force. In that scenario, you are trying to justify a circular motion using a net centripetal force with no equal and opposite counterbalance. If there is a net centripetal force in that scenario, then $$m\ddot r$$ cannot be zero. That aspect of 'rotating frames'/'fictitious forces' theory is fundamenatlly flawed and it is at variance with central force theory as per equations 3-11, and 3-12. David Tombe (talk) 07:58, 26 May 2009 (UTC)


 * We've been through this already. In a simple rock whirled on a string, when viewed from the NON-rotating frame (a person looking down on it, say) there is only one force, the centripetal force. This explains the non-linear motion of the rock. Whether you want to say $$m\ddot r$$ = 0 in this frame depends on how you define r. The scalar length of r is constant. But if r is a vector, its derivative will not be zero, because its direction is changing. So pick which ever one you like, but you can't have both. If r is the vector distance, then $$m\ddot r$$ is the vector acceleration, and the centripetal force provides this acceleration. In the case of the rock which is sitting on the ground, at the same radial distance r away from you, but traveling in a circle around you because you're twirling about on your foot, and have thus chosen a rotating frame, now you have the very same distance vector, and the same acceleration vector. The scalar distance does not change, but the acceleration vector does. Again, choose which one you like! One is zero, the other is not! This acceleration (if you choose the vector, not the scalar length of the vector) is now explained by a net force, which is the net centripetal force, and which explains the fact that the rock moves in a curve, not a straight line. This force is composed of two parts-- one part is radially outward, and is the centrifugal force caused by your rotating frame. The other is radially inward and is twice as large-- the radial Coriolis force. Together they add up to a net inward force vector which is precisely the same as the vector in the first case of the rock on the string. It provides the centripetal force which explains why the rock moves in a curve in your rotating frame. That's it. You can't complain it doesn't exist because the r vector is zero-- you're talking about a scalar, there. That component is zero exactly as in the first example, if you choose r as a scalar. But if you chose r as a vector, then its second derivative is a non-zero acceleration required by the fact that the direction of the vector changes (though not its length) if you choose r as a vector.  S  B Harris 08:46, 26 May 2009 (UTC)

SBharris, we are looking at the equation,

$$m\ddot r-mr\dot\theta^2=f(r)$$

This is equation 3-11 in Goldstein and it caters for every possible central force scenario. If $$m\ddot r$$ is zero, as will be so in the special case of circular motion, the centripetal force term f(r) has to be exactly balanced by an outward term of the form $$mr\dot\theta^2$$, which of course is the centrifugal force.

Originally you were instinctively aware of the fact that the Coriolis force is the transverse deflection of a radial motion in a vortex field. You knew that. Coriolis force is one of the terms in the transverse equation which contributes to the conservation of angular momentum. But you allowed yourself to be fooled by RRacecarr and SCZenz who made a private visit to you on your talk page on having seen your original heresy. You then willingly bought that nonsense about the Coriolis force swinging freely like a weather cock and being allowed therefore to swing into the radial direction. They drew your attention to the expression 2v×ω and the fact that the Coriolis force is apparently free to rotate in a plane that is perpendicular to the rotation axis. You returned to me with this new found wisdom as if I hadn't previously been aware of it and you instructed me in it like as if you were teaching me something that I had overlooked. When I showed you that the derivation of Coriolis force restricts the input velocity to the radial direction, hence restricting the resulting Coriolis force to the transverse direction, you just ignored it. You conceded 'nolere contendere' to RRacecarr and SCZenz and you then joined the majority against me.

The consequence is that you are now advocating that the Coriolis force can cause an inward centripetal force that overrides an outward centrifugal force on a stationary object as viewed from a rotating frame of reference. You do get a net inward centripetal force if you do that. But a circular motion is not the product of a net centripetal force. A circular motion arises from a net zero force in the radial direction, as per equation 3-11 above.

You are totally ignoring the centrifugal force that exists even in straight line fly-by motion relative to any arbitrily chosen point in space. A centripetal force causes curved path motion when rotation is involved. But the rotation causes a centrifugal force in the first place. In circular motion, the centripetal force merely cancels that centrifugal force. David Tombe (talk) 11:49, 26 May 2009 (UTC)


 * Nobody is "ignoring the centrifugal force that exists even in straight line fly-by motion relative to any arbitrily chosen point in space". It's a pseudo force that appears depending on the chosen refernce frame.  For a co-rotating frame with constant angular momentum, from a point of your choice, it's the reciprocal r cube pseudo force.  Who are you saying is ignoring it?  Dicklyon (talk) 21:45, 26 May 2009 (UTC)
 * Note also that in the straight gravity-less fly by, in coordinates that rotate to follow the object from a point of view, the traditional Coriolis and Euler forces cancel each other exactly. &minus;Woodstone (talk) 22:05, 26 May 2009 (UTC)
 * Woodstone is right. Additionally, read my lips: any frame which has a moving vector r, will not have dr^2/dt^2 = 0. The length of r may stay the same, but if the direction of r changes with time, its time derivative will change and thus be non-zero. So will the second derivative be nonzero. Thus, any frame in which you see the r vector MOVE in a circle (like a watchhand), will have a non-zero second derivative of r. That means your force term cannot be zero, unless the two terms cancel. Which they do if you merely look at a stationary object from a rotating frame. Or if you fly-by a stationary object, while rotating to keep your camera on it (the Woodstone case). Which causes its apparent motion to be linear, therefore inertial, therefore free of any net force.  S  B Harris 23:21, 26 May 2009 (UTC)

Dick, Once again, you have shown that you are one of the few that is capable of understanding this topic, but that something is holding you back from fully acknowledging your own understanding of it. You acknowledge the outward centrifugal force in straight line fly-by motion. That's good. And we all know that we get a different centrifugal force according to which point of origin that we choose.

You asked me who is denying it. Well SBharris is denying it.

You mentioned how the centrifugal force obeys the inverse cube law when angular momentum is conserved. Correct. Woodstone then reminded us all of the law of conservation of angular momentum, but without actually stating it explicitly. He pointed out how the Coriolis force and the Euler force (both transverse forces) cancel each other mathematically. We all know that he is correct on that point, but that it has got nothing to do with what we are talking about. SBharris then re-affirmed that Woodstone is correct, as if there might have been some doubt about it. SBharris even referred to the fly-by scenario as 'the Woodstone case'.

The most difficult thing to analyze above is the remainder of what SBharris has said. He makes a few very false statements. He seems to think that if the radial vector is rotating, that d^2r/dt^2 cannot be equal to zero. He then says that the force term cannot be zero, unless the two terms cancel. What can he possibly mean? He then says that the two terms do cancel if we look at a stationary object from a rotating frame. We need to look at the equation again,

$$m\ddot r-mr\dot\theta^2=f(r)$$

This is the radial equation for all central force scenarios. When we have circular motion, the $$m\ddot r$$ term will be zero, despite what SBharris says. If it is zero, then it follows that the centripetal force term f(r) must be equal and opposite to the $$mr\dot\theta^2$$ centrifugal force term. In other words, a circular motion requires both a centripetal force and an equal and opposite centrifugal force.

Do you agree with what I have written in the above paragraph? If not, please explain. David Tombe (talk) 00:06, 27 May 2009 (UTC)
 * I did make a mistake. The force is not zero if you see an object in any kind of curved motion. However, if you see an object move by in linear motion, as you do if you do a fly-by of a stationary object while rotating to watch it, then the forces on the object from your rotating frame must sum to zero, since you see the object as non-accelerated (ie, traveling in a line). Hope that clears it up. Of course, you must see a net (fictitious) force moving an object in a circle around you, even if you're making it do so by rotating yourself. In that case, the f term is non-zero. S  B Harris 01:16, 27 May 2009 (UTC)

SBharris, you are totally ignoring equation 3-11,

$$m\ddot r-mr\dot\theta^2=f(r)$$

It's quite simple. When circular motion occurs, the inward centripetal force f(r) must be equal and opposite to the outward centrifugal force $$mr\dot\theta^2$$ in order to make $$m\ddot r$$ equal to zero. David Tombe (talk) 18:40, 27 May 2009 (UTC)


 * Let's lay off trying to teach physics to one another and just look at sources. David, the main problem with your argument is that Goldstein does not call that term the "centrifugal force" when it appears on the left side of the equation. Rather, as seen in Chapter 1 (pg 25 1st edition/pg 27 3rd edition), and as I pointed out previously, he calls it a "centripetal acceleration term". A few other sources (Taylor, Tatum, Kobayashi,etc) also use similar terminology for this term when it appears on the "acceleration side" of F=ma. I agree that this is somewhat of a misnomer, since in the inertial frame the radial (centripetal) acceleration is $$\ddot r-r\dot\theta^2$$. Goldstein only calls the term the "centrifugal force" after 3-22 when the term has been moved to the other side. This is the biggest difference between Goldstein 3-11/12 and Leibniz's equation - the inverse-cube term (Harry Lime) appears on different sides of the equation. While which side it appears on is irrelevant mathematically to the orbital solutions and I'm pretty sure you'd say which side it appears on is trivial, multiple sources indicate that it isn't trivial when describing the physics. Having the term appear on the force side of the equation, as Leibniz did, is equivalent to transforming to a rotating frame - see Taylor Ch 9, the Kobayashi 2008 reference, Whiting, J.S.S. (November 1983) "Motion in a central-force field" Physics Education 18 (6): pp. 256–257, Tatum, and the list goes on. When it appears on the other side, it's a centripetal contribution to the radial acceleration times the mass. We even have a reference that states that the Leibniz equation is equivalent to the rotating frame formulation. This understanding is also supported by "From Eudoxus to Einstein", the same book you brought up, David. It states on page 264:
 * "Much of the Principia is concerned with the motion of bodies under the influence of central forces or, as Newton called them, 'centripetal force'. In this we see that Newton had realized crucially that it was much simpler to consider things from a frame of reference in which the point of attraction was fixed rather than from the point of view of the body in motion. In this way, centrifugal forces - which were not forces at all in Newton's new dynamices - were replaced by forces that acted continually toward a fixed point."
 * Since Goldstein doesn't mention frames in the Ch 3we cannot use Goldstein to support or counter (as much as I'd love to given how explicit the other references are) David's claim that the inertial centrifugal force exists in the inertial reference frame. However, David, since we do have so many sources (including the Goldstein text itself) that disagree with your interpretation Goldstein 3-11 and that do state explicitly that the Leibniz's centrifugal force only appears in rotating frames, you need to provide a reference that says otherwise in order to claim that it is a third way. Don't argue physics, don't insult other editors, and don't cry conspiracy and suppression - just provide a reliable source that says exactly what you want to put in. We've included the "two distinct centrifugal force concepts" because we've found sources that say exactly that. Now it's your turn. Provide a source or shut up.
 * To everyone else, personally I find that arguing physics from first principles with David does nothing to improve the article and is an exercise in futility. Nothing anyone says here will change David's mind on the subject, but reliable sources will determine what stays and what doesn't in the article. Those magnanimous few who are still wanting to try to show David the error of his ways, or are willing to let him try to convince them the error of their ways, please take it to your personal talk pages. Here I'd rather discuss the sources. --FyzixFighter (talk) 03:18, 28 May 2009 (UTC)

Generality of the planetary orbital example
The central force problem of planetary motion is not a paradigm for all discussion of centrifugal force. In fact, it is a special case surrounded by a lore that only confuses matters. It is much cleaner and more straightforward to consider simpler examples, like a ball on a string, or the rotating spheres example, which do not have a huge baggage. Brews ohare (talk) 16:35, 27 May 2009 (UTC)


 * Brews, Equation 3-11/3-12 is the general equation which caters for all central force problems, whether involving gravity or not. Any of your rotating sphere problems can be dealt with by using equation 3-11. David Tombe (talk) 18:37, 27 May 2009 (UTC)

Do you agree with the analysis at Rotating_spheres? Brews ohare (talk) 19:07, 27 May 2009 (UTC)


 * Brews, I've already looked at that bit a few times. I can't believe how complicated you have made what should be a simple problem based on equation 3-11. You have introduced two rotation speeds, yet we all know that only one of them is relevant. The only rotation speed that is relevant is the one that is measured relative to the background stars. That absolute rotation induces an outward centrifugal force which is one of the terms in equation 3-11. The centrifugal force then pulls the string taut. The induced tension in the string then causes an inward centripetal force to act, which is equal and opposite to the outward centrifugal force. The net result is circular motion.


 * Why can you not write it up in simple terms like that? Why all the extras about different rotation speeds and rotating frames of reference? Are you trying to mask the reality of the outward expansion? Is real outward expansion due to rotation not politically correct in modern physics? David Tombe (talk) 19:31, 27 May 2009 (UTC)

Two speeds are necessary: the rate seen by the rotating observers ωS and the absolute speed of the spheres seen in an inertial frame ωI, so that it can be shown that the tension can be used to establish the observer's absolute rate of rotation. Brews ohare (talk) 22:36, 27 May 2009 (UTC)


 * Brews, the issue of absolute rotation can be adequately demonstrated using a single rotating bucket of water. David Tombe (talk) 22:44, 27 May 2009 (UTC)

Not so. First, the rotating bucket provides a simple "yes or no" answer to whether rotation occurs, but a more quantitative answer is more complicated. The rotating sphere problem allows a quantitative answer with little complication. Second, the details of the more quantitative solution probably will lead to severe disagreements between you and the analysis presented. Those disagreements might just possibly sort things out. Brews ohare (talk) 23:07, 27 May 2009 (UTC)


 * Brews, could you elaborate on the disagreements that you are anticipating. David Tombe (talk) 23:16, 27 May 2009 (UTC)

For example, the article finds the fictitious force to be:
 * $$ \mathbf{F}_{\mathrm{Fict}} = -m \left( \omega_S^2 R -\omega_I^2 R \right) \mathbf{u}_R \ . $$

which has different direction depending upon whether the measured rate of rotation ωS is faster or slower than the absolute rate of rotation of the spheres ωI. Physically this change makes sense, because the measured tension must be diminished or supplemented by the fictitious contribution depending upon ωS/ωI 1. I seem to recall objection on your part to the fictitious force switching direction depending upon circumstance. This switch depends upon a change in the Coriolis force, inasmuch as the centrifugal force always has an outward direction.

As a particular case, if the spheres are actually not absolutely rotating (ωI = 0), the string tension is zero and cannot explain the motion, so the fictitious force is always inward to provide the rotating observer with a centripetal force to explain the apparent circular motion.

Assuming you object still, the way forward (I'd say) is to specifically point out the mathematical step in the derivation for this result that is in error (in your opinion). That is more fruitful than a purely verbal onslaught referring to Leibniz, Goldstein etc.. Brews ohare (talk) 11:18, 28 May 2009 (UTC)


 * Brews, there is no such thing as a radial Coriolis force, no matter what you have read in the textbooks. I have traced this error back to Gaspard-Gustave Coriolis himself. If you don't want to believe me, that's up to you. I'm not editing on rotating frames stuff anymore. I'll leave that to you. I am interested in the real outward centrifugal force that arises in conjunction with absolute rotation. David Tombe (talk) 13:31, 28 May 2009 (UTC)

The Reactive Force and the Third Law
Wolfkeeper has been getting interested in whether or not the so-called reactive centrifugal force obeys Newton's third law of motion. Wolfkeeper believes that it does. And indeed Newton invented the concept ostensibly based on the fact that it does. It's certainly very easy to buy the idea that in the special case of circular motion that there is a centrifugal force that is an equal and opposite reaction to the centripetal force, because we know that there exists such a centrifugal force and that it is equal and opposite to the centripetal force. Even I bought this line of reasoning last year before I had time to think about it properly. And when I was the one that advocated Newton's idea, Wolfkeeper's allies were very quick to argue against me. FyzixFighter was very quick to point out that centrifugal force does not form an action-reaction pair with centripetal force in a centrifuge. At the time, I was merely drawing attention to the fact that an outward centrifugal force existed which was equal and opposite to the centripetal force, and I made the mistake of saying that the two were an action-reaction pair. Wolfkeeper still believes that they are an action-reaction pair, and Newton claimed to believe it too. But now I know that FyzixFighter was actually correct on this technicality. To have an action-reaction pair we need to consider the situation over two bodies.

FyzixFighter however now makes a mistake in that by re-inserting the section 'reactive centrifugal force' on the main article, as it now stands, he is trying to correct Newton's error. He tries to explain reactive centrifugal force in relation to two bodies in order to be right with Newton's third law. But it was Newton himself who didn't apply his own third law correctly in relation to centrifugal force. Newton merely used his third law to confuse the deeper understanding that was provided by Leibniz's equation, and so Newton shares a large part of the blame for the edit war here. To answer Wolfkeeper's specific question, Newton's third law does not break down. But the fact that we have an equal and opposite centrifugal force/centripetal force in circular motion is not an appliacation of the third law because the two central forces are not in general equal and opposite. David Tombe (talk) 23:12, 27 May 2009 (UTC)


 * The centrifugal force that can be not equal to the centripetal force is not the same concept as the centrifugal reaction force, which is equal by definition. Dicklyon (talk) 00:53, 28 May 2009 (UTC)

Dick, there only is one centrifugal force. The reactive concept is a faulty way of looking at it in the special case of circular motion. David Tombe (talk) 13:25, 28 May 2009 (UTC)


 * Then why did you say the author of "In the Grip of the Distant Universe" has his head screwed on right? That book is totally about the reactive force due to inertia, and does not accord with the Leibniz view you like; the only point on which he agrees with you is that he doesn't like the "fictitious" concept.  Anyway, I'm no fan of the reactive force approach, but it's one that's out there, originated by Newton, and sometimes still taught.  It's very simple and doesn't lead to any problems; it's just not the same thing that the other approaches call centrifugal force, though in certain situations will be numerically equal, but acting on a different body. Dicklyon (talk) 20:16, 28 May 2009 (UTC)


 * Actually, there are some minor complications for non-circular orbits and such. The Graneaus sometimes refer to the entire reaction force in a central-force problem as centrifugal, and sometimes they resolve the reaction force into a linear component and a component radial to the osculating circle.  It would be better if they'd pick a definition and stick to it, but that problem is not unique to them.  Dicklyon (talk) 20:40, 28 May 2009 (UTC)

Break for new comment: are Coriolis forces "real"?
SBharris, There are two topics under discussion here,

(1) Planetary orbital theory, in which the Coriolis force is restricted to the transverse direction. According to that theory, Coriolis force can't be in any other direction and it is an integral aspect of the law of conservation of angular momentum (Kepler's law of areal velocity).
 * COMMENT. Kepler’s law of areal velocity is due to the conservation of angular momentum, for sure. But it happens just as surely to a twirling ice skater who pulls her arms in, so it’s got nothing to do with gravity, with the elipses and laws of planetary motion, or any of the rest of it. Furthermore, it’s got nothing to do with Coriolis force per se, since in non-rotating frames, there IS NO Coriolis force. If you look at a skater in a non-rotating frame, when she pulls in her arms she’s exerting a mechanical force on them, and that accelerates them. It’s not complicated. At the base of it, it’s like seeing an object moving along in a straight line, and giving it a pull exactly transversely. When you do that, it goes faster, and in a direction which passes closer to you (over time) than if you hadn’t pulled on it. There’s no Coriolis intrinsically there, any more than there is in any situation where you pull or push an object in a direction which is not exactly in the vector if its motion. This is not Coriolis force, it’s just force of the ordinary everyday kind. Coriolis is a NEW force which comes from having a rotating observer who has to “explain” new phenomena that don’t appear if the observer does NOT rotate. If your observer doesn’t rotate, Coriolis does not operate.  Along this line, I’ve been reading above where you’re saying some really odd things about Coriolis forces operating between something traveling in an inertial line, and a point off the line that the object passes. Nonsense! If the objects are too light or the distance too great for gravity to have any significant effect, then no force operates. If gravity is strong enough to bend the object hyberbolically, then that can be explained by straight pull mechanics and inertia, and there’s no reason to bring in Coriolis, Euler, or centrifugal or centripetal labels. In the latter case, only if the observer at the origin does something odd like rotating differentially to keep the object on the same line of sight, do you need any NEW forces. In that frame, now the incoming object behaves very oddly—coming in on a straight line directly toward the observer, then speeding up, then slowing down to a stop at a certain distance away, then immediately receeding again! All on the same line! That requires a lot of new forces to produce that motion—gravity alone will not do it. But they’re all a result of insisting on rotating the observer. Once again, Coriolis force does not even exist, unless you have put yourself in a rotating frame. That’s YOUR big error. If you’re in a frame where the stars are fixed, there’s no Coriolis force. There’s only the standard forces of nature, which act according to Newton’s laws.  No “standard force of nature” would cause an object to approach you, stop, then retreat, on the same line, without rockets or any other drive. To have that happen inertially requires something other than the pull of gravity. But if you don’t rotate, the pull of gravity suffices to describe the motion perfectly well. (All singley-indented answers are from  S  B Harris 01:52, 28 May 2009 (UTC))

(2) Rotating frames of reference/Fictitious forces. Modern textbooks have allowed the Coriolis force to be free to swing into the radial direction. I personally believe that that is a big mistake, but that is not the point at issue here. The point at issue is whether or not these two approaches to centrifugal force are the same. I say that they are different, for the very reason that in (1), Coriolis force is restricted to the transverse direction and tied up with Kepler's second law, whereas in (2), it is free to be in the radial direction also. You have now entered this discussion and drawn attention to what we all knew already. We know that the modern topic of fictitious forces allows for the Coriolis force to be in the radial direction. If you want to believe that, that's your problem. You think that you are being very clever when you point out the expression in vector product format and ask me if I am familiar with vector products. But you have wilfulfully ignored the derivation of that expression and the restriction that is inherent in it. And you keep repeating this error over and over again.
 * COMMENT. Hey, it’s not my derivation. But it is a perfectly good one. The derivation given is HOW WE DEFINE “Coriolis force” and the other fictious forces. And how they’ve been defined for centuries. If you want to write Tombe’s Textbook of Physics and have a Tombe Force which is different from Coriolis and only acts transversely/tangentially to a body’s motion, and never has a component which is radial, that’s fine. Go for it. But here on Wikipedia we’re talking about the Coriolis Force, not the Tombe Force. One fictitious force at a time, please.

The question is, 'why do we have one topic which clearly restricts the Coriolis force to the transverse direction and ties it up with Kepler's second law of planetary motion, whereas in another topic, the Coriolis force is free to be in any direction in the plane perpendicular to the rotation axis?'
 * And the answer is: that you assume facts not in evidence, because the Coriolis force is NOT tied up with Kepler’s laws of planetary motion or any other kind of motion (including the skater’s arm motion). The Coriolis force does not appear in any form unless you rotate your observer against the background of fixed stars. Until you do that, skaters and planets and all manner of systems can be described without recourse to Coriolis or Euler or centrifugal forces. In fact, no fictious forces of any kind are needed to describe their correct paths. Just the force of gravity, acting by Newton’s second and third laws, is quite sufficient. What you choose to call that force is up to you. You can call it “centripetal” if you like, just as you would in a centrifuge or a rotating space station (it’s what pushes up on the shoes of the astronaut). This one force is what keeps the planet from going off in a straight line ala Newton’s first law (and does the same for the astronaut). But no other force on the planet is needed if your observer does not rotate. There is no centrifugal force because the planet is moving in a curve, not moving in a line, so two forces adding to zero are not needed. And yes, the planet pulls on the Sun, but that’s not a new force ON THE PLANET (a force in the planet’s free-body diagram, which contains just one force). That’s the OTHER END of the force vector arrow, ala the 3rd law, and it applies to the SUN. It’s not fictitious, either.

I suggest that you now go to the central force chapter in Goldstein, and show us all how within the context of that chapter, the Coriolis force can walk out of Kepler's second law of planetary motion and walk into the radial equation at 3-11. When you can do that, then I'll believe Dick that these two approaches are one and the same topic.
 * Why would I want to do that? If Goldstein thinks that Coriolis force exists in systems which do not rotate, then he’s at odds with the definitions of modern physics also, and thus there’s no point in arguing with him over what Coriolis force is. The modern definition of Coriolis force is given above, and it exists only in rotating systems. Even using it in a system as simple as an incoming hyperbolic comet results (if you rotate in a somewhat trickily varying way, to keep the same line of sight between the objects) in a need for 3 new forces besides gravity to explain the very physically odd behavior of an object which 1) stays on a line but first approaches at a constant velocity, then 2) approaches faster, 3) slows, 4) stops, 5) recedes again, 6) recedes faster, and then 7) finally receds at a constant rate, once again. For a planet, it’s similarly irritating to watch it from constant line of sight, even if you’re on the primary (like the Sun). You can do it, but using the example of a planet or comet (where the rotation rate must be varied, introducing yet MORE complications) instead of a circling ball, adds no insight into fictitious forces at all, and only needlessly complicates the issue.

The punchline is that the fictitious forces topic has got it badly wrong. In a cyclone, the Coriolis force is a real transverse force that deflects the inward radial motion into the transverse direction. It is tied up with conservation of angular momentum. But in modern 'fictitious forces' study, the Coriolis force has somehow come to refer to the apparent transverse deflection that is observed from a rotating frame of reference. That entire topic has become loose at its hinges. But that's your problem if you want to believe it.
 * No, the punchline is that you believe that in a cyclone, exactly as with a skater, the translation of inward motion to faster “spin motion” (tangential rotation) is somehow connected to “Coriolis force” when in fact it has nothing whatsover to do with it. In a cyclone as in a skater, when you pull on something going by you, it goes even faster! Wow, call Physics News. That is Newton’s second law and it involves forces not fictitious (this is the only thing we agree on, probably). Coriolis forces only appear if you insist on viewing this situation (cyclone or skater or planet) from a rotating frame (where the fixed stars rotate also). But you don’t need to CHOOSE to do that. The arms of the skater and the winds of the cyclone still go faster when you pull them, but no fictitious forces are involved, because they may (if you wish) be banished by mere choice of coordinate system. The physics is all the same, if you just say “no”! I’m going to call this the Nancy Reagan Law of Coriolis Force.

Just don't try to tell us that it's all the same topic as planetary orbital theory. I copy out the radial equation 3-12 from Goldstein and you come along trying to tell me that I have left out the Coriolis force, and you try to justify it by copying out a pile of equations from another topic about rotating frames of reference? You basically just pushed Goldstein's chapter 3 aside and brought in another topic, and then claimed that Goldstein's chapter 3 is wrong because the Coriolis force doesn't appear in the radial planetary orbital equation at 3-12. David Tombe (talk) 22:42, 27 May 2009 (UTC)
 * Have it your way, then. But however you have it, please be assured that Coriolis force can always be removed by choosing your observer to be non-rotating with regard to the fixed stars. If you refuse to do that, the problems in store for you are your problem. Please don’t come here and tell us that they have to do the reality of WHY things happen. And as for describing how they happen, or the easiest way to calculate that, please stick to historical definitions, not your own. S  B Harris 01:52, 28 May 2009 (UTC)


 * So much nonsense. Coriolis force is purely transverse when the motion is purely radial, as in the co-rotating frame.  That's all. Dicklyon (talk) 00:54, 28 May 2009 (UTC)

Are there fictitious-looking "force terms" that arise in polar-coord descriptions of things seen by inertial observers?

 * There is a term in polar coordinates that always acts transverse (acts on the angular rotation) that is sometimes referred to as coriolis see (Polar_coordinates). That's Tombe's problem- he only understands the polar form; in the orthogonal vector form the coriolis force there can point in any direction. So it's not a planetary thing per se, it's polar. It's just that orbits are traditionally analysed using polar coordinates.- (User) Wolfkeeper (Talk) 12:46, 28 May 2009 (UTC)


 * I think that this article should probably mention the polar form of centrifugal force, as it's not quite the same as reactive or rotating reference frames.- (User) Wolfkeeper (Talk) 12:46, 28 May 2009 (UTC)


 * NO! You should probably go back and re-write the whole section you refer to. Because of the simplity of polar coordinate descriptions, there are terms in the equations for MOTION in polar coordinates which are referred to as though they were force-terms. But that's like writing "F = ma" for the linear case and saying "ma" stands for a force. Here, "ma" is just a motion caused by the force. Similarly the inertial observer will see terms in the polar equations for things moving in circles, which look like force terms-- such as mrω2, which looks like centrifugal force. But it's not a force-- it's simply a description of motion and doesn't require it's own special force to cause it, as a term. There are no "fictitious forces" in polar coordinate descriptions from inertial observers. There are only terms which describe motion, which you can (wrongly) imagine are each caused by some particular new ficitious force. It doesn't help for this simple case, where if you choose to have a co-rotating observer in a frame of rotation Ω = ω (and with the observer fixed at the origin of r), now you DO get force terms which look exactly the same: mrΩ2, except that Ω now no longer represents motion of the body, but rather the rotation of the FRAME, so the term containing it now must now represent a fictitious force, acting on a body which HAS NO MOTION described by that term (now that we removed it by co-rotating). So NOW in this case, NO MOTION IS BEING DESCRIBED. So that term now really IS a force-- a fictitious one called centrifugal force (which appears to EXPLAIN the fact that now we have no motion due to this term, where we did before). But don't make the mistake of thinking it's centrifugal force when it's merely a body-motion term in a polar inertial-observer equation. It's NOT. So it's still true that no matter what kind of coordinates you use, fictitious forces only arrise in accelerated frames.  S  B Harris 21:46, 28 May 2009 (UTC)

Wolfkeeper, it's an inertial effect. Polar coordinates are only a language used to describe it. It is the one and only Coriolis force and it is a transverse effect which conserves angular momentum. It can be felt directly when we try to restrain a rotating radial motion. As regards introducing a third approach to centrifugal force in this regard, that's exactly what I have been trying to do. But it is not a different centrifugal force as you seem to be suggesting. It is the most general way of looking at the one and only centrifugal force. David Tombe (talk) 13:24, 28 May 2009 (UTC)


 * Nah, there's 3 different equations for centrifugal force:


 * reactive centrifugal force (omega is the angular speed around the rotation centre, which is not necessarily stationary)
 * rotating reference frames centrifugal force (omega is the frame rotation)
 * polar coordinate centrifugal force (omega is the particle angular speed in the reference frame)


 * Reactive centrifugal force is always equal and opposite to another force.


 * Rotating reference frames centrifugal force appears when the frame is rotating.


 * Polar coordinate centrifugal force appears when the object moves around the origin (this can occur in addition to the rotating reference frame centrifugal force if the reference frame is rotating as well.)- (User) Wolfkeeper (Talk) 13:29, 28 May 2009 (UTC)


 * I think the polar coordinates analysis should be thought of not as a different approach, but some math that helps to connect the inertial frame analysis to the rotating frame analysis. In the polar coordinates, it's easy to take a centripetal force or acceleration in the inertial frame and move it across to be a centrifugal force in the rotating frame; you get Coriolis forces a the same time.  The relevant term is not the reactive centrifugal force, except that it happens to match in the case of circular motion.  The reaction force approach remains distinct; it's about an outward force on the body causing the curve path, not on the particle in the curved path.  It's too bad both use the same name, but that's the way it's been since Newton and his supporters; as Meli say, "Newton's theory of centrifugal force followed a case-by-case pattern."  Basically, different coordinate systems can lead to very different equations, but they don't mean different things.  Dicklyon (talk) 15:41, 28 May 2009 (UTC)

Wolfkeeper, those are three different approaches to centrifugal force. Are you going to side with me now against dicklyon and FyzixFighter who have been trying to suppress references to the third kind? David Tombe (talk) 13:36, 28 May 2009 (UTC)


 * No offense intended Wolfkeeper, but I disagree with you on the three types idea. And David, just because Wolfkeeper or any other editor thinks there's three does not mean that we get to put that in the article. Sources determine what goes in the article, not our opinions and original thoughts. Do we have any references that distinguish between the rotating frames and polar coordinate concepts? I would argue that Taylor Ch 9 and the Kobayashi reference indicate that the polar coordinate concept is a special case of the rotating frame concept, specifically that of a co-rotating frame. Even if I do come around to the idea, given that we have two references that say that there are two valid and distinct concepts of centrifugal force, we need another reference to say that there is a third distinct concept. We have some references that call the $$-r\dot\theta^2$$ term in the radial acceleration the "centripetal acceleration term" or something similar. Are there references that call it the centrifugal force when it appears on the acceleration side of F=ma? --FyzixFighter (talk) 14:03, 28 May 2009 (UTC)


 * They can be considered to be logically distinct because the omegas in each case are different. You're right that the rotating reference frame and polar coordinates are similar and highly related, but the coriolis force in polar coordinates and rotating reference frames points in different directions- the equations these are terms in are very different. You can make a rotating reference frame behave the same as polar coordinates, rotating reference frames are more general. There's also a point about coordinate systems and reference frames being logically different though.- (User) Wolfkeeper (Talk) 14:16, 28 May 2009 (UTC)


 * There's also practical problems with asserting that there's only two, because a lot of people reading the wikipedia won't have been exposed to rotating reference frames, whereas polar coordinates are widely taught. So even though it can be considered more or less a special case, it's not that helpful to treat it entirely that way.- (User) Wolfkeeper (Talk) 14:16, 28 May 2009 (UTC)


 * I agree with you on the Coriolis force comment. Taylor does as much, calling it the "Coriolis acceleration" (pg 29). Taylor does connect it up with the rotating frame concept in chapter 9 via the co-rotating frame.
 * I might be able to say that the polar coordinate concept is more closely tied to d'Alembert's principle, but most texts treat that as equivalent to the rotating frame formulation - to the point that we call fictitious forces d'Alembert forces. Kobayashi argues that there is a subtle difference, but ultimately lumps the two together, again the d'Alembert principle being the special case of co-rotating frame with axis at the origin. Note that in the corotating frame, the two omegas by definition are the same, but you are right that the general rotating frame formulation works even when the two omegas are not the same, in which case d'Alembert's effective equipollent force is not the same as the rotating frame's centrifugal force. An in-depth discussion of the subtlety would probably be more appropriate on the Centrifugal force (rotating reference frame) article rather than on this summary article.
 * Nevertheless, a source would be helpful. I ask this of David, and it would be unfair for me not to ask this of others and of myself. Let's not dumb down the subject to the point of being wrong. We have sources for the rotating frame and the reactive concepts, let's get a source for the polar coordinate one and try find an equitable compromise to include everything with a valid source. --FyzixFighter (talk) 14:48, 28 May 2009 (UTC)


 * I think that even if you consider the d'Alembert form to be a superset of polar coordinates (which it more or less is) then still for a considerable period of history the polar form seems to have been the only other game in town than the reactive force, so at least the history section needs to cover it, and it would be good to mention the exact way in which it is a superset.- (User) Wolfkeeper (Talk) 19:26, 28 May 2009 (UTC)


 * Are there any particular sources/references that you have in mind that can guide how this concept can be worked into the history section? I ask mainly because the few "history of physics"-type sources I've found seem to jump immediately from the emergence of Newtonian dynamics and the Huygens/Cartesian/Newton/Leibniz centrifugal debate to the rotating frame concept and the fictitious/pseudo centrifugal force in the second half of the 18th century and early 19th century. --FyzixFighter (talk) 19:47, 28 May 2009 (UTC)

There are only two equations involved in this entire topic
FyzixFighter, It's because of interventions such as that by SBHarris that we need to understand the physics as a priority before we can write a coherent article. We cannot, as you have just suggested, write a coherent article based on a patchwork of conflicting sources. Unlike SBharris, you do at least appear to have grasped the essentials of the topic, but you are playing silly games with names and references. We have two equations to consider in central force theory and these two equations totally describe the inertial path.

There is a radial equation which in essence is Goldstein's equation 3-11, with gravity inserted for the centripetal force,


 * $$ \ddot r = -G(M+m)r^{-2} + r\dot\theta^2$$

It is essentially Leibniz's equation. It contains the gravitational attractive acceleration (inverse square law), and the centrifugal repulsive acceleration. This solves to give a conic section inertial path. Kepler's first law of planetary motion is an example of this.

Then there is the transverse equation,


 * $$2\dot r\dot\theta + r\ddot\theta = 0$$

The transverse equation follows from Kepler's second law of planetary motion. It contains the Coriolis force and what you guys have been referring to as the Euler force. We can use the transverse equation to make the centrifugal force in the radial equation into an inverse cube law term in line with Leibniz's equation. The significance of the transverse equation is clear. In a cyclone, the inward radial motion will be deflected into the transverse direction. That is real Coriolis force as in an object following its inertial path. Rotating frames of reference don't enter into it. They are just an additional complication.

While you and Dick understand this, you are playing silly games. You are trying to deny the names of the terms, even though I have already produced sources which apply the names centrifugal force and Coriolis force to the respective terms in these equations. Dick is fixated on the fact that the Coriolis force is only restricted to the transverse direction in the special case when the inducing velocity is radial. But it can't be any other way. There is no provision in nature for it to be any other way.

SBharris clearly doesn't understand the topic at all. He tried to tell me that equation 3-12 in Goldstein is wrong because it doesn't contain a Coriolis force term. He didn't realize that the Coriolis term is in the transverse equation, and he is clearly incapable of seeing how it links in to the conservation of angular momentum. He has just tried to tell me above that the Coriolis force has got nothing to do with the conservation of angular momentum. The idea of writing wikipedia articles is to inform people. But your deliberate attempts to obstruct me in that regard have given the green light to people such as SBharris, who clearly haven't got the first clue about the subject, to come in and join your group and make themselves believe that they have got something positive to contribute to the article. David Tombe (talk) 13:18, 28 May 2009 (UTC)
 * Indeed, the Coriolis force has nothing to do with the conservation of angular momentum. If you stay away from radial coordinates, and you keep your observer in an inertial frame (two things you can always choose to do; and neither of which affects the physics), you never see a Coriolis force. And yet angular momentum continues to be conserved. THEREFORE the "Coriolis force" does not help conserve angular momentum. The Coriolis force isn't necessary. Since the Coriolus force can always be made to disappear by suitable observer choice and coordinate notation choice, it's not part of physics. Conservation of angular momentum is. S  B Harris 21:13, 28 May 2009 (UTC)


 * As I said before, there is a subtle distinction between Leibniz's equation:
 * $$\ddot r = -G(M+m)r^{-2} + r\dot\theta^2$$
 * and Goldstein 3-11/12, namely that Harry Lime is on different sides of the equal sign. As indicated by multiple references, when Harry Lime is on the other side it's part of the radial acceleration and the equation is for an inertial frame (Goldstein calls it a centripetal acceleration term). The sources also indicate that moving Harry Lime to the side that Leibniz writes it on corresponds to transforming to a rotating frame where it becomes the centrifugal force associated with that rotating frame.
 * As for comments on sources, I don't recall you providing any sources that apply the name centrifugal force to that term in the inertial frame. The sources we are using do not conflict, only your interpretation of them does. Again, provide sources that explicitly say what you want to include and we'll get along. The idea of writing wikipedia articles is to inform people using reliable sources, not using our own personal theories on the subject. Appealing to reliable sources allows us to easily correct mistaken ideas. I'd recommend that Sbharris take a look at the Whiting letter I mentioned above and the Kobayashi reference for a clear explanation of what I think he is trying to discuss with you. --FyzixFighter (talk) 14:24, 28 May 2009 (UTC)

FyzixFighter, I can see that you do now understand the topic. But you must realize that I am simply not going to buy the idea that a centrifugal force can become a centripetal force simply by shifting it to the other side of an equation, even if there are misinformed references that imply that. Dick also appears to understand the topic, but he has shown serious tendencies to want to follow up that idea about changing centrifugal force into centripetal force by changing it to the other side of the equation. So long as you and Dick can use confused references to confuse the topic, then we are not going to get anywhere.

Let's compare a few positions.

(1) Wolfkeeper. He has identified correctly that all is not the same as between the rotating frames approach and what he terms the polar coordinates approach.

(2) Dick. He claims that the two overlap in the special case of co-rotation.

My own position as you already know is that the rotating frames approach is total nonsense when it is extrapolated to non-co-rotation situations. This then leaves a large degree of agreement between myself, Dick, Wolfkeeper, and probably yourself as regards the underlying physics behind the co-rotation situations.

As regards co-rotation, I am advocating that we simply don't need to involve rotating frames of reference at all, and I have pointed to Goldstein as a gold standard reference which treats the inertial path without any reference to rotating frames of reference. My own view on all of this is that centrifugal force and Coriolis force are built into the inertial path. Wolfkeeper doesn't quite see it in such simple terms. Wolfkeeper rationalizes with it in terms of polar coordinates. Now I am all in favour of polar coordinates because they are the only viable language for expressing central force problems in. But centrifugal force is not a product specifically of polar coordinates, as Wolfkeeper seems to think. Centrifugal force and Coriolis force are properties of space. We get different centrifugal forces and Coriolis forces when we choose different point origins, and in that respect they are 'relative' quantities. But they are also absolute in the sense that absolute rotation relative to the background stars is what determines their value for a chosen point of reference. Such is the nature of space.

Rotating frames of reference have actually totally messed this subject up. And although I acknowledge that most of the modern textbooks on the science library shelves promote centrifugal force as being something that is only observed in a rotating frame of reference, there are still a few left which don't take this approach.

In my opinion, centrifugal force and Coriolis force are inertial forces and they don't need to be understood in terms of rotating frames of reference. I have got a few sources to back that idea up. I suggest that we totally remove the reference to 'two' approaches to centrifugal force in the introduction, because the literature clearly talks about at least three approaches. David Tombe (talk) 16:46, 28 May 2009 (UTC)


 * Start providing the sources then so that we can discuss them. As the 'two' approaches in the intro are supported by two references, removal of such and/or inclusion of a distinct third approach requires another reliable source that explicitly says as much. While you may believe the references are misinformed, they pass wikipedia's criteria for reliable sources, thus the viewpoint they contain goes in the article. NPOV says that we report all significant, verifiable viewpoints supported by reliable sources. --FyzixFighter (talk) 17:11, 28 May 2009 (UTC)

FyzixFighter, we can start with Shankar 1994. Here is a clear reference to centrifugal force outside of the context of rotating frames of reference. But I'm sorry that you have chosen to play this silly game. I'm trying to make the article correct and readable. You think you're playing a clever game by using the many conflicting sources in the literature to undermine what I'm trying to do.

And just for good measure, on page 179 in Goldstein (second edition (1980) before Poole and Shaftoe got the hold of it in 2002) writes,

"Incidentally, the centrifugal force on a particle arising from the earth's revolution around the Sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the Sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun."

There is no mention of rotating frames of reference in either the first edition (1950) or the second edition (1980). However in the 2002 edition, the new editors have added an extra bit in about rotating frames of reference to justify their own prejudices. They are obviously from that generation that have been brainwashed into thinking that you can't have a centrifugal force unless you strap a rotating frame of reference around the problem.

Also on page 78 in the second edition, beginning sixth line down on discussing planetary orbits, Goldstein writes,

"A particle will come in from infinity, strike the "repulsive centrifugal barrier", be repelled, and travel back out to infinite". Some illusion! David Tombe (talk) 17:22, 28 May 2009 (UTC)


 * Sorry but these do not support what you are trying to put into the article. Specifically they do not support the statement that the centrifugal force exists in the inertial frame. Lack of discussion of rotating frames is not the same as confining the discussion to an inertial frame. Especially when we have multiple other references that do the same analysis and explicitly state the transformation from an inertial to non-inertial frame.
 * For example, Shankar doesn't mention frames - so we cannot say that he supports the statement that the centrifugal force exists as a real force in an inertial frame. Note that he also refers to them as terms and not forces. This is probably due to the fact that he distinguishes between generalized forces and real forces. See his comment on the previous page:
 * "Although the rate of change of the canonical momentum equals the generalized force, one must remember that neither is pi always a linear momentum (mass times velocity or "mv" momentum), nor is Fi always a force (with dimensions of mass times acceleration)."
 * As to the Goldstein references, since Goldstein makes no comments about frames, he also cannot be used to either support or contradict your assertions. I would argue that Goldstein's description of the centrifugal force as the "reversed effective force" of the centripetal acceleration supports the "fictitious" designation per D'Alembert's principle. Also, your throwing out of the 2002 edition is unacceptable - if you disagree, we could always ask an admin to weigh in or to tell us what the criteria is for throwing out a reliable source. The editions are not mutually exclusive if you accept that no statement of a reference frame does not imply an inertial frame. I also object to your characterization as the rotating frame as a recent paradigm shift. As already indicated by one of the historical references, Lagrange stated it specifically that the centrifugal force is due to the rotating coordinate system and not inherent to the motion of the particle. Also, I've been able to find a 1904 reference that agrees with the rotating reference frame formulation (Whittaker, "Analytical Dynamics", 1904). Speaking of going from a inertial system to a rotating system, he states on page 41, "The term centrifugal forces is sometimes used of the imaginary forces introduced in this way to represent the effect of the enforce rotation."
 * If you disagree with my assessment of the sources, the best thing to do would be to get a third opinion or put request in over at the Reliable sources noticeboard to get some uninvolved editors/admins to comment. --FyzixFighter (talk) 18:43, 28 May 2009 (UTC)

FyzixFighter, we already know that the adminsitrators have been totally fooled by you. We saw the kind of comments that they made on the noticeboard when I went there to report you for wiki-hounding. I have given you reliable sources to show that it is not necessary to involve rotating frames of reference when considering centrifugal force. You have managed to present some false counter arguments that could only be swallowed in this particular arena. There are other editors here who can't agree amongst themselves, but for whatever reason, they have a mutual pact to make sure that they will religiously disgree with whatever I say, whether it is sourced or not. You are playing silly games at the expense of the reader. My suspicions are that you have got some vested interest in hiding the truth surrounding this topic. David Tombe (talk) 18:52, 28 May 2009 (UTC)


 * David, I've been trying to restrain my tendency to express my feelings when discussing technical topics, but just for the record, let me say that you are completely "full of crap". That's a technical term, like "bullshit", only more so.  Enough said. Dicklyon (talk) 18:57, 28 May 2009 (UTC)

No Dick, you and FyzixFighter have both got the same agenda. You are trying to mask the reality of the outward expansion that comes with absolute rotation, because it doesn't fit your own pet theories about relativity. You are breaking all the rules here and getting away with it because you have fooled the administrators. I have just presented some sources, and what you have just written above is the best that you can reply to them because you know fine well that you are in the wrong. You clearly understand this topic, but you have also been clearly trying to distort it. You want the article to be confused. David Tombe (talk) 19:03, 28 May 2009 (UTC)


 * There were no sources in the paragraph I was responding to; just personal attacks and paranoid accusations. That behavior, as well as your topical self delusion, is what is full of crap. Dicklyon (talk) 20:20, 28 May 2009 (UTC)


 * (after two ECs) Well, if you're not willing to go through the established channels for dispute resolution and you don't want to abide by basic wikipedia policies and guidelines like verifiability and reliable sources, then perhaps editing wikipedia is not the place for you and your opinions. I'm also open to both formal and informal mediation. I feel it's too bad we haven't heard much from Wilhelm recently. Perhaps you'd like to ask him as an acceptable neutral party to weigh in on my assessment of the sources? I really don't have any vested interest other than a desire to improve wikipedia. Do you have a vested interest in vehemently pushing this point of view of the topic? --FyzixFighter (talk) 19:06, 28 May 2009 (UTC)

FyzixFighter, you asked me for sources that dealt with centrifugal force as an inertial force outside of the context of rotating frames of reference. I gave you such sources. You responded to the extent that since my sources did not mention rotating frames of reference that they did not mean that centrifugal force could be dealt with outside of the context of rotating frames of reference. That is the kind of response that people make when they are playing to a biased crowd. We have a biased crowd here, and we always have had since this edit war began. You guys don't want any attention drawn to the reality of centrifugal force as a real outward expansion pressure. You want the readers to believe that it is just some mathematical illusion of transformation equations in rotating frames of reference. And you have fooled every adminstrator that has entered the arena, mainly because they are of that ilk that think that truth is a product of consensus. David Tombe (talk) 19:20, 28 May 2009 (UTC)


 * Actually I asked for sources that directly supported your claim that the centrifugal force is a real force existing in inertial frames. As to getting an unbiased commenter, that's why I suggested that you ask Wilhelm to weigh in. Maybe I misunderstand your opinion of him, but it appears that you have at least more respect for his opinion than that of the "hostile crowd" of editors and administrators you think I'm playing to. Otherwise, if you don't want to play by the rules of the community (ie WP:DR,WP:V,WP:RS,WP:OR), you are more than welcome to take your ball and go home. --FyzixFighter (talk) 19:39, 28 May 2009 (UTC)

FyzixFighter, There are references to support the fact that centrifugal force appears in the literature in connection with,

(1) rotating frames of reference. (2) As the inertial terms when Newton's laws are expressed in polar coordinates. (3) As a reaction to a centripetal force.

I have my own opinions regarding all three of these and where they link together. But at the moment, you are only recognizing (1) and (3) in the introduction. You have a vested interest in suppressing (2). Under wikipedia's rules, I could insert it. But we have all seen how wikipedia's rules are not always upheld by the powers to be when it comes to the crunch. I might claim that I had fully sourced an edit only to find myself blocked for something like going against a consensus. I'm not going to take the risk. I have shown you guys the underlying unity in the subject, so you can take it or leave it. I wouldn't have perservered for so long if it wasn't for the fact that there is a wider readership to consider. It was necessary to see if the system has a mechanism in place to deal with people like yourself who are engaged in a very subtle kind of vandalism. You have succeeded in pulling the wool over the eyes of the administrators for the simple reason that the topic is too complicated. You understand it, but you have a vested interest in distorting it, using conflicting sources, and the administrators simply can't see right through you. David Tombe (talk) 20:14, 28 May 2009 (UTC)