Talk:Centrifugal force/Archive 14

Cartoon
Objection is raised by Mintrick over using the cartoon to illustrate the point that centrifugal force has real effects. I think the objection is pedantic - there is no danger of misleading anyone, and the purpose is just illustration, not scholarly backup. Brews ohare (talk) 22:31, 19 June 2009 (UTC)
 * There's no illustration, it's merely an attempt at humor. There is no informative purpose to the link, and it should not be included. Mintrick (talk) 22:32, 19 June 2009 (UTC)

The informative purpose is stated accurately in the balloons. It does make you chuckle, and the point is dead on. Brews ohare (talk) 22:33, 19 June 2009 (UTC)
 * There's no informative purpose; it's merely a restatement of the facts already in the article. The only point is an attempt at humor, which is not an encyclopedic reason to include a link. Mintrick (talk) 22:34, 19 June 2009 (UTC)
 * Being redundant is not a reason for removal. Neither is being humorous.  In fact, that's where it gets its power.  Dicklyon (talk) 05:03, 20 June 2009 (UTC)
 * External links need to have an encyclopedic purpose. This one does not have it (and I've seen no legitimately argue that it does). I'm sure we're all very pleased about nerd humor, but it simply doesn't belong here. There is no new information in the comic, and thus it does not merit a link. Mintrick (talk) 05:58, 20 June 2009 (UTC)
 * I agree with Brews ohare and Dicklyon - I think the cartoon link should stay. Actually, it illustrates an important point. In either frame of reference it is the centripetal force that actually crushes Bond. The villain mistakenly assumes that the rotating Bond is in equilibrium so he believes the centripetal force must be balanced by an equal and opposite centrifugal force. In the villain's inertial frame of reference we can see the villain's mistake - Bond is not in equilibrium, so the forces on him do not need to balance, and there is no centrifugal force. Bond wins again.Gandalf61 (talk) 16:45, 20 June 2009 (UTC)
 * I don't think you correctly understand the cartoon, but in any case, the cartoon should stay. I just wish the license was compatible. Cartoons have a long and illustrious history in physics textbooks and so forth.- (User) Wolfkeeper (Talk) 14:59, 21 June 2009 (UTC)


 * Gandalf61, there would be no centripetal force in that scenario unless there were a centrifugal force to begin with. The centripetal force is a reaction to the centrifugal force, just as the upward normal reaction of a surface is a reaction to downward gravity.


 * Your argument would be the same as saying that gravity doesn't kill somebody who falls over a cliff. The truth is that it is the combined effect of the gravity and the normal reaction that kills somebody when they fall over a cliff. Likewise, it is the combined pressure of the centrifugal force and the centripetal force which is going to kill the man in the sketch.


 * As regards the sketch itself, I disapprove of it because it backs up that modern misinformed viewpoint that centrifugal force does not exist, and it cheapens the tone of the article. David Tombe (talk) 10:25, 21 June 2009 (UTC)


 * David - your analogy with gravity is absolutely correct. A person in free fall in a 1g gravitational field (or even in a 100g gravitational field) feels nothing - they are not "crushed" by gravity. The centrifuge exerts a centripetal force on Bond and Bond exerts an equal and opposite force on the centrfuge - but Bond cannot be crushed by a force that he exerts himself. You are confusing the forces exerted on an object with the forces exerted by an object on other objects. But your fundamental mistake is to think that the forces on Bond must be balanced - they are not, as he is not in equilibrium. Gandalf61 (talk) 11:35, 21 June 2009 (UTC)


 * Gravity has never killed anyone. It's the impact that does that; and this is not simply a joke.- (User) Wolfkeeper (Talk) 15:12, 21 June 2009 (UTC)


 * The cartoon is useful precisely because it helps to illustrate the meaning of fictitious force, a standard physics concept that some, as David Tombe illustrates, just do not get. Dicklyon (talk) 17:49, 21 June 2009 (UTC)

The centrifuge exerts a centripetal force on Bond BECAUSE OF the centrifugal force which is already acting on Bond. The centripetal force in this situation is a reaction to the inverse cube law centrifugal force in the Leibniz equation. Likewise, the normal reaction at the surface of the Earth kills a falling person BECAUSE OF gravity. In either of these two scenarios, there would be no lethal centripetal force nor any lethal normal reaction if it were not for the pro-active centrifugal force or the pro-active gravity in the first place.

As regards the force which Bond transmits to the wall of the centrifuge, this is not actually what is being catered for by the concept of 'reactive centrifugal force'. The so-called 'reactive centrifugal force' of Isaac Newton acts on the same body as the centripetal force. That is clear from the 1961 Nelkon & Parker reference which I once supplied. I know that you will all immediately say that Newton's third law must act over two bodies. And so it does. But Newton's concept of 'reactive centrifugal force' is not actually compatible with the very third law that he invented it to be compatible with. Newton was just being twisted when he stated that centrifugal force is the equal and opposite reaction to a centripetal force. He was being twisted because he was jealous of the fact that Leibniz discovered the inverse cube law relationship for centrifugal force.

As regards the cartoon, I don't think it's the kind of method that would be used in Encyclopaedia Britannica or Encyclopaedia Americana. The cartoon basically exposes two viewpoints on centrifugal force. Bond takes the A-level High School approach that centrifugal force doesn't exist and that only centripetal force exists. Bond's enemy takes the rotating frames\fictitious approach that centrifugal force exists but only in a rotating frame of reference.

But all this does is further confuses a topic which is already in a state of gross confusion. Neither Bond nor his enemy consider either Newton's erroneous approach to centrifugal force or Leibniz's approach. The fact is that Bond will be crushed if his enemy gets his way. That crushing will be a reality which will not be dependent upon which frame of reference the situation is being observed from.

You guys have already accepted that the erroneous Newtonian centrifugal force is observed from any frame of reference. The Newtonian centrifugal force is in actual fact a special case of the Leibniz centrifugal force for circular motion. It is the one and only Leibniz centrifugal force in conjunction with the reactive centripetal force that will kill bond.

The cartoon compares two faulty viewpoints against each other and neglects the true explanation. That is my main reason for objecting to the cartoon. The cartoon is misleading. David Tombe (talk) 10:35, 22 June 2009 (UTC)


 * See what I mean? Dicklyon (talk) 14:56, 22 June 2009 (UTC)


 * Yes. David Tombe can't do the maths, and doesn't believe people that can do the maths. Expressing something in polar coordinates is not the same as describing something in rotating reference frames.- (User) Wolfkeeper (Talk) 16:48, 22 June 2009 (UTC)

As usual, David adopts the frame of reference attached to Bond in which the centripetal and centrifugal forces both appear on the force side of Newton's law. Thus it is a bit of a "hen or egg" problem which "causes" which. It's probably a more neutral stance to suggest simply that both forces are present, and not try to attribute one to the other.

My impression looking at the older literature is that what we see here on the talk page is the very same debate that occupied many minds in and around Newton's times. Thus, the main criticism of David's view is that it is stuck in the past, before the time that people realized that frame of reference was a major consideration. It readily fogs things up because the local frame of reference is so intuitive it simply grabs the mind and detaches it from the formalism. However, the formalism is a much better guide than intuition in synthesizing all the facts, particularly when it comes to relating the experiences of observers in different states of rotation.

An example that David might enjoy as he loves planetary theory, would be the theory of the tides from (i) the Earth's point of view, (ii) the Moon's point of view and (iii) the Sun's point of view. Brews ohare (talk) 20:17, 22 June 2009 (UTC)


 * Brews, the theory of the tides is indeed a very interesting topic. I doubt very much if the estbalished theory is correct. I was recently engaged in a debate on a forum in which alternative ideas were being suggested, but wikipedia rules would not permit the discussion of those ideas here.


 * As regards rotating frames of reference, I can only see the need for such a concept where it represents a physically real entity. For example, meteorology can be analyzed in relation to a rotating frame of reference because we are dealing with the atmosphere which is being dragged by the rotating Earth. I would differ however from established thinking in that what they would consider to be the 'pole centred' Coriolis force, I would see as being merely an apparent deflection due to a lack of dragging force. I would see the real Coriolis force as being 'cyclone centred' and tied up with the law of conservation of angular momentum.


 * As regards a planetary orbit, I can see absolutely no need to introduce a rotating frame of reference. The radial equation (as per Leibniz, and equation 3-12 in Goldstein) perfectly exposes the centrifugal force as an outward inverse cube law force without the need for a rotating frame of reference within which to comprehend the concept.


 * This whole issue becomes of great important when we consider the multi-body problem. Although we cannot solve the three body problem (or higher) analytically, we can still consider the question of whether centrifugal force is the product of a single rotating frame of reference, or if it is a mutual effect over any chosen pair of particles. In the latter case it would lead to the idea that two adjacent two-body orbits would repel each other if the rotation speeds were suitably high. This is the principle that Maxwell uses when he explains magnetic repulsion. But I have seen no reference in the literature to this idea since the time of Maxwell. Nevetherless, we all know that two rotating objects will expand radially if they are soft, and that they will therefore push each other apart when they come into contact with each other. It is this very real outward pressure aspect of centrifugal force which is being denied by the rotating frames/fictitious approach. We can nevertheless see the principle in operation in Newton's rotating bucket. David Tombe (talk) 12:38, 25 June 2009 (UTC)

Unsourced assertions
Dick: I don't know where you get the idea this stuff you deleted is unsourced. Just prior to the footnote the numbers are provided with their sources. Then in the footnote itself a pdf file is cited from the geodesic society that gives the accepted number for 1/f. So the two estimates are sourced and irrefutable. Is the problem that calculating the 23% difference is unsourced arithmetic? Would you like a sub-section with sources explaining how to calculate a percent error??? Or could it be that you just did a knee-jerk reaction here without realizing the numbers all are sourced?Brews ohare (talk) 22:36, 25 June 2009 (UTC)


 * The footnote read "The error looks worse if the common measure of flattening f is used (see Clairaut's theorem), the ratio of the difference between semi-major and semi-minor axes divided by the semi-major axis. The flattening by Newton is f = 1/230, while that from the measurements is f = 1/298.4623304, an error of about 23%. See also Table 1.1 of the report by the International Association of Geodesy."


 * The assertion that "the error looks worse" is unsourced. The number 1/298.4623304 is unsourced, even though a statement of 10 significant digits practically screams for a source.  The linked article has a different number, and fewer digits.  The "error of about 23%" is your interpretation of the relationship between the numbers, I presume, but is there a source for that way of comparing flattening?  No source provided.  I don't understand how you don't understand what unsourced means.  Read WP:V and WP:RS.  Dicklyon (talk) 05:12, 26 June 2009 (UTC)

Well Dick here is how it goes. The modern estimates of semimajor and semiminor axes are sourced as the values 6356.77 km & 6378.14 km leading to an f of (6378.14 - 6356.77)/6378.14 = 0.003350 or 1/298.4623. The cited Table 1.1 has f = 1/298.25642±10−5, not enough different to matter here. Newton's numbers are sourced as a ratio of diameters of 229 to 230 or an f =(230-229)/230 = 1/230 = 0.004348. Taking the modern estimate as the more accurate the size of percent error is (|0.003350- 0.004348|)/0.004348 × 100 ≈ 23 %. How would you like this information to be presented? For a definition of flattening f see Clairaut's theorem. Brews ohare (talk) 05:38, 26 June 2009 (UTC)

Inertia
Dick, what you have done is to replace a more specific meaning (momentum) with a more general term (inertia) that has got at least two meanings. Even if you look at the wikipedia article about inertia, you will see that some editor has realized that the word inertia has got a common meaning of momentum which differs from its more accurate meaning of 'resistance to change'.

As regards 'centrifugal force', when we use the word inertia in this context, we are talking about momentum as opposed to the more accurate meaning of inertia which is 'resistance to change'.

I think that your reversion of my clarifying edit was motivated more by your own inertia (in the more accurate sense of the word) rather than by any desire to help clarify the wording.

Your point about the momentum being orthogonal to the centrifugal force is a true fact in its own right but it in no way diminishes the accuracy of stating that centrifugal force is an outward force that is associated with momentum.

It can of course be argued that the whole essence of momentum is its resistance to change, hence making the two meanings tend to blend into one. But there is still a subtle distinction between the two meanings because by the same token, we can equate inertial mass with inertia, yet nobody is trying to say that momentum is the same thing as inertial mass. The word inertia truly is a classical archaic broad spectrum terminology. I was merely trying to write the introduction using modern scientific terminologies.

On reflection, how about simply stating that centrifugal force is the outward force that arises in connection with rotation, and totally dropping all mention of either inertia or momentum? The simpler the introducing line, the better. David Tombe (talk) 11:34, 5 July 2009 (UTC)

Planetary Orbital Theory
FyzixFighter, you have removed a fully sourced section on the false grounds that Leibniz's views are already covered in the history section. That has got nothing to do with the fact that the planetary orbital equation in question is still used in modern textbooks. This is nota matter of history. I am therefore going to restore the section because it is accurate, fully sourced, and totally relevant to the topic. What legitimate reason can you possibly have for objecting to its inclusion? Even if you think that the centrifugal force in question is a manifestation of the fictitious force, that is still not a reason to remove the information in question. David Tombe (talk) 16:17, 9 July 2009 (UTC)


 * If it's going to be in there, it needs to point out that it's talk about a pseudo-force induced by the fact that the r coordinate is measured along a vector that is co-rotating with the planet, and that it's just a special case of that rotating system approach. Probably should be integrated into the relevant section.  Dicklyon (talk) 17:47, 9 July 2009 (UTC)


 * I agree with you in part Dick. The planetary orbit equation is a subset/special case of the fictitious force concept. It really is only of interest in this general article in terms of the history of centrifugal force. Multiple sources have been provided that explicitly state that Leibniz's centrifugal force is tied a rotating frame. For example, from the Swetz reference about Leibniz's and Newton's early concept of centrifugal force:
 * "Considered as an endeavor of the circulating body, or a force acting on the body itself, [the centrifugal force] does not exist. But if we consider a reference frame fixed in a the body and rotating with it, the body will appear to have an endeavor to recede from the centre. This of course is a fictitious force reflecting the acceleration for the reference frame."
 * Therefore, I'm going to fold some of the disputed section into the history section where most of the material in the disputed section appears. --FyzixFighter (talk) 19:43, 9 July 2009 (UTC)


 * I agree, but I wouldn't object if it also had a brief mention in the section on fictitious force in rotating frames. Dicklyon (talk) 19:56, 9 July 2009 (UTC)

The fact that planetary orbits can be dealt with without involving rotating frames of reference means that rotating frames are not an essential part of the analysis. It may well be that some textbooks have tried to integrate the Kepler problem into the rotating frame of reference analysis, but that is no reason for consigning the topic of planetary orbits to the history section.

You have both stated your own opinion that the centrifugal force in planetary orbits is a special case of the fictitious force in a rotating frame of reference. Since you have got sources which agree with your opinion, you are entitled to add that opinion to the section which I put in yesterday. However, I will also add on top of that my opinion that planetary orbital theory does not require a rotating frame of reference in the analysis, and I will also cite sources to back that idea up. At any rate, there was absolutely no justification whatsoever for deleting that new section on planetary orbits lock, stock, and barrel, without any discussion on the talk page. David Tombe (talk) 11:51, 10 July 2009 (UTC)


 * Hi David: As you know, the Lagrangian approach does not explicitly involve any reference frame: it just picks out the Jacobi coordinates and cranks away. So to that extent the rotating frame is not "an essential part of the analysis". However, the analysis can be done many ways, and while the Lagrangian method may have the advantage of being an approach with wide application, the other methods based upon explicit use of rotating frames arguably have more (or at least different) intuitive content. Evidently, intuition is a fallible guide, but it is a great source of innovation. Brews ohare (talk) 14:58, 10 July 2009 (UTC)

Brews, I have no major quarrel with the Lagrangian approach in this respect. However I do think that Lagrangian can be seriously lacking when it comes to gyroscopic analysis. Lagrangian is an 'energy accountancy' system, but it is totally silent as regards crucial causative forces such as the axial Coriolis force which prevents a spinning gyroscope from toppling under gravity.

As regards rotating frames, it does indeed seem that some attempts have been made to do the Kepler problem within the context of rotating frames. But I can't see how the angular velocity that is associated with a rotating frame can be in any way adequate to deal with all the permutations of pairs of mutual angular velocity as would occur in two adjacent two body Kepler orbits. This scenario is what Maxwell used to generate the very real centrifugal force of repulsion between his vortices to account for magnetic repulsion.

Furthermore, trying to strap a rotating frame of reference around a two body planetary orbit would be a most cumbersome endeavour as it would involve a variable angular velocity. Why bother? As far as I am concerned, we only need to introduce rotating frames of reference if the actual physical scenario being analyzed contains one naturally. For example, in meteorology, we have the Earth and the entrained atmosphere. That is ideal for the introduction of a rotating frame analysis. Radial water pipes on rotating turntables would be another such example. David Tombe (talk) 15:36, 10 July 2009 (UTC)


 * The main reason for my removal of the planetary orbit section is that it is a special case of either one of the two more general sections. And actually Brews has summed up one of the reasons why I didn't fold the planetary orbit stuff into the rotating frame fictitious force section. This is supposed to be a general article which should cover the material generally and direct to the more specific articles. That means we describe the two Newtonian mechanics uses of the phrase, the Lagrangian mechanics use of the phrase, and the history of the term and its importance in the whole absolute rotation debate. I don't see the centrifugal force of planetary motion as a separate and distinct topic from these general topics. The planetary motion figures prominently in the history section, so that's why I merged the info into there. But I don't see why it should get special mention outside of that section. Again, it's a special case of the general fictitious/inertial/pseudo- centrifugal force - associated with a non-stationary frame (or in other words, refers to terms moved from the acceleration to the force side of F=ma) in Newtonian mechanics or to extra terms that appear in the generalized force of Lagrangian mechanics.
 * So because this is the general centrifugal force article, I'm going to again remove the special case subsection - remerging the information into the history section. I'm also going to try my hand at expanding the intro and the fictitious force section to include the three contexts that Lagu brought up. --FyzixFighter (talk) 18:36, 10 July 2009 (UTC)

I think your argument about the role of this page is valid. The example appears in some form on the rotating CF page, but I'm not sure it is all covered there.

The "three contexts" introduces under the guise of polar coordinates what is really a Lagrangian attack on the problem, and discussion of this aspect should go there. See the following comments under. Brews ohare (talk) 21:57, 10 July 2009 (UTC)


 * Hey Brews, I hope you don't mind me merging the planetary orbit example into the main subsection. I think a separate sub-subsection of an example starts getting too far into a specialized article, but to come to a compromise we can all agree on I left in a good portion of it but moved it to were I felt it would flow well with the more general text right after the central potential discussion. I also trimmed some of the historical Leibniz stuff since (1) it's covered in the history section and (2) I think Leibniz didn't derive it using Lagrangian mechanics, but with a formalism that more closely paralleled Newton. In your opinion is this an equitable solution? If not, why and what would you suggest as a compromise? --FyzixFighter (talk) 22:32, 10 July 2009 (UTC)

There is only one universal centrifugal force. The planetary orbit is a very important manifestation of that force and hence it needs to have a section of its own. It is in fact the most general manifestation of the centrifugal force. The planetary orbit example can then be extended to the rotating spheres example by attaching a string between the two objects when they are in a state of mutually outward motion. The string will be pulled taut. This is the so called 'reactive centrifugal force' kicking in, which in turn induces an inward centripetal force due to the tension in the string.

It is wrong to claim that the centrifugal force in planetary orbits is a special case of the 'rotating frame' centrifugal force. We don't need a rotating frame in order to analyze the planetary orbital problem and the centrifugal force in the Leibniz equation is a 'polar coordinates' centrifugal force measured relative to the inertial frame. The centrifugal force in a planetary orbit is the centrifugal force that is built into the inertial path. That centrifugal force is just as much the so-called 'reactive centrifugal force' as it is any other kind of centrifugal force. Indeed, it was in the context of planetary orbits that Newton concocted the concept of the 'reactive centrifugal force'.

Hence, we put in a short and simple section on planetary orbits, much as Brews has just done, and we give that section the appropriate title. There is no need to juggle it all around and merge sections together in order to try and dilute the planetary orbit concept and the Leibniz equation. David Tombe (talk) 00:45, 11 July 2009 (UTC)

Brews's alternative section
Brews, your alternative section covers the main points. I will not make any amendments to it until I have studied the details. At the moment, I am wondering whether or not the variable r is the distance to the centre of mass as you say, or if it is the actual distance between the two objects. I have a feeling that it is the latter, but I need more time to think about it. David Tombe (talk) 12:09, 10 July 2009 (UTC)


 * On thinking more about it, it's probably OK because I can see that you have used the language of reduced mass. David Tombe (talk) 14:22, 10 July 2009 (UTC)


 * David: Are the initial energy and angular momentum sufficient to determine the solution? The angular momentum is subsumed under the parameter $$\ell$$, but the equation is second order and so appears to need another initial condition. Brews ohare (talk) 15:07, 10 July 2009 (UTC)

Brews, The general solution is a conic section. A conic contains two parameters that need to be determined. One is the eccentricity and the other is the semi-latus rectum. As you say, we are dealing with a second order differential equation, and hence we will have two arbitrary constants that need to be determined. I do believe from memory that the two arbitary constants in question are indeed the eccentricity and the semi-latus rectum. The eccentricity is determined by the initial kinetic energy for the particular radial distance at the kick-off point. The semi-latus rectum is determined by the angle of projection.

It's thirty years since I did these problems in applied maths and I'm rusty. If you have any more questions, I'll look it up for you. But I can now see that we are dealing with three factors that determine the full solution. Not only do we have the initial kinetic energy and angle of projection, but also the initial radial distance. However, I think that when all combined, this will reduce to initial energy and initial angular momentum. I remember a formula for the eccentricity which involved speed and radial distance. David Tombe (talk) 15:23, 10 July 2009 (UTC)

Three contexts
The third context is equivalent to the Lagrangian discussion and duplicates points made in that section. I have added the references.

This topic is separate from the "rotating reference frame" topic because it (i) doesn't invoke a rotating frame (ii) has applicability where no rotating frame is involved and (iii) leads to endless confusion when believed to have some connection to Newton's fictitious forces. For example, the "third context" centrifugal force is not "fictitious" because it doesn't vanish when the frame doesn't rotate. Brews ohare (talk) 21:47, 10 July 2009 (UTC)


 * Thanks Brews for the edit. I really prefer how you've connected the "third context" to the Lagrangian formalism than how I had included the idea. My only minor qualm is more about policy than content. The Bini article which introduces the "three contexts" does all three from a Newtonian mechanics viewpoint. In Bini's third context, F=ma is written out in polar coordinates and then, to make the equation look like the Cartesian coordinate counterparts (ie $$ m\ddot\eta=\sum F_\eta$$), we move Goldstein 3-12's "centripetal acceleration term" over to the force side and call it a force. Personally I much prefer your redirection to the Lagrangian formalism since, IMO, arbitrarily moving a term from one side of the equation to the other does not suddenly transform it from a term in the radial acceleration to a force term. When this is done, it completely throws the Newtonian definition of "force" out the window. But the Lagrangian formalism gives moves all the arbitrariness to the choice of coordinates (where it should be) and in a consistent and logical fashion cranks out the "generalized forces". However, again I worry if casting the third context as an extension of the Lagrangian formalism strays to far from the (IMO somewhat lacking and disingenuous) description in the Bini source. --FyzixFighter (talk) 22:26, 10 July 2009 (UTC)

FyzixFighter, you are making alot of unnecessary complications. There is only one centrifugal force. I'm happy enough to have a section on the Lagrangian treatment of centrifugal force. But we do not mix such a section with the Leibiz treatment of the Kepler problem. The Leibniz equation is not a Lagrangian equation. It is a force equation. It is a second order differential equation in the radial distance. Lagrangian mechanics is about conservation of energy.

And as regards moving things from one side of an equation to the other, that never converts a centrifugal force into a centripetal force. You are getting the inertial path equation mixed up with the two body Kepler problem. The former does not involve a gravitational field and it is a hypothetical situation which never exactly happens in nature. The latter has a gravitational field involved. The term that refers to centrifugal force in the latter refers to centripetal force in the former. There is no moving terms to the other side of the equation going on. They are two different equations for two different physical secnarios. David Tombe (talk) 00:53, 11 July 2009 (UTC)


 * David, Leibniz's equation can't be a force equation, at least not in the standard, Newtonian mechanics definition of force. There are only two ways to get Leibniz's equation from first principles: using Lagrangian mechanics or Newtonian mechanics. When the two body Kepler problem is done using Newtonian mechanics, the only force that needs to be included in F_net is gravity - no centrifugal force is included in the sum of forces. As Bini and Strommel note, the $$-mr\dot\theta^2$$ term in the radial acceleration (which Goldstein calls the centripetal acceleration term) is moved to the force side of the equation - that is how the centrifugal force term arises. It's not a real force, it's just a term from the radial acceleration that we've moved. See the end of Strommel's discussion on pg. 36-38. Bini also classifies it this as a fictitious force that is implied by the frame of reference. --FyzixFighter (talk) 03:43, 11 July 2009 (UTC)

FyzixFighter, you are just playing around with words. The Leibniz equation and planetary orbits are the most general way of explaining centrifugal force. You don't want it in the article because it doesn't involve the use of a rotating frame of reference. It's as simple as that. All your arguments above are totally specious. David Tombe (talk) 09:00, 11 July 2009 (UTC)


 * At least three references explicitly support the "fictitious" interpretation of Leibniz's centrifugal force (two of which you initially provided):
 * From Swetz, "Learn from the Masters!", pg 269
 * Considered as an endeavor of the circulating body, or a force acting on the body itself, [the centrifugal force] does not exist. But if we consider a reference frame fixed in a the body and rotating with it, the body will appear to have an endeavor to recede from the centre. This of course is a fictitious force reflecting the acceleration for the reference frame.
 * From Linton, "From Eudoxus to Einstein", pg 413
 * 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.
 * From Aiton, "The celestial mechanics of Leibniz in the light of Newtonian criticism"
 * 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.
 * and
 * Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference.
 * So if we get to Leibniz's equation from Newtonian mechanics (ie the traditional definition of force), his centrifugal force is a fictitious force that vanishes from the list of forces acting on an object in Newton's 2nd law when the dynamics is described from the inertial frame. --FyzixFighter (talk) 13:47, 11 July 2009 (UTC)

FyzixFighter, centrifugal force only appears to vanish in the inertial frame of reference when the inertial path is described in Cartesian coordinates. It shows up when we use polar coordinates. And yes, the centrifugal force in planetary orbits is the same centrifugal force that arises in the Lagrangian formulation, and in the rotaing frames formulation in the special case of co-rotation. But that is not a basis for hiding a section on planetary orbits inside the Lagrangian section as you have been attempting to do. This article is about 'centrifugal force'. The sections of the article are for the purpose of illustrating centrifugal force. Planetary orbits present the best directly observed illustration of centrifugal force as an outward inverse cube law force. The equation which was used in that section by both myself and Brews was Leibniz's equation. Leibniz's equation is not Lagrangian mechanics even if it is being used to describe something that can equally be described using Lagrangian mechanics. So you have got absolutely no grounds whatsoever to hide this section inside the Lagrangian section.

Likewise with the centrifugal force in the inertial path. Polar coordinates do not involve a rotating frame of reference. The 'inertial path' centrifugal force is indeed the same centrifugal force that arises when an object co-rotates with a rotating frame of reference. But that is not grounds for deleting all mention of the treatment of centrifugal force in connection with polar coordinates in the absence of rotating frames.

As for your extension to the introduction, you cannot be serious. It doesn't exactly read very well. What is the point of your extension? David Tombe (talk) 19:02, 11 July 2009 (UTC)


 * Look again at both the Bini and Stommel reference which talk about the polar coordinate centrifugal force. Both call it a fictitious force. For example from Bini after discussing the different CF contexts including the polar coordinate context:
 * "In other words, the "fictitious" centrifugal force is a convenience that only has meaning with respect to some implied reference frame"
 * And from Stommel:
 * "Sometimes equation (2.14a) is written with one of the acceleration terms on the righthand side
 * $$\ddot r = r\dot\theta^2+F_r$$.
 * The term $$r\dot\theta^2$$ then looks like a force, and it actually has a name: "the centrifugal force" [per unit mass]. It is always positive and directed away from the origin. But it is really not a force at all, and so if we want to make use of it in a formal sense, then we could call it a virtual, fake, adventitious force."
 * This is because, as Stommel states, $$\ddot r$$ is not the true radial acceleration, the true radial acceleration is $$\ddot r - r\dot\theta^2$$. While Leibniz's radial equation is mathematically valid, since $$\ddot r$$ is not the radial acceleration, then we cannot use Newton's 2nd law to interpret the other side as a true force or sum of forces. It's that simple. In polar coordinates in the inertial frame, the $$mr\dot\theta^2$$ term is part of the acceleration, not a force acting on the circulating body. In all the fictitious CF cases, both the rotating frame contexts and the polar coordinates, the "centrifugal force" and other fictitious forces arise when we take Newton's 2nd law and start moving terms that appear in the acceleration, $$\ddot\vec r$$ and move them to the force side of the equation and interpret them as "forces". In the rotating frame case, the terms arise from the time dependency of the basis vectors for the rotating frame; in the polar coordinates, it's the centripetal acceleration term as Goldstein calls it. --FyzixFighter (talk) 21:24, 11 July 2009 (UTC)

The comparative table
One way or the other, something needed to be done about the comparative table because it didn't cater for situations in which centrifugal force is treated outside of the context of rotating frames of reference. An alternative approach would be to reduce it once again to two columns but amend the bit where it says 'rotating frame' in relation to the fictitious force, to read 'inertial frame'. In Lagrangian, polar coordinates, and co-rotation, the centrifugal force is measured relative to the inertial frame. It is only in non-co-rotation that any motion can be considered to be relative to the rotating frame of reference. David Tombe (talk) 19:23, 11 July 2009 (UTC)


 * I don't think such situations exist. The r in the planetary equation is clearly a measurement along a direction that co-rotates with the planet, such that treating its second derivative as an acceleration is exactly what that viewpoint is about.  Dicklyon (talk) 03:10, 12 July 2009 (UTC)


 * David: You are right that the table is intended to clarify the difference between the reactive and the fictitious CF concepts. I don't think this table should be changed to include the Lagrangian CF, because it will make the whole comparison too complicated. Perhaps a second table should be constructed to contrast the fictitious CF and the Lagrangian CF? Brews ohare (talk) 04:54, 12 July 2009 (UTC)

Brews, something certainly needs to be done to generalize the situation. I'm personally of the opinion that the Lagrangian centrifugal force, the polar coordinates centrifugal force, the rotating frames centrifugal force in the special case of co-rotation, and the Leibniz centrifugal force are all the same force. The so called reactive centrifugal force is merely a knock-on effect of that force. The problem with the original table was that it stated that the fictitious force arises in a rotating frame of reference. But we all know that the Lagrangian centrifugal force and the polar coordinates centrifugal force are relative to the inertial frame and definitely don't involve rotating frames of reference. Hence there is a dilemma which needs to be addressed one way or the other. By all means edit the table again, but you need to bear these points in mind when doing so. David Tombe (talk) 12:16, 12 July 2009 (UTC)


 * David, I think you go wrong in saying "we all know that the Lagrangian centrifugal force and the polar coordinates centrifugal force are relative to the inertial frame and definitely don't involve rotating frames of reference." Certainly we don't agree here.  The polar coordinates centrifugal force is just a way to use a co-rotating reference frame; the Lagrangian approach is a generalization of that concept, which in the special case of planetary orbit with co-rotating r dimension is not different from it.  None of these correspond to any forces in the inertial frame, as there are no such forces.  Dicklyon (talk) 17:25, 12 July 2009 (UTC)

Dick, you've got it the wrong way around. Yes indeed the polar coordinates centrifugal force and the co-rotating frame centrifugal force are one and the same thing. But the polar coordinates are variables which are referenced to the inertial frame. One of those variables is angular displacement which is clearly relative to the inertial frame, and it is that angular displacement which appears in the centrifugal force formula. The centrifugal force is in the radial direction and that direction rotates, but that doesn't mean that the acceleration itself is relative to any rotating frame of reference. This seems to be the common mistake. People see that the radial vector rotates and they immediately jump to the erroneous conclusion that a rotating frame of reference must be involved. David Tombe (talk) 18:11, 12 July 2009 (UTC)


 * Forces don't depend on what coordinate system you measure things in. The forces and accelerations you get by analyzing things in polar coordinates in an inertial frame are the same as what you get by measuring in Cartesian coordinates; they just have different expressions.  CF only comes in when you jump to interpreting the second derivative of r as acceleration, which makes sense only in a frame co-rotating with the vector along which you measure r.  But I've explained that more than a dozen times over the last many months, so why am I wasting my keystrokes on you?  Dicklyon (talk) 18:35, 12 July 2009 (UTC)

Dick, we'll have to agree to differ on that. But it's got nothing to do with the current dispute. The current dispute is over FyzixFighter's attempts to prevent the theory of planetary orbits from being used as an illustrative example of centrifugal force and as a means of stating that centrifugal force obeys the inverse cube law. You saw the short section that Brews wrote and which was essentially a revised version of what I wrote. It was a very helpful and informative section and very relevant to the topic. But you have chosen to side with FyzixFighter's decision to delete it. FyzixFighter's reasons are empty of any logic. He says that planetary orbits are a special case. They are not. They are the most general case of centrifugal force that exists. There is no other example of centrifugal force that you could show me that is not the inverse cube law centrifugal force in the planetary orbital equation. The rotating bucket or whatever, it's all the one and only inverse cube law centrifugal force as in the Kepler problem.

Nowhere now is it stated in the article that centrifugal force obeys an inverse cube law when angular momentum is conserved.David Tombe (talk) 19:30, 12 July 2009 (UTC)


 * If that's the dispute, let's fix it by putting this material into the section on the rotating frame approach. OK?  Dicklyon (talk) 19:40, 12 July 2009 (UTC)


 * Dick, that is indeed the dispute. But I've already explained to Brews above why the 'rotating frames' re-direct is not an appropriate venue for this material. Whereby I have conceded that most modern textbooks treat centrifugal force in terms of the rotating frames approach, I think that you ought to equally concede that most textbooks don't use the rotating frames approach for planetary orbits. It is not accurate to insert the planetary orbital example under the banner of 'rotating frames of reference' when only a few sources treat the problem that way. The rotating frames re-direct is not an appropriate venue for that material.


 * Ideally we shouldn't have any re-directs. Centrifugal force related material should all be on this page. There is no need to have a separate article for 'reactive centrifugal force' and 'centrifugal force in rotating frames'. A common thread runs through all centrifugal force along with a historical narrative. The only appropriate alternative venues that I can think of are Kepler's laws of planetary motion, the Kepler Problem, and Orbits. I've already put it into Orbits. If you want a compromise, you might consider supporting the inclusion of Leibniz related stuff on centrifugal force in these articles along with a comment in this article referring the topic of centrifugal force in planetary orbits to these topics. —Preceding unsigned comment added by David Tombe (talk • contribs)


 * So that's the impasse we've been at for about 15 months. You add the planetary stuff as if it's something different, everyone objects and takes it out, and Brews reacts by adding more and more complexity.  But no matter how you cut it, the material is way too much for a single article; this is supposed to be the summary article, not a place to collect all those other details and digressions.  Maybe if we recognize the pattern we can adjust. Dicklyon (talk) 21:48, 12 July 2009 (UTC)

In this instance, what complexity did I add? Definition of notation, maybe? A one-line connection to Lagrangian formulation? "More and more", eh? No opportunity missed for gratuitous insult. Brews ohare (talk) 21:55, 12 July 2009 (UTC)


 * I'm just explaining how the article got to be so big, well away from its original intent. You only added a little over 1 KB on Friday, only about 10 KB in each of May and June, so maybe you're right – only half of it is from you.  Dicklyon (talk) 22:28, 12 July 2009 (UTC)

No Dick, I didn't add the planetary stuff as if it was something different. I added it as an illustration of centrifugal force in a context which didn't need a rotating frame of reference in its analysis. So what particular point of view are you referring to that I haven't been able to persuade everybody else of? It's more a case of other editors reverting out of spite rather than anything to do with wikipedia's rules. And as regards Brews, I'll say in his defence that he appears to be the only one that is genuinely trying to learn, and acting on what he has learned. You and FyzixFighter have learned alot too, but you are not always willing to act on what you have learned. You both appear to have some investment in playing down the real push and pull aspects of centrifugal force, and so you are both keen to dress it all up in coordinate frame transformations.David Tombe (talk) 23:44, 12 July 2009 (UTC)

FyzixFighter is trying to provoke an edit war
FyzixFighter, you wrote this when you did you reversion,

"I still think planet orbits are a special case and should not be mentioned - - -".

Planetary orbits are indeed one specific illustrative case of centrifugal force. That is not a reason for arguing that they should not be mentioned in the article.

You began this edit war over a year ago on the grounds that my attempts to insert the planetary orbital approach were original research. Now that we all know that you were wrong in that regard, you are scraping the barrel. You are now down to the pathetic argument that planetary orbits shouldn't be mentioned because they are a special case.

Every example of centrifugal force is a special case. David Tombe (talk) 21:10, 11 July 2009 (UTC)


 * You do realize with that last revert you just surpassed the three reverts in a 24-hour period:
 * 1st revert 23:24, 10 July 2009
 * 2nd revert 09:03, 11 July 2009
 * 3rd revert 18:39, 11 July 2009
 * 4th revert 21:02, 11 July 2009
 * --FyzixFighter (talk) 21:32, 11 July 2009 (UTC)

It's strange how I can be the one to put in a new edit to improve the article. You come along in your usual fashion and delete it. Brews writes an alternative version of it. You delete it too. Brews an I both endeavour to retain his version in the article, and suddenly I am being accused of being in breach of the three revert rule.

What you really need to do is explain to everybody your real reason for intervening in this topic. You certainly aren't interested in it in the normal course of events. Your interest seems to be limited to reverting edits which I make. Your reasons for trying to keep the planetary orbital equation out of the article have changed dramatically over the last 15 months from allegations of original research to a mere statement of the fact that the centrifugal force in planetary orbits is a special case. I would hope that any administrators that are watching this will take note of that reason and ask themselves why you are trying so hard to keep that topic off the page on the mere grounds that you see it as a special case. Few others would ever be as concerned about that as you seem to be. And I hope that all the editors who agreed with you last year that I was trying to introduce original research can now see that the planetary orbital equation is not original research at all. We are now long past the stage of sources. The sources are well established and the authenticity is no longer in dispute. You really will need to come up with a better reason for trying to keep that section out of the article. David Tombe (talk) 22:00, 11 July 2009 (UTC)


 * He may be edit warring, but I think you get the credit for the provoking. If you'd respond sensibly to feedback, you could incorporate this special case in an acceptable way.  But you never have responded sensibly to feedback, so on it goes.  Dicklyon (talk) 03:08, 12 July 2009 (UTC)

Dick, let's analyze what you said more carefully. Are you saying that my insertion of planetary orbits as an illustrative example was the provocation? We all know that it is fully sourced and authentic and that it presents a clear picture of centrifugal force in action. Last April 2008 I tried to get this stuff in and FyzixFighter went to the administrator's notice board and complained. The administrators believed FyzixFighter that I was engaging in disruptive editing and trying to promote original research. I ended up finding myself arguing against up to eleven or twelve editors at once, and I got blocked repeatedly on dubious grounds. I ended up getting blocked permanently for the crime of communicating with another editor while blocked.

We all know now that what I was trying to insert was not original research. I am the one that has now requested administrator intervention. But unlike last year, the administrators don't want to get involved. They were very keen to get involved when they throught that planetary orbits were my original research, but now that that has proved not to be the case, they have all gone away.

FyzixFighter is still trying to veto the inclusion of the planetary orbital example, ultimately for reasons which aren't yet altogether clear. His original reason that it was my original research has collapsed and he is now scraping the barrel. He is arguing that planetary orbits are only a special case of centrifugal force and so shouldn't be included in the centrifugal force article. That argument would be laughed out of court because it is a nonsense argument. And having then realized that there were two editors trying to insert the relevant passage, he attempted to jettison it into the middle of the Lagrangian section where it didn't belong. The section contained no Lagrangian in it. He might as well have jettisoned it into the middle of the wikipedia article on giraffes. It's true that planetary orbits can be analyzed using the Lagrangian method, but that doesn't mean that planetary orbits as a topic in their own right should be categorized under 'Lagrangian mechanics'.David Tombe (talk) 12:33, 12 July 2009 (UTC)


 * David you're misrepresenting me on at least three counts:
 * In April 2008 I reported you for wikistalking editors who disagreed with you (ie undoing their constructive and anti-vandalism edits on completely unrelated articles). I find it interesting that you have never acknowledged wrong-doing in this matter.
 * I think have been very clear on why I am vetoing the inclusion of the planetary orbital example here - it's a special case. This is a general (preamble as Brews calls it) article. The planetary orbital example and centrifugal force discussion is already on the more specific pages. I'm not fighting for the removal of the planetary orbital example from those pages.
 * I wasn't the one who first put the planetary orbital example in the Lagrangian section. Brews was.
 * Since the RFC hasn't appeared to have brought in previously uninvolved editors, perhaps we should try WP:3O (I don't know if this would be appropriate since Dick and Brews are also involved, though currently not as vehemently as you and I), informal mediation, or formal mediation. Thoughts on the appropriate next step in WP:DR? --FyzixFighter (talk) 15:42, 12 July 2009 (UTC)

FyzixFighter, Planetary orbital theory is an illustrative example of centrifugal force. You, for whatever reason, have decided that you don't want this example to appear in the centrifugal force article. The reason which gave last year was that it was original research on my part, and you succeeded in convincing many editors that this was the case. Now that the truth has come out, most of those editors have gone home. You have nevertheless decided to continue to veto the inclusion of this topic on new specious grounds. Your new grounds are simply not a legitimate basis to keep this example off the page, and your insistence on keeping this topic hidden from view is having a detrimental knock-on effect in that you are putting unnecessary complications into the article in order to justify yourself. These extras are merely clouding the whole topic. Your latest extras in the introduction are incoherent and of no use to anybody. You have even changed your position from last month, from 'two kinds' to 'three kinds'. You are only confusing the whole article and you are changing with the wind according to who you can find to be on your side.

Planetary orbits expose the outward force that is generated due to transverse motion. The example can then be elaborated on to explain the so-called reactive centrifugal force simply by inserting an adjoining string and considering the tension that arises when the string is pulled taut by the centrifugal force. The planetary orbital example serves as the best all round general illustration of the subject of the article. So why not tell everybody what your real reason is for objecting to this example. Saying that it is a special case is not going to wash.

It seems from your edits above that you are somewhat puzzled as to how Leibniz arrived at the inverse cube law formula for centrifugal force. You say that you have never seen how Leibniz derived it. Neither have I, and I would indeed like to see how Leibniz derived it. I have seen some modern textbooks deriving it using some dubious method in which the total radial force in polar coordinates is reversed in, and the convective term, which had been a centripetal force in the polar coordinates in isolation, suddenly becomes a centrifugal force when gravity is involved. This is clearly not satisfactory and it amounts somewhat to 'force fitting', but it yields the correct end result. And so I agree with you that it would be very interesting to find out how exactly Leibniz derived it in the first place. This is not the only case in physics where a considerable degree of mystery hangs over the derivation of a very important result, and where the result itself is not in dispute. Maxwell's displacement current springs to mind. Few people doubt the authenticity of Maxwell's displacement current. But even fewer people can ever derive it without raising question marks. Not even Maxwell's own derivation is free from question marks. The amazing thing is that the end result is not only correct, but it is one of the most important results in modern physics along with perhaps the Leibniz equation which you are so keen to hide. David Tombe (talk) 17:02, 12 July 2009 (UTC)


 * You're a bit confused here. The 3rd viewpoint, the Lagrangian, was introduced by Brews, not by F.  It's just a generalization to other things called centrifugal force that are like the CF that arises from coordinates measurements that don't correspond to coordinates in inertial reference frames; it effectively includes the rotating frame approach, by a different mathematical route.  As to your statement that "Planetary orbits expose the outward force that is generated due to transverse motion," we think you're delusional; there's no such force in an inertial frame; your F=ma equation only gets such an F when you take "a" to be the second derivative or r, which is the coordinate measured along the co-rotating r-hat unit vector – a rotating reference frame.  As I mentioned before, I think we can discuss the equation in the section on rotating frames; F has provided detailed sourcing for this interpretation, which he quoted above.  If you will agree it's OK, then I'll encourage F to put it in, or I'll put it in.  But if you insist it doesn't belong there, we're better off just leaving it out.  Dicklyon (talk) 17:31, 12 July 2009 (UTC)

Dick, I'm not the one who is confused. There is only one centrifugal force. A rotating frame of reference is only needed when the physical scenario dictates. Examples are the rotating Earth and co-rotating atmosphere, and rotating turntables where dragging forces are involved which react against the already existing inertial forces.

When you are clear on this point, we will be agreed that the centrifugal force in such a co-rotaing scenario is the one and only centrifugal force that is described by either Lagrangian or polar coordinates.

Planetary orbits can be treated using rotating frames of reference, but it is not necessary to do so and it is indeed rare to see it done that way. I know that you have produced sources which do it that way, but most textbooks don't do it that way. I did the course many years ago and I checked out many textbooks for different ways of solving the planetary orbital equation. I never saw a book that used rotating frames of reference in this topic. So you cannot put a topic under the banner of 'rotating frames of reference' when it does not generally speaking fit under that banner. By all means support FyzixFighter and keep the planetary orbital topic out of the article altogether. But if you do so, you are merely indulging in a cheap numbers game at the expense of the reader. You will be deciding that anybody who googles up centrifugal force and inevitably gets led to the wikipedia article should not be allowed to read about the role of centrifugal force in planetary orbits, simply because you decided to side with FyzixFighter who has been actively and repeatedly deleting constructive edits that I make to physics articles. You have shown a capability of understanding these issues. But you have also shown a tendency to side up with other editors and work against your better instincts. You should be able to see by now that FyzixFighter's departure from his other edits to physics articles has been, not for the purposes of improving the articles in question, but for the sole purpose of undoing what I have just done. If wikipedia can't deal with that kind of subtle vanadalism then it will eventually become viewed with cynicism by the wider readership. David Tombe (talk) 17:49, 12 July 2009 (UTC)


 * How can you say there is only one centrifugal force? Read the article.  Look at the table.  Two different things going by the same name, acting of different objects, and not equal in magnitude except in the case of circular motion.  You've had well over a year to find support for your POV, but it hasn't happened.  Whether you arrive at your equation by Lagrangian or other methods, it describes the pseudo force in a system with rotating r vector, not a real force in an inertial system. Dicklyon (talk) 22:45, 12 July 2009 (UTC)

OK then Dick, you give me an example of centrifugal force that is exclusively one kind as opposed to the other. And while you're at it, can you tell me if the centrifugal force in the rotating bucket is the reactive centrifugal force or the 'rotating frames' centrifugal force? I remember you once tried to tell me that the centrifugal force in the planetary orbit was the reactive centrifugal force. And indeed there are some sources which back up that idea. But recently you have been wanting to put it into the 'rotating frames' section. FyzixFighter tried to bury the planetary orbital centrifugal force right in the middle of the Lagrangian section and now he wants to put it into the 'rotating frames' article.

So, I'll be interested to hear the example that you give me which is exclusively one kind of centrifugal force as opposed to another. I'll bet that what ever example you produce, I will be able to expose it as the one and only centrifugal force which is the inverse cube law force in the Leibniz equation. David Tombe (talk) 23:19, 12 July 2009 (UTC)


 * In any inertial-frame analysis, bucket or otherwise, the real forces are exclusively the centripetal force and the corresponding reactive centrifugal force. The other centrifugal force only comes up only as an apparent force in rotating reference frames.  This is well known; you seem to be unique in not admitting that this is standard physics. Dicklyon (talk) 05:28, 13 July 2009 (UTC)

OK Dick, so you are saying that the water in the rotating bucket that pushes against the edge of the bucket is the 'reactive centrifugal force' and measured relative to the inertial frame. And no doubt it will satisfy the polar coordinate term for centrifugal force as referenced from the centre of rotation. And no doubt it will obey an inverse cube law when angular momentum is conserved. And no doubt if we should so choose to involve a rotating frame of reference, it will be the associated centrifugal force in the rotating frame. And this reactive centrifugal force will no doubt correspond to the centrifugal force that arises if we analyze the problem using Lagrangian mechanics or if we analyze the problem using the concept of centrifugal potential energy.

You haven't convinced me that there is more than one centrifugal force involved. David Tombe (talk) 08:02, 13 July 2009 (UTC)

FyzixFighter Reinvents Physics
As far as I can see this fellow FyzixFighter appears to advocating a revisionist physics. If you want to reinvent physics to fit your own views of the world, I dont think you should do it here. The idea that centrifugal force keeps planets in their orbits is a central idea of modern physics. I remember being taught that in the school books. Apparently you didnt read them or didn't understand the point. If there is no centrifugal force, the planets fall into the sun. Is that not obvious to you? Apparnetly this discussion has become so embroiled in personal nastiness on your part that such obvious facts are being overlooked. If there is no centrifugal force keeping the planests from falling into the sun, please explain what does, Mr FizixFighter, and please dont invent any new physics or appeal to any obscure sources. Just give us a simple reason that can be understood that justifies why you are creating this unnecessary edit war.72.84.73.235 (talk) 14:27, 13 July 2009 (UTC)


 * That's not exactly the modern view. All you need to keep planets from falling into the sun is inertia, via Newton's law F=ma, with the only force being the force of gravity.  Physics was "reinvented" this way by Newton a long time ago.  Dicklyon (talk) 14:51, 13 July 2009 (UTC)


 * I was just about to say much the same thing. Gravity stops the planets from flying off in a straight line.Martin Hogbin (talk) 14:54, 13 July 2009 (UTC)

User talk:72.84.73.235: You are not wrong in your statements; it's all a question of frame of reference: Dicklyon and Martin Hogbin use an inertial frame; you (perhaps unconsciously) use the frame of reference of the planet. The planet is at rest in the frame of the planet because the centrifugal force and the force of gravity balance. The most natural frame of reference, the one instinctively adopted in an amusement park ride or a turning car, is the frame attached to the body. Brews ohare (talk) 15:12, 13 July 2009 (UTC)


 * Centrifugal force is due to inertia. So you can't deny centrifugal force on the grounds that it is the effects of inertia. 72.84.73.235 is using the language of centrifugal force. And that's what this article is about. You can't veto the most important example of centrifugal force on the grounds of switching language to Newton's law of inertia. And we all know that Newton had a chip on his shoulder because Leibniz got to the inverse cube law before him, and so Newton played down centrifugal force in his later works. David Tombe (talk) 15:18, 13 July 2009 (UTC)


 * I'm not denying centrifugal force, or the fact that it's due to inertia. I agree it is.  But in the inertial frame, it's not a force; what balances the F on the left of F=ma is the ma on the right; this is how Newton incorporates inertial effects in inertial frames. Dicklyon (talk) 18:02, 13 July 2009 (UTC)


 * Really!? I'm using obscure sources? I'm appealing to the same sources that David first inserted into the article, namely Linton's "From Exodus to Einstein" and Swetz's "Learn from the Masters!". Both of which support the idea that the centrifugal force, more specifically Leibniz's centrifugal force, is absent in the inertial frame. See page 264 in Linton, and near the top of page 269 in Swetz. I've listed the full quotes in a section above, so I won't belabor the other editors by posting them again. If those are obscure sources, then you better get on David's case too for bringing them up in the first place. --FyzixFighter (talk) 15:40, 13 July 2009 (UTC)

FyzixFighter, the sources which I inserted were for the purpose of backing up my assertion that the centrifugal force is an outward inverse cube law force. It is neither here nor there what additional opinions the authors held on the matter. You have just deleted a section which states that the centrifugal force is an outward radial force which obeys the inverse cube law. Your reason for doing so does not match your determination. Why would anybody be prepared to have an edit war on this issue simply on the grounds that they don't think that the section is necessary? You removed that section for the sole reason that you have got a chip on your shoulder. It has got nothing to do with any arguments in physics. And you are taking advantage of a hostile environment of editors who are paranoid about centrifugal force because of the threat which it poses to their favourite theory of relativity. We're seeing an example of it right now as regards the latest objections to the 'absolute rotation' section. In fact, I strongly suspect that you yourself began this edit war for this very reason when you first noticed in April 2008 that I had edited on this page to state that centrifugal force is the radially outward force that arises in connection with mutual transverse motion. You have never declared your motives so far. You are playing out a clever little game of pretending to be merely interested in ensuring that wikipedia's rules and regulations about sources are being upheld. And you know exactly how to use the wide range of contradictory sources to mess the article up. Why would somebody who normally edits on non-physics articles be so keen to ensure that sources are being correctly used on the centrifugal force page and then proceed to delete material that has been fully sourced? David Tombe (talk) 21:04, 13 July 2009 (UTC)

Consensus on the Planetary Orbital Topic
Once again, FyzixFighter has removed the section on planetary orbits and left no part of the article, apart from the history section, to explain the fact that centrifugal force is an inverse cube law force. And in doing so, FyzixFighter claims that he has got consensus on his side.

Let's examine that consensus. I initiated the section as the most general illustration of centrifugal force. FyzixFighter immediately came along and deleted it. Brews re-worded the section and re-inserted it. FyzixFighter deleted it again.

The final analysis is that Dick was initially disinterested in the edit, but as usual supported FyzixFighter when it came to the crunch. However Dick didn't actually object to the content of the edit as such. He agreed that the edit could be put into the re-direct article 'centrifugal force (rotating frames of reference). But the problem with that is that planetary orbits are not normally dealt with in connection with rotating frames of reference, and so it would be totally inappropriate to put the planetary orbit section into the re-direct article about rotating frames of reference.

Anonymous 72-- -- -- restored the section. Wolfkeeper's popup mechanism automatically undid 72's edit within minutes. I don't count Wolfkeeper's popup mechanism in relation to anything to do with consensus on this issue because he hasn't been involved in the debate.

So the evidence is that myself, Brews, and 72 are in favour of the edit. Dick is ambiguous in that he is comfortable enough with the edit providing that it doesn't appear on the correct page. So I very much doubt that consensus on balance can be said to be in favour of FyzixFighter's desire to delete the edit.

Here we have a situation where FyzixFighter, who only concerns himself with the centrifugal force page when I have made an edit, comes along and deletes such an edit on the very weak grounds that the content matter is a special case of centrifugal force, and that as such he doesn't think that it should appear in the article. And he is prepared to have an edit war over the issue.

It is because of the likes of FyzixFighter that it is impossible to work constructively to improve this article.

The question is, 'where do we now mention the inverse cube law relationship in this article? Do we mention it in the introduction or do we write a special section to say that Leibniz demonstrated that the centrifugal force obeys an inverse cube law relationship in the radial distance?'. It's currently mentioned in the history section but it is still very much a part of modern physics. David Tombe (talk) 19:34, 13 July 2009 (UTC)


 * David, why are you so keen to mention the inverse cube relationship? It is there, but only if angular momentum is constant, for example a particle in a central force field.  Is it perhaps because you have your own theory on the subject?  This is a quote from an abstract of your theory, 'It is widely believed that centrifugal force does not exist. It will now be shown that centrifugal force is a dipole force field comprising of a sea of tiny rotating electron-positron dipoles which constitutes the luminiferous medium. Centrifugal force is the inverse cube law repulsion that emanates from the net positive charge that is generated in the dipoles when they are subjected to certain kinds of forces'. Martin Hogbin (talk) 21:09, 13 July 2009 (UTC)

Martin, yes. I'm glad you understand that. Few others do. Conservation of angular momentum leads to an equation which can be substituted into the centrifugal force expression to make it into an inverse cube law relationship. My objective here is to help others to learn about centrifugal force. I edit on pages about topics that I have a particular interest in. That's what wikipedia is all about. The centrifugal force page is there for people to learn about centrifugal force. I have been trying to create a simplified and coherent article with all the important aspects and with the most general illustrations. The two body problem is the singular best illustration, because ideally we can't ignore the gravitational field. If however we do ignore the gravitational field, and consider the random motion of two objects, we will find that this motion can be resolved into a translational motion of the centre of mass and a rotation about the centre of mass. Hence, centrifugal force is a real radial force that is related to inertial mass because the inertial mass will determine the actual centrifugal acceleration relative to the common centre of mass. This is confirmed when we attach a string between the two objects. The string will go taut, due to centrifugal force, and the two objects will perform circular motion about the common centre of mass.

My question to you is, 'why would we want to hide the inverse cube law fact from the readers?'. What aspects of centrifugal force would you see as being the most important and most interesting? David Tombe (talk) 21:25, 13 July 2009 (UTC)


 * I do not want to hide anything but the inverse cube law is more a property of a central force. For example I could equally well say that centrifugal force is constant (for a fixed length string) or that it is zero (for motion in a straight line).  Centrifugal force is about motion in a circle and the essential variables are velocity and radius.  With just these two there is no inverse cube law, that it a property of a constant angular momentum system. Martin Hogbin (talk) 21:55, 13 July 2009 (UTC)


 * I think it's worth mentioning, too, as it's an important application of the concept of CF to planetary orbits. I just don't think we can accommodate David's interpretation of it as different from the usual pseudo-force due to the rotation of the direction along which the coordinate r is measured. Dicklyon (talk) 22:12, 13 July 2009 (UTC)


 * You have seen the reason that David is so keen on this! The inverse cube law only applies to a specific application CF, it is not a general result. Martin Hogbin (talk) 22:26, 13 July 2009 (UTC)


 * I have no idea why he's so keen on it, but I agree it is a rather narrow application. But it's an important one, both historically and even for modern orbit calculations, and as an illustration of how CF can be derived and applied.  His deep confusion about it, shared now and then by an anon who supports him, suggests that it is worth treating carefully and correctly. Dicklyon (talk) 22:34, 13 July 2009 (UTC)


 * I am not suggesting that it is not an important application (although the two body problem is rarely treated using centrifugal force) but noting that it is just that, an application. The inverse cube law is more part of the application than a property of the force itself. Martin Hogbin (talk) 22:55, 13 July 2009 (UTC)

Carfeul here, the inverse cube law is the most general case. Circular motion on the end of a string involves a fixed radius and that is only a special case. Martin seems to think that centrifugal force is something that only arises in circular motion. That is a common error. Centrifugal force arises in the inertial path, and the inertial path is in general a conic section with the centrifugal force being a variable inverse cube law quantity. One special case of the inertial path is a straight line motion in the case of zero gravity.

And Dick, I was never saying that the centrifugal force in planetary orbits was a different concept from other centrifugal forces. In fact, I have been consistently saying that there is only one centrifugal force. I drew your attention to the rotating bucket of water and showed how there is only one centrifugal force. That very same inverse cube law force in the inertial path pushes the water to the sides. It causes the centrifugal potential energy in the water and it causes the push on the sides that you would classify as the reactive centrifugal force. I am still waiting to hear your comments on that. David Tombe (talk) 13:09, 14 July 2009 (UTC)


 * David, I'll repeat my comments. In the planetary orbit, the centrifugal reaction force is the equal and opposite force that the planet exerts on the sun, with reciprocal-r-squared dependence, because it is just gravity; the pseudo-force CF is reciprocal-r-cube.  In a circular orbit they are equal, or in balance (for the right value of angular momentum for that orbital radius).  But in general they differ, because they are completely different things.  Same way for a weight on a string or a bucket of water; the two concepts of CF are equal only in circular motion; they are not at all the same thing.  Dicklyon (talk) 02:35, 14 July 2009 (UTC)

And the reason that I am so interested in the Leibniz equation (not knowing until recently, thanks to you, that it was actually Leibniz's equation) is because it so perfectly embodies everything to do with this topic, plus more. It contrasts the two opposing central forces with their respective inverse square laws and inverse cube laws. The two different power laws yield the stability node which makes planetary orbits stable. If perchance we happened to have inverse cube law gravity, then the planets would spiral into the Sun. The stability node gives a picture of elliptical planetary orbits as like a two dimensional spring that is stretching and compressing, and it clearly illustrates gravity as a 'pull' or tension, and centrifugal force as a 'push' or pressure.


 * That's just nuts; there are not two different central forces – just gravity. The other is a made up pseudo force to allow you to pretend that you have a one-dimensional problem in r; that's all.  Not very fundamental, really.  Dicklyon (talk) 02:35, 14 July 2009 (UTC)

It's an interesting subject and I don't see why attempts to present it clearly and concisely have met with so much opposition. David Tombe (talk) 00:21, 14 July 2009 (UTC)


 * The reason is that you insist on presenting it as something that it's not, in contrast to the many sources, none of which support you in this. Dicklyon (talk) 02:35, 14 July 2009 (UTC)

Dick, it was actually Brews who wrote the deleted section, and I fully support the way that he wrote it. Can you please elaborate on exactly how it presents the centrifugal force as something that it is not. At any rate I have a compromise idea that will involve a short introduction section pointing out the key historical points in the evolution of the modern ideas. David Tombe (talk) 11:57, 14 July 2009 (UTC)

Suggestions
For what it is worth I have added an 'oppose' comment to the RfC section regarding the Leibniz inverse cube statement.

I have also put the 'Fictitious force' section first in the article as it is the one most used in physics today. I appreciate that the other definition may still be current in engineering but I suspect that this is in a relatively informal context. Anyway, all I have done is changed the order.

The section on absolute motion does not, in my opinion, belong here, especially if this article is intended to be a summary of centrifugal force. I suggest that it is removed completely.

Martin Hogbin (talk) 09:04, 14 July 2009 (UTC)


 * Martin, an article is an article. This is an article on centrifugal force. I don't know where the idea of it being a 'summary article' stems from. There are indeed two re-direct articles, but there are aspects of centrifugal force which either straddle the two re-direct topics or don't accurately fit into either of them. Where do you suggest that we put such topics? The absolute rotation section is one such example. The rotating water in the bucket involves all aspects of centrifugal force. It can be analyzed using rotating frames or using the inertial frame, and it involves centrifugal potential energy as well as pressure on the walls of the container. Dick said yesterday that it was a 'reactive force' topic, but I am waiting to hear his comments on the fact that the inertial force acts in the water itself as well as against the wall of the container. David Tombe (talk) 13:06, 14 July 2009 (UTC)


 * There are many interesting applications of centrifugal force but we do not want them all here. The absolute motion section is really all about Mach's principle.  If we have a section on a different but related subject we could also have sections on centrifuges, turbine blades, fairground rides, cyclotrons etc. Martin Hogbin (talk) 13:18, 14 July 2009 (UTC)

Martin, and why do we not want all those topics to be in a centrifugal force article? David Tombe (talk) 13:24, 14 July 2009 (UTC)


 * Because, if we decribed every related topic in every article, WP would be cumbersome and unusable. Martin Hogbin (talk) 13:39, 14 July 2009 (UTC)


 * Reasons to support the absolute rotation section have been stated here. Brews ohare (talk) 20:05, 14 July 2009 (UTC)

RfC: Content dispute on Leibniz equation and inclusion of planetary orbit equation
Ongoing content dispute over the different treatments of the centrifugal force and whether Leibniz's centrifugal force represents a distinct and separate concept. FyzixFighter (talk) 03:49, 11 July 2009 (UTC)


 * FyzixFighter, the centrifugal force in the Leibniz equation does not represent a distinct and separate concept as compared to any other approach to centrifugal force. There is only one centrifugal force. You are misrepresenting what this dispute is about. The dispute is about the fact that you have consistently attempted to remove all mention of the centrifugal force in connection with situations that don't require a rotating frame of reference in the analysis.


 * This latest round began when you removed my new section on planetary orbital theory. At first you tried to argue that it belonged in the history section. Brews then restored his own amended version of what I had written. You removed that too. After your attempts to remove it failed, you then blended it with the Lagrangian section when in fact the Leibniz equation has got nothing whatsoever to do with Lagrangian mechanics. David Tombe (talk) 08:57, 11 July 2009 (UTC)

My comment: There are exactly two sourced concepts of centrifugal force. The planetary one fits with the fictitious or pseudo force definition; it's due to measuring location r along a co-rotating direction vector. But David knows that already, just hasn't accepted it over the last year or so. Dicklyon (talk) 03:13, 12 July 2009 (UTC)


 * There are three sourced concepts, all in the article. One is the reactive CF, sometimes referred to as simply the CF. A second is the Newtonian CF, which appears only in rotating frames of reference and transforms as a vector force. A third is the Lagrangian generalized CF, which again is often referred to as CF, and has very little to do with the Newtonian concept, and a lot to do with a formal analysis based upon a space of generalized coordinates. The Lagrangian generalized CF has these differences from the Newtonian: (i) it does not require a rotating frame, (ii) it can be nonzero in an inertial frame (iii) it does not transform like a vector under coordinate transformations.


 * In the case of planetary motion involving only two bodies, the Newtonian analysis in a co-rotating frame is mathematically identical with the Lagrangian formulation based upon the Jacobi two-body coordinates (r, θ) as generalized coordinates. The Leibniz approach might be seen as a precursor of the Lagrangian method, as Leibniz' ideas about action had a lot to do with the background of the Lagrangian methodology.


 * Many physics problems can be approached with different intuitive ideas that lead ultimately to the same equations. That means they all predict the same thing. However, the intuitive notions behind the various schemes often are different, and may be valuable in themselves as they may point to useful ways to analyze other problems. The Newton scheme is tied to the notions of inertial frames and vector forces. The Lagrangian scheme is tied to variational principles based upon scalars. These intuitive schemes are not all the same, even if they all lead to the same mathematical equations. All roads lead to Rome, but all roads aren't the same road. So far, little stress has been placed upon whether the Leibniz scheme brings yet a fourth viewpoint to the problem. I don't know if it does or doesn't. Brews ohare (talk) 04:29, 12 July 2009 (UTC)


 * Ah, right, I forgot the Langrangian generalization. My "two" only applied to the conventional centrifugal forces.  Dicklyon (talk) 04:35, 12 July 2009 (UTC)


 * I'd add that the inclusion of the Leibniz scheme is warranted in this particular article only if it brings a special viewpoint to the notion of centrifugal force. For example, does the Leibniz approach include ideas that lead more directly to the equations than the Lagrangian or the Newtonian views? If Leibniz' approach is of interest only as an example of one of the others, it is best dealt with in the the more detailed articles, rather than in this summary or pre-amble article. Leibniz' special viewpoint (if it exists) need not be dwelt upon here in great detail, but should be outlined in the appropriate more detailed article. Brews ohare (talk) 04:44, 12 July 2009 (UTC)


 * From my point of view, the Leibniz scheme is only interesting from the historical perspective. Three of the historical references we're using (Swetz, Linton, Aiton - I've listed the quotes in the above section) equate Leibniz's scheme to the special case in Newtonian mechanics of a co-rotating frame, ie that he was describing motion within a frame tied to the planet. I know we have sources, like Goldstein, that derive the radial equation using the Lagrangian scheme, but don't make a connection with Leibniz's ideas. What we need is a source that gives the details of Leibniz's reasoning. However, as far as I can tell when people use his radial equation today, they arrive at it via Newton and therefore an implied non-inertial frame, or via Lagrange in which case it's a generalized force. I don't think I've seen a consistent derivation of Leibniz's radial equation that is distinct from these two. --FyzixFighter (talk) 05:03, 12 July 2009 (UTC)


 * After perusing the Aiton reference, Aiton seems to support the rotating frame view of Leibniz's scheme. He states:
 * "Influenced perhaps by Galileo's treatment of the motion of projectiles, Leibniz was aware of the principle of vectorial composition of motion, as is evident from one of his letters to Huygens. Resolving the motion of the planet into components along and perpendicular to the radius vector respectively, he considered these component motions separately. The motion perpendicular to the radius vector gave rise to an outward force, acting on the planet, and it was this force that Leibniz termed the centrifugal force of the circulation. Leibniz attempted to relate the other component of the orbital motion, namely, that along the radius vector, to the forces acting in this line. Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference. Eventually he succeeded in showing that the acceleration along the radius vector was proportional to the difference of the centrifugal force and the attraction."
 * and later
 * "Leibniz's centrifugal force arises from the acceleration of his frame of reference. The motion along the radius vector is a motion relative to a rotating axis and Leibniz understood that, relative to this axis, the body experienced a centrifugal force."
 * and in the end
 * "The use of a rotating axis was a distinctive feature of Leibniz's contribution."
 * Do we have any reliable sources that say otherwise, or that cast Leibniz's derivation within the framework of Lagrange or something similar to Lagrange? --FyzixFighter (talk) 06:06, 12 July 2009 (UTC)

FyzixFighter, you are completely missing the point. The point is that planetary orbits present an illustrative example of centrifugal force, and it is perfectly in order that such an example should be included in an article on centrifugal force. There are plenty of sources with quite a variety of methods which show that planetary orbital theory does not require a rotating frame of reference in the analysis. The fact that you can also produce sources that show that certain people have attempted the analysis using rotating frames of reference is not a justifiable reason for deleting the planetary orbital example or for relegating it to the history section. Planetary orbital theory is not history. David Tombe (talk) 12:10, 12 July 2009 (UTC)


 * David: You have not addressed the pertinence of an example in this article whose role is as a preamble to the other articles. As a preamble, its role is not to provide detailed examples, but to guide the reader to the appropriate other section. As such, the most that can be done here (assuming the Leibniz approach is subsumed) is to point out that centrifugal force in planetary motion is discussed at length in Centrifugal force (rotating reference frame) and in Mechanics of planar particle motion. Brews ohare (talk) 14:15, 12 July 2009 (UTC)

Brews, The problem is, which of the two re-direct articles would you send it to? I don't want to put it into the centrifugal force (rotating frames of reference) article when the topic in question is seldom dealt with in the context of rotating frames of reference. I had conceded that centrifugal force as a topic is dealt with on the modern science library shelves predominantly in connection with rotating frames of reference. I had conceded that point. But you should all likewise concede that planetary orbital theory is predominantly dealt with by methods that don't use rotating frames of reference, even if there are some exceptions. So I don't think that centrifugal force (rotating frames of reference) is the correct page for planetary orbits. As for the so-called reactive centrifugal force, there are some grounds for putting it there too. Some of you guys have been a little confused about the reactive concept and you have been wrongly trying to justify it in line with Newton's third law of motion. Unfortunately, it is not as simple as that. A web-link which Dick kindly provided, explains the history very well. Newton's reactive concept was born out of Leibniz's planetary orbital equation on specious grounds. I gave a clear quote from the 1961 Nelkon & Parker as to exactly what Newton's erroneous concept was. It was deleted and the correct definition of the reactive concept is not currently reflected in either this article or the 'reactive centrifugal force' article.

As you know, my own view is that the two re-direct articles should be deleted and this article should be the one single article on centrifugal force. Newton's erroneos reactive concept could be explained as a follow on to a section on planetary orbits and the Leibniz equation. Newton's erroneous concept still gives correct results for the special case of circular motion, and as you know, it is used by engineers. Alot could be written about the modern changing attitudes to centrifugal force citing examples of revised texts as in Nelkon & Parker (1961 v. 1970) and the Goldstein (1980 v. 2002). But unfortunately, even the revisionism has proved to be uncomfortable for certain editors.

We have material for a good interesting combined technical and historical article, but it is not getting off the ground because I have been working against too much opposition. There is opposition to anything that involves centrifugal force being exposed as an actual outward 'push' or 'pull' in the absence of rotating reference frames. And there is opposition to any mention of revisionism. That opposition needs to be examined. Why are certain editors so strenuously opposed to these things? It was actually you that wrote the current planetary orbital summary that has just been deleted. It is a re-write of my own version, but your version brings in 'reduced mass'. It is a very good short summary section. You really don't want to waste it. It gives interesting details such as the inverse cube law relationship for centrifugal force and the conic section shape of planetary orbits. It opens up the readers minds to the fact that centrifugal force has a variable value and is not simply an equal and opposite reaction to centripetal force as many people wrongly believe. David Tombe (talk) 17:29, 12 July 2009 (UTC)


 * Who is the intended audience for this page? I would suggest that it would be mainly students of physics.  No one here has the expertise to write for a more advanced audience.


 * On that basis I would suggest that only one definition of centrifugal force (fictitious force) should be discussed in the main section of the article and that all other definitions should be moved to the history section. Martin Hogbin (talk) 21:37, 12 July 2009 (UTC)


 * The original purpose of this article was to have a short article summmarizing the different conceptions, and main links to the articles on the details at Centrifugal force (rotating reference frame) and Reactive centrifugal force. Unfortunately, it has become quite bloated.  But it would be better to prune it back than to have it take over the role of Centrifugal force (rotating reference frame).  Dicklyon (talk) 21:44, 12 July 2009 (UTC)


 * Yes, I see. In that case I think the title is a little misleading.  It should something like 'Centrifugal force (different concepts) or 'History of centrifugal force'.  Either that or the article should be pruned heavily and also make clear the concept that is most commonly taught today. Martin Hogbin (talk) 22:00, 12 July 2009 (UTC)


 * I would not agree that only one definition should be discussed, and do not agree that all others are somehow only of historical interest. The sources show all three versions have strong modern adherents. Brews ohare (talk) 21:48, 12 July 2009 (UTC)


 * Other concepts are of historical interest only are for anyone trying to understand the subject for the first time. Other uses of the term, which I am sure do still exist, are very confusing to beginners.  It would be best to refer to them along the lines of, 'In some areas of engineering the term is used to mean...'. Martin Hogbin (talk) 22:00, 12 July 2009 (UTC)


 * It's not really different areas, just different conceptions. The reactive force concept is simple and easy to understand; the pseudo-force is more useful and more widely taught.  We don't need this article at all except to summarize these two and dispatch to the main articles, in my opinion, but Brews jumped in the with the big middle section on "Centrifugal force and absolute rotation", which dispatches to more related articles, and the "Lagrangian formulation of centrifugal force", which I'm still not sure what to make of.  Perhaps he's trying to attract some readers to his articles Bucket argument, Rotating spheres, Clairaut's theorem, Mechanics of planar particle motion, etc.  Maybe he's actually writing a book, and these are his chapter drafts.  Hard to say... Dicklyon (talk) 22:12, 12 July 2009 (UTC)


 * I disagree that the reactive concept is easy to understand. It might be easy to apply in some cases where the physics is not important but what is described as 'revisionism' in this article is the realization by teachers of physics that the reactive concept of CF is confusing to most students.


 * If we use this page as a short disambiguation type page then we should still make clear that the only concept taught to students of physics is the 'rotating frames' one. Martin Hogbin (talk) 22:28, 12 July 2009 (UTC)


 * Most common, yes; but only, no. Here's a 2004 physics book that teaches the reactive CF.  Here is a 2001 book that has it both ways.  There are lots of other examples, so let's not push a single POV when there are several that can be represented as easily as one.  Dicklyon (talk) 22:37, 12 July 2009 (UTC)

Your first reference clearly describes the reaction force as the centrifugal reaction. It then goes on to describe the centrifugal force in terms of a rotating frame. For this article to call what the book describes as a centrifugal reaction as the centrifugal force is confusing and incorrect.

The second source clearly describes CF as an apparent force in a rotating system. Martin Hogbin (talk) 08:18, 13 July 2009 (UTC)


 * Yes, you're right; the first uses the term "centrifugal reaction" for what we're calling reactive centrifugal force; the second says "the reaction to this force [centripetal] is the centrifugal force. Here is a 2002 Physics for Geologists book that teaches "the centripetal force (the equal and opposite reaction being the centrifugal force)".  These are not "incorrect", just a different thing than the one thing that you want to call correct; it's OK to discuss what we think is correct, but in the article we need to represent actual uses, and try to de-confuse them rather than pretending there's only one.  The point of this article was to compare and contrast these two things, and vector off to the main articles on each; but it has gotten way out of control, as you can see.  The comparison table was one that Brews made up to try to explain the difference to David, and I recommended we use it here for this purpose; I think it makes very clear that the two things called centrifugal force are two different thingss.  In the process, I also learned that there are two things called centripetal force, but they're usually nearly the same; sometimes in a planetary orbit situation, the central force is taken to be centripetal, even for non-circular orbits, but the more strict definition usually taught is that the centripetal force is only the component perpendicular to the velocity vector.   It's another case where it would be better to show both uses and compare them, rather than pretend the "incorrect" one doesn't exist. Dicklyon (talk) 22:27, 13 July 2009 (UTC)


 * The Roche reference used in the article is the one that I have found the most helpful with respect to your question Martin. In it he states:

What question?


 * "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."
 * He later clarifies the engineering definition:
 * "But we must leave the final word to the engineers. The stresses that develop in rapidly rotating turbine blades are thought of by mechanical engineers as being due to centrifugal forces. To take a simple example, an object whirled on an elastic string pulls the string outwards, creating the tension in the string. Both the inertial centrifugal force acting on the string and the elastic centripetal force acting on the moving body are reaction forces—they call each other into existence. Centrifugal and centripetal force are equal and opposite here but do not balance because they act on different bodies.
 * In a rotating turbine, for example, each outer section of the blade exerts an outwards pull on the portion between it and the shaft, while at the same time the latter exerts an elastic inwards pull on the former. It is the stresses in the blades and their causes that mainly interest engineers, rather than the centripetal forces. It follows that both elastic centripetal forces and inertial centrifugal forces act in a rotating solid body."
 * The Kobayashi reference says something similar:
 * "The term centrifugal force then has two meanings: one is the inertial force due to the rotation of the noninertial frame relative to the inertial frame and the other is the reaction force of the centripetal force to produce acceleration toward the center of rotation. The origins of these forces are different from each other."
 * --FyzixFighter (talk) 15:10, 13 July 2009 (UTC)


 * Yes, I know. What is the point of this article?  Who is it intended to help and what is it intended to help them do? Martin Hogbin (talk) 16:14, 13 July 2009 (UTC)


 * Sorry, I misunderstood your concern. I meant to address your comment that the rotating frame/fictitious CF is the only concept taught today. Is not just physics education that we need to address, but also engineering education in which the reactive centrifugal force and Lagrangian centrifugal force are not just a historical conceit. Anyways, sorry again for the misunderstanding and thanks for starting the section below. --FyzixFighter (talk) 19:16, 13 July 2009 (UTC)


 * Oppose introduction of Leibniz inverse cube centrifugal force. Now that I have understood what the question is I will state my opinion on the subject.  Leibniz' treatment of CF as an outward-acting inverse cube force should only be presented in the history section.  There should be no statement of an inverse cube law of centrifugal force in the rest of the article. Martin Hogbin (talk) 08:54, 14 July 2009 (UTC)

Martin, it's both history and present. The Leibniz equation is still the planetary orbital equation which is used in modern textbooks to obtain the elliptical, parabolic, or hyperbolic solutions for the two body problem. I have suggested an introduction section which deals with the conflict between Newton and Leibniz on this point, because it is very relevant to the three different aproaches which exist today for centrifugal force. David Tombe (talk) 13:15, 14 July 2009 (UTC)


 * Judging from Linton's exposition, Leibniz's view of centrifugal force was quite different from those adopted in current mainstream treatements. As such, it is only of historical interest, and any mention of it should be confined to the history section.
 * Although modern treatments do obtain the same equation that Leibniz did for the radial acceleration in the two-body and single-body problems with a central force, this should not be used as a pretext for labelling them as "Leibniz's approach", or even as having that approach as a "basis", as was done in the previous introduction recently removed (justifiably, in my opinion) by FyzixFighter.
 * Since the one-body and two-body problems with central forces are rather special cases, I don't see why it should be necessary to mention Leibniz's equation outside the history section, even as a merely illustrative example of the modern usage of the term "centrifugal force". I tend to agree with Martin Hogbin that it's likely to be more confusing than enlightening to the average reader.
 * In the history section, the inverse cube term in Leibniz's equation is currently referred to as a "law". This seems a rather grandiose term for what is, after all, a very special case (the "law" doesn't hold in systems of more than two gravitating bodies, for instance).  Do we have any reliable sources that refer to it as a "law"?  If not, we shouldn't do so either.
 * &mdash;David Wilson (talk · cont) 07:57, 18 July 2009 (UTC)


 * David, You acknowledge that modern treatments do obtain the same equation that Leibniz did for the radial acceleration in the two body and single body problems with a central force. That is absolutely correct. And that is all that I have ever been saying since this dispute began. The idea of calling that equation 'Leibniz's equation' has only entered the debate very recently as a result of a reference supplied by Dicklyon. Whether we call that equation 'Leibniz's' equation' or 'the radial planetary orbital equation' is only a matter of semantics. I don't mind which name is used. Likewise with the inverse cube law centrifugal term. It doesn't matter to me whether you write it in the inverse cube law format or the rω^2 format. David Tombe (talk) 13:55, 18 July 2009 (UTC)


 * I apparently may need to clarify my second bullet point above. I have no objection whatever to the article's calling the equation in question "Leibniz's equation". What I was objecting to was the categorisation of modern derivations or analyses of that equation as being "Leibniz's approach" or "based on Leibniz's approach".
 * &mdash;David Wilson (talk · cont) 16:13, 18 July 2009 (UTC)

David W, This dispute began in 2007 because the modern "derivations" or "analyses" of that equation were being denied entry into the article. It had nothing to do with terminologies, or with how Leibniz first derived the same equation. I was trying to insert the radial planetary orbital equation into the article as an illustrative example of centrifugal force. That was all. And the attempts to suppress that piece of physics led to endless false allegations that I was trying to insert original research. You can now see those false allegations being parroted at ANI by persons who know absolutely nothing about the content matter of the dispute. David Tombe (talk) 19:49, 18 July 2009 (UTC)

History articles in general
There are times when a history section rightfully belongs at the bottom of an article. That would be in the case when there is a long chronology of obselete ideas, such as with the history of the periodic table. But there are other occasions in which the modern day understanding of a topic is very closely tied to its historical evolution. And if that topic remains ambiguous in the present day literature, it is very important that a brief historical lead in to the topic appears early in the article.

The current confusion over the reactive centrifugal force concept can't be fully understood in the absence of a mention of Leibniz's equation. And Leibniz's equation is still used today in planetary orbital theory, and so it is not entirely history.

The story is that Leibniz produced the planetary orbital equation which included the inverse cube law centrifugal force. Newton objected to that equation and claimed that centrifugal force is an equal and opposite reaction to the centripetal force.

The problem that we have here is that the most common modern approach to centrifugal force as a topic in its own right is neither the Leibniz approach, nor the Newtonian approach. On the other hand the modern approach to planetary orbits cannot be done in the absence of centrifugal force even though there has been a remarkable dilution in recent years as regards explicit mention of that fact.

The matter is further complicated by the fact that there is even a divergence as regards what the reactive approach actually entails. Some texts cite the reactive approach exactly as per Newton, acting on the same body as the centripetal force, and even apply it to planetary motion. Other texts look at the transmitted knock on effect which this centrifugal has on another body and try to reconcile it all in terms of Newton's third law of motion over two bodies.

For a compromise, we need to have a short introduction to the article which points out these important points. What follows next in the main sections will depend entirely on which editors decide to write more on their particular area of interest. David Tombe (talk) 11:54, 14 July 2009 (UTC)


 * Leibniz was an excellent mathematician but his concept of centrifugal force plays no part whatsoever in modern physics. His assumed inverse cube law happens to be the case for a particle in a central force field but his theory is of historical interest only. Martin Hogbin (talk) 13:37, 14 July 2009 (UTC)


 * Martin, how can it be of historical interest only if it is still used today. I used it at university. It is in my applied maths notes. It is equation 3-12 in Goldstein's 'Classical Mechanics'. This is one of these situations where the historical evolution and the dispute with Newton forms a necessary lead in to the differeing approaches to centrifugal force that appear in the modern textbooks. You cannot hope to explain the reactive concept (in either form) without some reference to the story of Newton's reaction to Leibniz's equation. In fact. I'll show you this reference so that you can read about it. See here David Tombe (talk) 16:32, 14 July 2009 (UTC)


 * The current sources (such as Aiton, Swetz, and Linton) that address Leibniz and his role in the history of the centrifugal force are also clear that his description of the dynamics is tied to the co-rotating, non-inertial frame. All modern sources that get the planetary orbit equation or something similar get there via Newton's laws and non-inertial frames or Lagrangian mechanics and generalized forces. --FyzixFighter (talk) 14:43, 14 July 2009 (UTC)

FyzixFighter, my intention was to fully address that issue. I am looking for a compromise. I had every intention of mentioning the fact that most modern textbooks introduce centrifugal force in connection with rotating frames of reference. However, planetary orbital theory is not in general treated using rotating frames of reference even if there are exceptions such as you have cited.

My planned wording was going to finish something along the lines of what I have just said. Ie. " Subsequent to the time of Leibniz, the concept of a rotating frame of reference became gradually more prevailent in physics. That concept features prominently in the important works of Gustave Coriolis (1835) and nowadays it is the most common context in which the centrifugal force is introduced - - - ".

I think that this would be a fair compromise. The next section could then deal specifically with centrifugal force in rotating frames of reference. David Tombe (talk) 16:19, 14 July 2009 (UTC)


 * I think it could be mentioned in the history section in some such way (maybe it is already, I'll have to review); but be sure to say it in a way that you can back up with a source; and we don't really need the equation in the history. Dicklyon (talk) 16:59, 14 July 2009 (UTC)

Dick, I've put in a short introduction. It duplicates material from the history section, but the particular aspects of history in question are important for the purposes of leading in the subject. If that introduction is acceptable, then the edit war is over. Discussions may continue, but the edit war will be over because the controversial material will have been given its due place, albeit in a very much watered down manner from what I would have preferred. David Tombe (talk) 19:40, 14 July 2009 (UTC)


 * Dick is correct that sourced and non-OR bits of your "compromise" introduction are already in the history section. If stating the history is important to leading into the subject, then I would suggest moving the history section to earlier in the article. But I think the modern science understanding is the best way to lead into the article. What do others think, do we need a detailed history/intro section? --FyzixFighter (talk) 21:58, 14 July 2009 (UTC)

David's proposed introduction

 * Sir Isaac Newton said that centrifugal force is the equal and opposite reaction to a centripetal force as per his third law of motion. However, the circumstances in which Newton made this conclusion need to be carefully considered. Newton was responding to the planetary orbital equation which had been derived by his arch rival Gottfried Leibniz. Leibniz's equation indicated that centrifugal force is a radially outward force that obeys the inverse cube law in the radial distance. Leibniz's idea contradicts Newton's concept of centrifugal force in that in Leibniz's view, the centrifugal force does not have to be equal in magnitude to the centripetal force. It is believed that Newton was once working on a similar approach to Leibniz but that he adopted this contradictory stance on first seeing Leibniz's equation for the sole purpose of denigrating Leibniz's work. Both of these approaches to centrifugal force are still found in the literature today. The Leibniz approach is still the basis for solving the two body central force problem, albeit that explicit references to the centrifugal force term in this context are becoming increasingly diluted in the literature. Meanwhile, the Newtonian approach is also rapidly disappearing from the textbooks.


 * The most common approach to centrifugal force in modern textbooks uses the concept of rotating frames of reference. The concept of rotating frames of reference began to arise in physics in the 18th century and this concept features prominently in an important paper written in 1835 by Gustave-Gaspard Coriolis. Centrifugal force is nowadays considered to be a fictitious or an inertial force which arises when a situation is viewed from a rotating frame of reference.

Discussion
As I stated before, this is pretty well covered already in the history section. However, there are several points where this text is lacking and OR: As I stated above, if we want a section like this at the beginning of the article, let's move the history section up. However, I think the history section works better after the extremely mainstream summary explanations. --FyzixFighter (talk) 21:58, 14 July 2009 (UTC)
 * 1) First line about Isaac Newton - actually Newton totally dropped the idea of centrifugal force in his Principia (see Linton, pg 264). Only when he started arguing with Leibniz did Newton make this argument and mis-applied his 3rd law. As Swetz notes, Newton and Leibniz were using the term centrifugal force in different senses.
 * 2) "...need to be carefully considered." - POV and unsourced editorializing.
 * 3) Leibniz's approach description - fails to mention that he was working in a rotating frame (see both Swetz 269, and various parts of the Aiton paper)
 * 4) "...increasingly diluted in the literature...rapidly disappearing from textbooks" - completely unsourced opinion
 * 5) Second paragraph, again already covered in the history section


 * Personally, I usually prefer a history section early, to help position the concepts. I haven't determined whether that is necessarily better in this article, but it might be. Dicklyon (talk) 22:08, 14 July 2009 (UTC)

FyzixFighter, I appreciate that certain items are duplicated in the history section. But my intention here was to highlight the key historical aspects which most directly lead into the concepts in modern usage. If we can sort the introduction out first, then we can tidy up the history section afterwards. Like I explained earlier, there are times when it is best to have a history section early, and there are times when it is best to have it later. A lengthy history section is best at the end of an article.

As regards rotating frames of reference, that issue was adequately dealt with. I clearly stated that the idea crept in and took root as early as Coriolis's 1835 paper. Leibniz himself didn't use the concept. We cannot retrospectively impose the concept unto the Leibniz approach simply because modern authors who were writing about him stated their own opinions on how they thought it should have been, based on the paradigms of the era that we now live in. I think that you are going over the top a bit on this rotating frames issue. You are using sources disproportionately. The majority of textbooks on planetary orbital theory do not use rotating frames of reference. It is therefore quite wrong to describe the historical Leibniz equation in that context. I stated the Leibniz approach and the Newtonian approach and then went on to point out that we then moved into an era of rotating frames of reference. It that not a sufficient compromise? Don't forget that we are trying to get a compromise to end the edit war. This is instead of having a full section on the two body problem with equations. David Tombe (talk) 23:40, 14 July 2009 (UTC)


 * Then let's fix up the history section and move it earlier in the article. Honestly IMO the history section is pretty good, though it jumps around a bit at the beginning - I'll see what I can do on that. I'm not in favor of moving it up, but if most of the editors feel that it belongs at the beginning of the article then that's what we'll do. Thoughts Martin and Brews? Moving it for me it's a flow/aesthetic issue and not a content issue.
 * As for going over the top with casting Leibniz in the rotating frame paradigm, unfortunately all of the historical references we have that talk about Leibniz do this. Do you have a reference that talks about Leibniz and doesn't talk about rotating frames?
 * I'm highly skeptical of your statement that the majority of textbooks on planetary orbital theory do not use rotating frames of references. The only instant where they would not is if they are using Lagrangian mechanics (such as Goldstein and Shankar), in which case it highlights the distinction between a Newtonian force and a generalized force and the Lagrangian section covers those instances. If they are using Newtonian mechanics, using F=ma, to get the radial equation then they are using rotating frames. In Newtonian mechanics, centrifugal forces do not appear on the force side of F=ma for planetary orbits; to paraphrase Linton, Leibniz's centrifugal force disappears in Newton's Principia, it's not needed, only a centripetal forces exist.
 * Read Aiton's article. He does a good assessment and analysis of Leibniz's derivation. Leibniz had the brilliant idea to cast his problem by only considering motion along the rotating radius vector, in modern parlance Leibniz was describing his dynamics in a rotating reference frame (as Aiton clearly indicates multiple times). When Leibniz was considering motion along the rotating radius vector, he found that Kepler's laws leads to a radial equation of the form that we are all familiar with, r-double-dot on one side and a negative inverse square term and a positive inverse cube term on the other side. We agree that the equation is mathematically valid. But the question that sums up our disagreement is whether Leibniz's early concept of centrifugal force can be interpreted meaningfully. The answer according to all the secondary sources is this: in the inertial frame, considered as a force (using the traditional since the days of Newton definition of force) acting on the circulating body itself, his centrifugal force does not exist (see Swetz, pg. 269). Only in a reference frame rotating with the circulating body does the body appear to have an endeavor to recede from the center (again, Swetz, pg 269). I don't see how we can write anything else without being true to the sources. Is there anyone besides David that disagrees with this summation? Are there any sources that disagree with this? --FyzixFighter (talk) 03:19, 15 July 2009 (UTC)

FyzixFighter, It's more the case that I agree with Leibniz's interpretation as you have described it above. I see it in that exact same way. We have a radial equation with two radial forces. And I can assure you that in 1979/80, I never once saw a textbook that dealt with planetary orbits any other way, although, as I said in the edit, explicit references to the word 'centrifugal force' were rare. I originally did the course using Williams's 'Dynamics'. It contained the relevant equation and it didn't use rotating frames of reference. But equally, there was no explicit reference to the word 'centrifugal force' in relation to the corresponding term that Leibniz would have called centrifugal force. The book I used the next year was Goldstein. I didn't do planetary orbital theory from Goldstein. We used that book for 'Lagrangian mechanics'. Nevertheless, the same equation appears in the planetary orbit chapter of that book, and Goldstein does call the term 'centrifugal force'. However, his use of the term leaves the application somewhat ambiguous and hence leaves the situation open for some, such as yourself and Dick, to claim that he was only using the term in connection with the equivalent one-dimensional fictitious problem. On the other hand it is also obvious that the term when written in the form that uses angular speed, can only be referring to equation 3-12 which is written in relation to the real two dimensional problem. That's what I meant when I said that explicit references to centrifugal force in the context have become increasingly diluted. I could even give you the comparative quote between pages 176-179 as between the two editions of Goldstein (1980 v. 2002) to illustrate the changing attitudes. Likewise, I could show you the comparative quotes in Nelkon & Parker as between 1961 and 1970 which also show the corresponding changing attitudes to the Newtonian concept in our times.

So if we are going to mention the Leibniz equation, then we should mention it without imposing what some authors consider to be the modern interpretation of it. The correct balance is to state Leibniz's position and then state that the move then drifted towards rotating frames of reference, and that modern textbooks mostly introduce centrifugal force within the context of rotating frames of reference. If you insist on connecting rotating frames of reference directly with the Leibniz equation, then you are indulging in revisionism and you are using sources selectively to back up your own point of view. Likewise if you claim that the Leibniz equation is purely historical, you are then denying the truth that it is still very much used today, irrespective of the differing interpretations that are found throughout the literature. There is a way of writing these complex issues in a truthful and balanced matter which is in line with the sources.

You on the other hand are using sources in a manner such as to impose a modern viewpoint on top of a historical viewpoint. It's known as re-writing history. The bottom line is that I think that Leibniz was right (apart from his solar vortex model) because it's the only way that you can treat the centrifugal force between mutual pairs of objects in a three body problem or upwards. The rotating frames approach only considers one sigle angular speed and it ignores the individual centrifugal forces between any pair of particles in a multi particle system. That's why I have my point of view. But you haven't declared your motives for being so strongly opposed to the Leibniz point of view, and you are hiding behind selected sources claiming to be on the side of wikipedia's rules, when in actual fact, the situation regarding those rules leaves a considerable degree of leeway. That's why I have wanted the involvement of an administrator who is knowledgeable of the facts of the dispute. This dispute cannot be allowed to be won on a head count of editors who know absolutely nothing about the topic.

As for the history section itself, I agree that it needs to be tidied up a bit. But what do you want to do to it? Do you want to re-write history by imposing the modern attitudes on rotating frames of reference on top of old ideas that didn't use such a concept? As far as I am concerned, it all went off the rails when Coriolis failed to see the physical link between the Coriolis force and the associated rotating frame of reference. But that is my opinion and I will not be writing that in the article. Likewise I would hope that you would equally show respect for viewpoints as they arose at the time in question, and also in relation to the differing viewpoints which exist even in the modern literature. We cannot allow history to be re-written by 'some' selected modern sources. David Tombe (talk) 11:09, 15 July 2009 (UTC)


 * Goldstein's planetary section is done using Lagrangian mechanics - so that source is covered by the Lagrangian section. Interestingly enough, when the mr*theta-dot^2 term appears on the left hand side, he calls it a centripetal acceleration term. Since all the reliable sources we currently have place Leibniz's derivation squarely in the rotating frame paradigm, that is how his scheme will be presented, both historically and in how his radial equation is used today (at least when derived using F=ma). --FyzixFighter (talk) 13:43, 15 July 2009 (UTC)

FyzixFighter, Goldstein calls the radial convective term 'centripetal force' in connection with polar coordinates in the absence of a gravitational field. That has got absolutely nothing to do with the topic in question. In the planetary orbital equation, that same mathematical expression is unequivocally the centrifugal force. This is an example of you trying to distort the facts. Under no circumstances can the inverse cube law term in the Leibniz equation be the centripetal force. As regards the reversion which you did, the contents alone are not what was important. It was the manner in which the contents led the topic in. Your arguments for removing that material are totally barren. You are putting up an outward show of intellectual argument, but what you are saying is so badly wrong. You know the truth, but you are intent on twisting the facts. As I have said, you are merely playing a clever card game with sources which takes advantage of the confusion in the literature. You are using sources selectively to sabotage the overall understanding of the topic. David Tombe (talk) 13:59, 15 July 2009 (UTC)


 * There are so many things wrong with this diatribe by David that it can serve no purpose other than to illustrate what a crank he is. Dicklyon (talk) 18:21, 18 July 2009 (UTC)

What is the purpose of this article?
What is the purpose of this article? I we cannot all agree on this it is going to be hard to agree on the wording.

Is it:

1) A form of disambiguation page to direct readers to the appropriate article to meet their needs.

2) A list of all the different ways in which the term 'centrifugal force' has been used, with some discussion of each.

3) Something else. Martin Hogbin (talk) 17:09, 13 July 2009 (UTC)


 * I'd say 2. More than a disambig, but a WP:Summary style article.  Dicklyon (talk) 17:59, 13 July 2009 (UTC)


 * I agree with Dick - #2, covering the different ways the term has been and is being used. One section that I'm having trouble seeing fit into that scheme is the current "absolute rotation" section. But maybe once we agree on the purpose, we can discuss that concern more directly. --FyzixFighter (talk) 19:06, 13 July 2009 (UTC)


 * I agree that the 'absolute rotation' section does not fit in at all. Why not remove it then? Martin Hogbin (talk) 20:02, 13 July 2009 (UTC)


 * The section was copied in from another article on 13 May by David Tombe in this diff with summary (bringing across interesting section from the branch article. But it needs to be drastically reduced in size). I questioned it in this talk diff; see Brews and David followups.  Brews seems to share some concern about the section relative to the purpose of the article, but decided to side with David and expand it.  These two guys tend to be on opposite ends of most arguments, and their disagreements invariably lead to article bloat, as in the centrifugal force (rotating reference frame) article that we're trying to avoid duplicating here, which is where it was imported from.  I agree we should either get rid of or greatly reduce this section; maybe even make a whole article on this interesting topic, which is pretty off topic for a summary article. Dicklyon (talk) 16:55, 14 July 2009 (UTC)


 * In keeping with summary style, I made an article out of this section and left a summary paragraph and main link to it. Dicklyon (talk) 16:53, 21 July 2009 (UTC)

Well of course Martin, at the end of the day it is 'absolute rotation' that is the thorn in the neck for relativists, and so from your perspective it would be better that such a section should not be seen. I can see from your intervention here that you are very keen in singularly promoting the 'rotating frames of reference' approach as being the only legitimate approach, and so you want to scotch all aspects of centrifugal force that don't sit comfortably with your preferred approach. You clearly don't like the idea that absolute rotation causes pressure in the water in a bucket. This is of course an article about centrifugal force, but you obviously want all the readers to be taught that centrifugal force is merely an illusion that arises when observations are made from a rotating frame of reference. I don't support your idea to remove that section. But I doubt if my viewpoint will get majority support in this arena. David Tombe (talk) 20:17, 13 July 2009 (UTC)


 * Absolute rotation: I don't see why the article has to have a single purpose: usages of the term. It also has the purpose of introducing articles of interest to centrifugal force. Certainly the history is is one such. Absolute rotation is another, inasmuch as this plays a key role in the history and in the applications. It also is key to understanding the difference between inertial and noninertial frames, the origins of general relativity, and the distinction from the Lagrangian approach. All these sections refer the reader to other WP articles likely to be of interest. I do not think a person looking up centrifugal force here is looking for a dictionary: they may have other interests and simply chose "centrifugal force" as an entry point hoping to find what they really are looking for. Brews ohare (talk) 20:35, 13 July 2009 (UTC)


 * As I was the one who brought this up, maybe I should elucidate a bit. I could see including it as a subsection of the historical part. What is the current status of the absolute rotation debate? The first two parts, the bucket argument and rotating spheres seem to me to be directly tied to the early debates about absolute rotation. (These parts also make parts of the detailed "see also" section redundant). I don't see how the third section enters in the absolute rotation debate; I see it more as a historically interesting application of the centrifugal force concept. In other words, the references provided do not establish that the oblateness of the earth entered into the absolute rotation debate like the other two parts do. --FyzixFighter (talk) 21:06, 13 July 2009 (UTC)

FyzixFighter, that's all shear sophism. Nobody could possibly follow your point. Basically you want 'absolute rotation' off the page for the same reason that you wanted the planetary orbital equation off the page. You want to erase all evidence that centrifugal force is associated with a real pressure. You've got centrifugal force as an inverse cube law force off the page. Now your target is 'absolute rotation'. Next it will be the Lagrangian section. Finally it will be the 'reactive centrifugal force'. Then you will feel that you have successfully fought to make physics pure and relativistic. You will have a nice clean article based on solid relativistic values. David Tombe (talk) 21:13, 13 July 2009 (UTC)


 * I support removing the section entirely; it's already in the "main" article that we link to on rotating reference frames; let's get back to summary style, and move these debates to the relevant pages.  Dicklyon (talk) 16:56, 14 July 2009 (UTC)

Dick, I agree with your earlier proposal that this section should be reduced in size. In fact, if you examine the edits carefully from May 2009, you will see that I made this very point myself. I said that this section should ideally be drastically reduced in size. I even made suggestions as to which key points should be left in. I gave Brews a rough sketch of a derivation for the centrifugal potential energy equation. Interestingly, it was originally in the rotating frames re-direct article. But it straddles all kinds of centrifugal force. Hence we need a summary of it in this summary article. David Tombe (talk) 18:29, 14 July 2009 (UTC)


 * I agree with Dick, remove it completely, it is different subject. Martin Hogbin (talk) 13:53, 15 July 2009 (UTC)


 * I didn't say it's a different subject, just not right for summary scale; a size reduction could be an OK fix, since several people want to keep it. Dicklyon (talk) 17:56, 15 July 2009 (UTC)

Martin, can you explain how centrifugal pressure and centrifugal potential energy as generated by rotation is a different subject that doesn't belong on the centrifugal force page? Once again I am detecting a case of somebody wanting material removed from view because it doesn't sit comfortably with certain other topics in physics. This kind of censorship cannot be allowed. David Tombe (talk) 14:05, 15 July 2009 (UTC)

Issues with Lagrangian formulation
There are some issues with the way this article describes the Lagrangian formulation.

First, it tries to distinguish between the Newtonian formulation and the Lagrangian formulation. However, these are just two of several mathematically equivalent formulations of classical mechanics, and thus not really separate from each other. —This is part of a comment by Cardamon which was interrupted by the following:
 * Naturally the two formulations are equivalent; if they were not, then one or the other world be incorrect. However, although equivalent so far as predictions are concerned, the formulations are different: one is based upon variational principles and scalar quantities; the other is based upon vector forces, Newton's laws and frames of reference. If you would like to read about the differences, see Lanczos. —Preceding unsigned comment added by Brews ohare (talk • contribs) 04:03, 21 July 2009 (UTC)

Second, it implies that generalized coordinates are specific to the Lagrangian formulation. However, generalized coordinates can be used in, for example, the Hamiltonian and Poisson bracket formulations of classical mechanics. So generalized coordinates are not specific to the Lagrangian formulation —This is part of a comment by Cardamon which was interrupted by the following:
 * This is a misreading of the article: it does not say that Lagrangian mechanics is the only place that generalized forces come up; what it says is that they do arise in Lagrangian mechanics, and in Lagrangian mechanics they are different from Newtonian vector forces. Brews ohare (talk) 04:03, 21 July 2009 (UTC)

While it is a little difficult to use generalized coordinates directly in an F = ma approach, it is often possible to first get a set of differential equations in Cartesian coordinates from an F= ma, and then change variables and do some algebra to get these differential equations in a set of generalized coordinates. For example, this will work to derive the equation 3-12 of Goldstein for the 2-body central force problem, which one of the frequent contributors to this page is enamored of.

That equation can also be derived in many other ways; it is not specific to any one formulation of classical mechanics. It can't be; it is a property of how an object moves. All mathematically equivalent formulations of classical mechanics must predict the same motions, or classical mechanics has been disproved. Not surprisingly, they yield the same differential equations. —This is part of a comment by Cardamon which was interrupted by the following:
 * While possibly true, the relevance of this discussion to the differentiation of the "generalized" from the "Newtonian" forces is unclear. Again, the issue is not one of whether one arrives at the same equations. (The comparison of the Lagrangian approach based upon generalized coordinates (r, θ) and the equations found using the co-rotating frame in Newtonian mechanics is discussed at length in several places; for example Centrifugal force (rotating reference frame); Mechanics of planar particle motion; Lagrangian mechanics.) Brews ohare (talk) 04:03, 21 July 2009 (UTC)

Thus discussing the meaning of the L^2/r^3 term with respect to the details of its derivation in just one of the formulation of classical mechanics (the Lagrangian formulation) would be beside the point.

Yes, the L^2/r^3 term has sometimes been called “centrifugal force”.Cardamon (talk) 20:28, 20 July 2009 (UTC)


 * You miss the point that the users of the Lagrangian approach, Hildebrand for example, use the term centrifugal force even in an inertial frame when polar coordinates are used, despite the fact that the centrifugal force of Newton is zero in any inertial frame.
 * I believe you are pointing out that deciding which of these formulations is correct is a mistake. That is so, but is not the point. The point is the usage of terminology: the same terms are used with different meanings in different contexts. In one case centrifugal force is a consequence of the choice of generalized coordinates, and in the other case the consequence of the observer's acceleration. Sometimes it doesn't matter, but sometimes it does. This difference is really, really evident in the field of robotics: please take a look at the cited sources, which all are available on line. Brews ohare (talk) 04:03, 21 July 2009 (UTC)


 * The correct way to deal with this subject, on which there clearly is a some disagreement, is to find a reliable secondary source which clearly states that the term 'centrifugal force' is used with a distinct and special meaning in Lagrangian mechanics.


 * To make what I mean clear. We have two agreed and different meanings of the term CF, the fictitious force and the reactive force.  If we are going to say that the term is used in Lagrangian mechanics with a third meaning, we need to find a reliable secondary source which says something along the lines of, 'In Lagrangian mechanics the term CF means... and is applied to terms...'.  In is not acceptable to find a source that just says that a particular term is the CF.  We need a secondary source that clearly states that there is a specific meaning to CF in Lagrangian mechanics, and ideally clearly explains what that meaning is. Such a source should not be too hard to find if there really is a third meaning of the term.Martin Hogbin (talk) 08:43, 21 July 2009 (UTC)

I gave a reply to Cardamon above which was deleted by Dicklyon. I'll not bother reinstating it because there are now new comments to be addressed. I said in my first reply to Cardamon that there is only one universal centrifugal force and that the term in Goldstein's equation 3-12 caters for any real case scenario which anybody could possibly imagine. It will cater for the force between two bodies in mutual transverse motion that will pull a mutually attached string taut.

What it does not however cater for is the situation in which an object is stationary in the inertial frame and being viewed from a rotating frame, and where no centrifugal force exists. This is where the controversy arises and where the three way argument occurs.

Some will continue to argue that the centrifugal force in Goldstein's 3-12, or in the Lagrangian formulation caters for that scenario, and that the Coriolis force will swing around like a weather cock in the prevailing wind and cancel the centrifugal force out.

I personally cannot go along with that idea. This is a classic case of maths having come off the rails as far as the real world is concerned.

Brews on the other hand sees that something is amiss. He rationalizes with it on the basis that he sees two different kinds of centrifugal force at play. He sees one kind that can arise in an inertial frame of reference, and he sees another kind that can only arise in a rotating frame of reference.

But as far as I am concerned, there is only one universal centrifugal force and it is the centrifugal force that arises in Goldstein's equation 3-12, and in the Lagrangian formulation, and it is measured relative to the inertial frame. It is an inertial force that is built into the straight line inertial path. It is the centrifugal force that is related to centrifugal potential energy in a spinning object or in a rotating bucket of water. It is the very same centrifugal force which is felt in an actual rotating frame of reference, such as a turntable, when dragging forces cause an object to co-rotate. David Tombe (talk) 10:36, 21 July 2009 (UTC)

Lagrangian centrifugal force
The suggestion has been made that the Centrifugal force section is superfluous, or invented "to attract attention" to other articles (apparently connecting to other articles related to Centrifugal force is evil). However, I'd like to draw attention to long debates over "curvilinear centrifugal force" that involved editors SCZenz, Paulo.dL, Rracecarr, PeR, Wolfkeeper, TimothyRias, FyzixFighter. Tstone T, Fugal which involved the notion that Newton's concepts were at a minimum antiquated and probably wrong, that everything depended upon the metric of the coordinate system chosen and that centrifugal force that was zero in Cartesian coordinates suddenly showed up in polar coordinates. The way out of this round-robin was the Lagrangian formulation, which agreed with that viewpoint, but was historically understood in relation to the Newtonian formulation. Do you all really want to open that can of worms again? As soon as the Lagrangian formulation disappears, the whole cycle starts over again. And BTW, the Lagrangian formulation is (i) currently in active use, (ii) a topic of great importance & (iii) very well documented. Brews ohare (talk) 21:03, 14 July 2009 (UTC)


 * My short answer is no, let's not revisit it. The references provided that identify the Lagrangian centrifugal force as corresponding to the (q-dot)^2 terms in the generalized force are sufficient for me to demonstrate that it isn't superfluous and I think the current section adequately and accurately reports what's in the sources. The concept is certainly is not as prevalent in most common discussion and education settings, but the references show that it is significant and used by some (robotics as you've pointed out previously) today. The only thing that I would add is a line or two at the "redirect" from the fictitious CF section describing the "hand-waving" way of getting the Lagrangian CF in the simple, polar coordinate case from a Newtonian mechanics approach by moving the centripetal acceleration term to the other side and reinterpreting it as a "force", and of course the short disclaimer that by doing so the Newtonian definition of force has gone out the window. --FyzixFighter (talk) 21:22, 14 July 2009 (UTC)

Brews, the topic was new to me too. I had never heard of the Lagrangian approach to centrifugal force before. So in that respect, I learned something new, which is what wikipedia is all about. I was particularly interested in the bit where you showed that centrifugal force was i^2 whereas Coriolis force was i×j. Those simple products of the components of the coordinates provide a fascinating insight into the nature of the forces. The question then arises, what happens if we bring in a k? Do we have an axial Coriolis force with a jxk? David Tombe (talk) 21:37, 14 July 2009 (UTC)


 * FyzixFighter, you have often brought up the mystery of how the centripetal force in polar coordinates becomes a centrifugal force when it appears in the planetary orbital equation. I agree with you that this is a very interesting question. But it's an example of something that the textbooks are not going to solve for you. The answer ultimately lies in the fact that the inertial path can't be analyzed in the absence of a gravitational field. The modern textbooks 'force fit' the polar coordinate expressions to get the correct result in the radial planetary orbital equation. That of course opens up the minefield of terminologies. The modern textbooks like to use the term radial acceleration for the entire sum or r(double dot) and the centripetal term. These are the areas where all the controversy lies. But they can be glossed over in the article. David Tombe (talk) 21:44, 14 July 2009 (UTC)

It is not clear to me whether the terminology in which terms are referred to as centrifugal force is a generally accepted one or just what the authors chose to call those terms in their particular calculation. Can anyone give me evidence that this terminology is in widespread use? Martin Hogbin (talk) 22:34, 14 July 2009 (UTC)


 * It appears to be most prevalent in the robotics engineering community:
 * Adaptive neural network control of robotic manipulators Shuzhi S. Ge, Tong Heng Lee, Christopher John Harris (1998)
 * Fundamentals of robotic mechanical systems: theory, methods, and algorithms‎, Jorge Angeles (2003)
 * Robotics and Control, R.K. Mittal and I.J. Nagrath (2003)
 * Robotics and automation handbook, Thomas R. Kurfess (2004)
 * These are few that a quick search brought up; Brews might have some more references. Is this sufficient to establish it as a generally accepted usage of the term, at least within a significant group of researchers/engineers? --FyzixFighter (talk) 23:04, 14 July 2009 (UTC)


 * Yes, in robotics it is very common, and in numerical solutions of the Euler-Lagrange equations of motion. In the case of polar coordinates, three or four citations are provided in the articles where the Lagrangian approach is used and the term "generalized centrifugal force" is referred to without the "generalized" adjective. Brews ohare (talk) 23:37, 14 July 2009 (UTC)

It looks to me as though this is a rather specialized usage of the term. The article should therefore make this clear by saying something along the lines of, 'In robotics engineering it is common to use the term 'centrifugal force' ...'. Martin Hogbin (talk)


 * Martin, it is not a specialized use. As the sources pointed out to you indicate, it is employed routinely in discussing polar coordinates and the planetary orbit problem. See also Mattheij; Marsden; Mondié.  Brews ohare (talk) 18:39, 15 July 2009 (UTC)

In the firs two references you quote it looks to me like the centrifugal force mentioned is the normal inertial force although the context is Lagrangian. In the last reference 'centrifugal force' is mentioned but mixed up with the Coriolis force. Martin Hogbin (talk) 19:23, 15 July 2009 (UTC)


 * Martin: It's hard to see what you expect. Naturally, and as pointed out in the WP article, all methods lead to the same radial equation. In a co-rotating frame the interpretation of $$mr^2 \omega^2$$ is the standard vector centrifugal force, but only in the co-rotating frame. The Lagrangian approach does not explicitly refer to such a frame, and one problem that arises is that this same term, found using the Lagrangian approach, is interpreted as though it were a Newtonian force in an inertial frame. If that word "generalized" were tacked on (as it rigorously should be) that problem would not arise, because no-one would expect the generalized force to be a Newtonian force, and the question of whether this were true would be examined, rather than assumed. You might find this clearer if you looked at the source in the WP article Hildebrand which states: "Such quantities are not true physical forces, they are inertia forces. Their presence or absence depends, not upon the particular problem at hand, but upon the coordinate system." That statement is totally at variance with the Newtonian view that centrifugal force depends not at all upon the coordinate system but upon the acceleration of the observer. More generally than polar coordinates, these "coordinate" centrifugal forces are related to the Christoffel symbols of the particular coordinate system chosen. Brews ohare (talk) 22:24, 15 July 2009 (UTC)


 * Would a slight modification of Martin's proposal be an equitable compromise: "This terminology is especially common in the field of robotics engineering." at the end of the first paragraph of that section or something else along those lines? --FyzixFighter (talk) 00:05, 16 July 2009 (UTC)


 * I am not convinced that the term centrifugal force has a special use withing Lagrangian dynamics except as a raether specialist usage in robotics. Martin Hogbin (talk) 00:23, 16 July 2009 (UTC)

Hildebrand is typical of general works treating this problem from a Lagrangian standpoint, and confusing statements about centrifugal force being a result of the choice of polar coordinates just like his have shown up on this talk page ( or Centrifugal force (rotating reference frame) time and again (Fugal; TimothyRias; Paolo.dL). I don't think this viewpoint should be played down. Brews ohare (talk) 04:00, 17 July 2009 (UTC)


 * It is not really a viewpoint that I am talking about. My question is whether the term 'centrifugal force' has a specific and well-defined meaning in general Lagrangian mechanics that is not the same as either of it other meanings. Martin Hogbin (talk) 11:25, 17 July 2009 (UTC)

Martin: It would answer many of your questions if you would read the WP article and consult its sources. How can the Lagrangian CF be the "same" as the other two meanings. First, the other two meanings are distinct, so Lagrangian CF can be like only one or the other of the two other meanings. In fact, it is not like the reactive CF (a true vector Newtonian force), and is "like" the second meaning (a fictitious force) only for the particular problem of a single body in a central force field, and then only if a co-rotating frame is chosen in the Newtonian approach. And the Lagrangian CF is non-zero in a inertial frame, depends on the choice of coordinates etc. etc., none of which is true of the Newtonian vector CF. As for being well defined, the WP article defines it very specifically in terms of the time derivatives of the generalized coordinates, which coordinates in general have absolutely nothing to do with a Newtonian formulation. For example, these coordinates may involve a mixture of inertial and non-inertial frames of reference.Brews ohare (talk) 14:17, 17 July 2009 (UTC)


 * What you need is a good secondary source that that clearly makes the statement that the term 'centrifugal force' has a widely used and clearly defined meaning in Lagrangian mechanics that is distinct from any other usage of the term. Asking me to do my own OR to follow up yours is not satisfactory. Martin Hogbin (talk)


 * Martin:Ott; Ge demonstrate clearly that in robotics there is a clearly distinct use of Centrifugal force in Lagrangian mechanics. Hildebrand Bhatia show this usage at work in everyday mechanics texts where Lagrangian methods are introduced. You can argue that the method is not distinct, which means you don't understand the sources or the WP text. You can argue that they are not clear; so spell out your confusion. Brews ohare (talk) 14:30, 18 July 2009 (UTC)
 * Brews your opinion is not sufficient, we need a secondary source that clearly states that the distinction that you claim is in widespread use. Martin Hogbin (talk) 14:46, 18 July 2009 (UTC)

Are you saying that the above sources are insufficient? Why? What more could possibly be said? Brews ohare (talk) 15:36, 18 July 2009 (UTC)


 * Yes, you need a secondary source that clearly states what you are claiming. But I have said my bit on this subject, I will leave it to you chaps to fight it out. Martin Hogbin (talk) 16:27, 18 July 2009 (UTC)

A "secondary source"? The provided sources say everything, and I'd say they are secondary. The primary sources are probably from the 18th or 19th century. Brews ohare (talk) 16:47, 18 July 2009 (UTC)


 * I think there's an obvious sensible compromise here: just a summary paragraph with a main link to Lagrangian mechanics or some such place (that article doesn't presently mention centrifugal force, but probably should if that's what they call such terms).  Dicklyon (talk) 18:23, 18 July 2009 (UTC)


 * It seems to me that there is at least one serious problem with the current section on the Lagrangian formulation of centrifugal force. The article's classification of centrifugal force as a generalised force is not supported by any is not consistent with the terminology adopted in most of the sources provided, according to the definitions they give for those concepts.  Although the sources provided are not quite consistent in what they call a generalised force, in no case do they define it in way that includes what they have defined to be the centrifugal forces. Taylor's Classical Mechanics is the only one of those I have looked at in detail that defines it in such a way that it includes the term corresponding to the centrifugal force.


 * According to the definition usually adopted in Lagrangian mechanics (and as given in the Wikipedia article) the generalised forces are the terms appearing on the right side of the following form of Lagrange's equations:
 * $$\frac {d}{d t} \left ( \frac {\partial T}{\partial \dot{q}_j} \right ) - \frac {\partial T}{\partial q_j} =  Q_j$$,
 * where $$T$$ is the kinetic energy of the system. As one might expect this is the definition used by most of the sources.  At least two of the sources on robotics, however, (viz. Ott, and Kurfess) don't include the conservative part of $$Q_j$$ in what they are calling the "generalised forces".  In their treatments, $$Q_j$$ is the sum of a conservative part, given by the (negative) gradient of a potential, and non-conservative "external" forces.  It is only the latter term which these two sources refer to as a "generalised force".
 * In all cases, however, the terms which the sources define to be "centrifugal forces" come from the terms on the left side of Lagrange's equation. In the example of a single body moving under the influence of a central force, for instance, the generalised force corresponding to the $$r$$ coordinate is $$-\frac{dU}{dr}$$, which doesn't include the centrifugal force.  The latter in fact comes from the second term, $$\frac{\partial T}{\partial r}$$, on the left of the corresponding Lagrange equation.
 * Taylor's Classical Mechanics differs from the other sources in defining the generalised force to be $$\partial T\!/\!\partial q_j + Q_j$$, rather than simply $$Q_j$$ as the others do. According to that definition, of course, the generalised forces would include any terms corresponding to a centrifugal force.
 * &mdash;David Wilson (talk · cont) 16:07, 19 July 2009 (UTC)

David W., What you have just said above may well be correct, except that I don't agree with you that it is a serious problem. Just like in the case of the points that you raised in the other section further up the page, I see the issue in question as being merely a matter of semantics. The semantical issues raised here can be extended to all the inertial forces. There was a discussion last autumn on the talk page at Kepler's laws of planetary motion. That discussion came to deadlock when there was no agreement reached for the names of the six terms in the two planetary orbital equations. Once again, it was the same old story regarding a reluctance on the part of most editors apart from myself to acknowledge the name 'centrifugal force' in the radial equation and the name 'Coriolis force' in the transverse equation, despite the existence of sources to confirm those names. But even without sources, it should be patently obvious to anybody with any knowledge of the subject matter, that those names are not in any doubt.

What seems to be the big problem here is that when the inertial forces are being considered in the context of rotating frames of reference, the editors here seem to be quite comfortable with the names 'centrifugal force' and 'Coriolis force'. But as soon as these same inertial forces arise in the planetary orbital equation, and the analysis is done in the absence of any rotating frame of reference, any attempt to use the correct names for these inertial forces seems to end in war. There are those who will insist that the analysis must involve rotating frames of reference. But I'm still waiting to see how they deal with a precessing frame of reference in a three body non-planar problem with three mutual pairs of angular speed being involved. David Tombe (talk) 19:55, 20 July 2009 (UTC)


 * In my comment above I was a little hasty in asserting that none of the references supplied in the article or on this talk page supported the article's current use of terminology in the section on Lagrangian mechanics. On checking more carefully, I have found that one of the references given (Taylor's Classical Mechanics) does define "generalised force" in such a way that a centrifugal force would normally be included as part of it. I have now amended my comment accordingly.


 * But please also note that in my comment above about centrifugal force not being classified as a generalised force, I was referring quite specifically to the terminology used by the references cited, both in the article and here on this talk page, and it may not necessarily be true of the terminology used in other hypothetical references yet to be supplied. However, I stand by my assertion (as now amended) that the terminology currently used in the article is inconsistent with that used in most of the references cited. Taylor's Classical Mechanics is the only partial exception I have so far come across.


 * Brews ohare wrote on my talk page:


 * " ... It seems that there are various Lagrangians possible for a system, for example, a Lagrangian for a rotating system of coordinates and a Lagrangian for a stationary system. It seems likely that the generalized forces vary with the choice. In particular, it seems likely that centrifugal forces come up in one form and not in another. For example, in a rotating frame the centrifugal force shows up as a potential and therefore is part of the generalized forces.  ... "


 * I have responded at length on my talk page. Here I will simply note that the last sentence appears to me to be a non-sequitur. It seems to be suggesting that if the generalised coordinates are taken with respect to a rotating reference frame then the centrifugal force must be included as one of the forces which are used to construct the generalised forces $$Q_i$$ which appear on the rightt side of the Lagrange equation as given in my comment above.  While one can do this, it is certainly not necessary, and none of the cited references actually ever do it.  Taylor's Classical Mechanics, in fact, quite explicitly disallows such use of pseduoforces on page 241 where it says " ... we must nevertheless be careful that, when we first write down the Lagrangian $$\mathcal{L} = T - U$$, we do so in an inertial frame."  It's not quite so clear to me whether the authors of any of the other sources would exclude the use of pseudoforces in this way, but the fact remains that when they actually describe the general procedure for setting up Lagrange's equations, the forces which they prescribe for use in their definitions of the $$Q_i$$ are proper forces, not pseudoforces.
 * &mdash;David Wilson (talk · cont) 14:15, 29 July 2009 (UTC)

David W., I looked at your lengthy response on your talk page. You have correctly linked the three inertial forces to kinetic energy. You have named them by their names, and you have shown that we don't need to involve rotating frames of reference. This two and a half year dispute came about because of a reticence on the part of most of the other editors here to use the names and to admit that rotating frames of reference are not needed in the analysis. The recent intervention by yourself and Cardamon has merely confirmed what I was trying to say all along.

What we really need to investigate now is why there has been this reticence. It's been partly due to the fact that modern texbooks are using the Leibniz approach in orbital theory while simultaneously trying to distance themselves from Leibniz by playing down the associated terminologies. David Tombe (talk) 08:12, 31 July 2009 (UTC)

Still sceptical that there is a Lagrangian formulation of centrifugal force
I have started this section to avoid disrupting other discussions already in progress. Firstly, just let me make clear that I mean exactly what I say in the section title. I am not asserting that there is no such thing as a Lagrangian formulation of centrifugal force, but it is terminology that I have not come across before and I am therefore sceptical that it is widespread use. Can anyone convince me?

To explain further what I mean, the reactive centrifugal source may be considered by many to be non-standard terminology, so the question could be asked, 'Is the term in reasonably common use?'. The answer to this is given by the references cited in this section. For example, we have from an academic source, In the example of the airplane pilot at the bottom of a vertical circular turn, the (upward)centripetal force is the force of the seat on the pilot. The centrifugal force is the force of the pilot on the seat.'' This is clearly a reliable source telling us that the term 'centrifugal force' is used generally in the way claimed and giving a specific example.

The problem is that we do not have any references making this kind of clear statement regarding the claimed Lagrangian formulation. The article makes this statement about Lagrangian dynamics, Among the generalized forces, those involving the square of the time derivatives {(dqk/dt)2} are called centrifugal forces. When I look at the two references quoted there is nothing like the clear support for the statement made in the article. Firstly these references are both about a specific application of Lagrangian dynamics. In the first reference there are some terms referred as centrifugal and Coriolis forces and mention of a Coriolis/centrifugal matrix in on reference and in the second it says that certain terms are referred to as 'centrifugal forces', but there is no indication that this terminology is not specific to this paper or subject.

For there to be a section in the article on the Lagrangian formulation of centrifugal force we need a general reference on Lagrangian mechanics clearly telling us that there is such a thing; currently we do not have one. Martin Hogbin (talk) 13:45, 21 July 2009 (UTC)

Brews ohare (talk) 14:43, 21 July 2009 (UTC)
 * Hi Martin: You say: "The problem is that we do not have any references making this kind of clear statement regarding the claimed Lagrangian formulation." I have already provided to you many such sources, and you somehow do not find them adequate. I don't know why. In the field of robotics, the article states (notice particularly the definition in the quote in note 4): Within this formulation the motion is described in terms of generalized forces, using in place of Newton's laws the Euler-Lagrange equations. Among the generalized forces, those involving the square of the time derivatives {(dqk/dt)2} are called centrifugal forces.
 * How does that not fit your requirements? It provides a completely clear-cut definition of the Lagrangian centrifugal force that is clearly distinct form the Newtonian centrifugal force. You say that these references "might" be specific to the source and not general; that is why several sources are provided that say the same thing. If you were truly unconvinced, of course you could explore the usage using google. Your stance is that is not your job. So maybe you'd like twenty to forty more citations to the same thing?  Brews ohare (talk) 14:43, 21 July 2009 (UTC)
 * Possibly you feel that this definition is not sufficiently widespread? In that regard the article provides the following: The Lagrangian approach to polar coordinates that treats (r, θ ) as generalized coordinates, $$(\dot r, \ \dot \theta )$$ as generalized velocities and $$(\ddot r, \ \ddot \theta) $$ as generalized accelerations, is outlined in another article, and found in many sources.
 * This example is one common in mechanics texts; quite outside the realm of robotics, and making the same claims about centrifugal force in the context of this problem. Brews ohare (talk) 14:43, 21 July 2009 (UTC)


 * Perhaps if you would critique what is lacking in these sourced excerpts instead of making broad, vague claims of inadequacy, some progress could be made. Brews ohare (talk) 14:43, 21 July 2009 (UTC)


 * What is lacking is a clear and simple statement along the lines of what we have for the reactive centrifugal force, Newton's third law says that for every force there is an equal but opposite" force, and the force equal but opposite" to the centripetal force is called the centrifugal" force. Can you refer me to an online source that makes a statement that is as clear and generally applicable (to Lagrangian mechanics) as that.  If your preferred source is not available online then perhaps you could give me a verbatim quote from it. Martin Hogbin (talk) 15:15, 21 July 2009 (UTC)
 * "In the above Euler-Lagrange equations, there are three types of terms. The first involves the second derivative of the generalized co-ordinates. The second is quadratic in $$\boldsymbol{\dot q}$$ where the coefficients may depend on $$\boldsymbol{q}$$. These are further classified into two types. Terms involving a product of the type $${\dot q_i}^2$$ are called centrifugal forces while those involving a product of the type $$\dot q_i \dot q_j$$ for i ≠ j are called Coriolis forces. The third type is functions of $$\boldsymbol{q}$$ only and are called gravitational forces."Ge


 * “In the above equation there are three types of terms… The second are quadratic terms in the first derivatives of q, where the coefficients may depend upon q. These are further classified into two types. Terms involving a product of the type $$\dot{ q}_i^2$$ are called centrifugal', while …” Spong.


 * "$$h_{ijk}$$ = Centrifugal force coefficient at joint i generated due to angular velocity at joint j. The centrifugal force acting at joint i due to velocity at joint j is given by $$h_{ijj}\boldsymbol{\dot q_k}^2$$."Nagrath


 * You may object that these statements are mathematical, not common English, but if the definition involves $$\dot q_k ^2 $$, what is to be done? Brews ohare (talk) 15:44, 21 July 2009 (UTC)


 * I object to the fact that all three references you quote refer to specific robotic systems (and in fact it looks as if the forces at the joints that are described in the papers are the normal centrifugal forces). There is no evidence that thes terminolgy applies to Lagrangian dynamics in general. Martin Hogbin (talk) 17:44, 21 July 2009 (UTC)

These recent references (see subsection below as well) refer to robotic systems and to chemical systems. The treatment based upon Christoffel symbols is entirely general; see Felseger; Silberstein; Choset; Khorrami for example, and applies to robotic systems, chemical systems and to the two-body central force problem. It also applies to general relativity. I find no support for your resistance to these facts. You simply are interpreting sources to suit your prejudices. Brews ohare (talk) 00:19, 22 July 2009 (UTC)
 * Brews - You have a lot of sources on control theory that call generalized forces proportional to $${\dot q_k}^2$$  "centrifugal forces".  You also have a lot of sources using Christoffel symbols in more general contexts.  But, do you have sources that call generalized forces proportional to $${\dot q_k}^2$$  "centrifugal forces" in a general context?  So far I'm about ready to say that some sources use this terminology.  Cardamon (talk) 08:02, 22 July 2009 (UTC)


 * Brews, as I made clear at the start of this section, I have no prejudices or strong opinions on this subject I am just waiting to see the normal WP standard of reliable source that actually supports the claim that you are making. As yet, you have not produced a reliable source that backs up what you are saying without requiring a somewhat idiosyncratic interpretation. All that could be justified in the article at present would be a statement that the term 'centrifugal force' may be used in a third sense in some Lagrangian treatments of robotic systems. Martin Hogbin (talk) 10:14, 22 July 2009 (UTC)

The important point in all of this is that Lagrangian mechanics provides an example in which centrifugal force is being treated in a context that does not require a rotating frame of reference. It is likewise in orbital theory, whether we use Lagrangian or not. If the introduction insists that there are only two kinds of centrifugal force, and then cites (1) the fictitious force in rotating frames of reference, and (2) the reactive force, then the Lagrangian approach clearly is a third way that has been ommitted. I believe that this error has now been rectified, but it all makes for a very clumsy introduction. My own opinion is that there is only one universal centrifugal force, and that the introduction should not even bother attempting to count how many kinds there are.

In the main body of the article, there needs to be at least one section that deals with centrifugal force in the absence of rotating frames. This could either be a Lagrangian section, just as Brews has done, or it could be a two body planetary orbital section without using Lagrangian. As it stands, Brews has successfully combined these two options. I am supporting the retention of Brews's section on Lagrangian, although I am opposing any comments in that section which state that the Lagrangian centrifugal force is a different concept. It is not a different concept. It is the one and only centrifugal force that is tied up with centrifugal potential energy. David Tombe (talk) 11:05, 22 July 2009 (UTC)


 * Your interpretation or my interpretation of what the term CF means is not important. What is important is what reliable sources say that it means.  We clearly have sources that support two interpretations of the term.  We do not have a reliable source that states that there is a third interpretation in common use. Martin Hogbin (talk) 11:56, 22 July 2009 (UTC)


 * Martin: I am coming to the view that the only support you would accept is one that says in so many words "there are three different meanings for centrifugal force; they are: etc. etc." Of course, that would be great (provided you accepted this source), but it is not necessary to do this. What has been done with all three usages is to provide sources where the various usages are employed. There is absolutely no doubt that such references have been provided for the Lagrangian case (both in robotics, general mechanics texts, chemical reactions and in general math via Christoffel symbols). Moreover, the behavior of the Lagrangian version is entirely different from the Newtonian version as applied to inertial frames (see section below). I simply do not understand your reservations on this matter. Brews ohare (talk) 14:50, 22 July 2009 (UTC)


 * You are not far off. What I want is a source that says that the term 'centrifugal force' has a specific and clearly defined meaning that is in common use in Lagrangian mechanics.  What is the problem?  If this is indeed the case then such a source should not be too hard to find.  We have sources that say the same kind of thing for the other meanings of CF. Martin Hogbin (talk) 15:18, 22 July 2009 (UTC)

The problem is that I find that the fact that "the term 'centrifugal force' has a specific and clearly defined meaning that is in common use in Lagrangian mechanics" already is documented to death. I don't see what is missing. Brews ohare (talk) 15:26, 22 July 2009 (UTC)


 * What is missing is a secondary source that makes the above quoted statement. Martin Hogbin (talk) 19:13, 22 July 2009 (UTC)


 * Martin, the matter has been well sourced. The section in question provides an excellent illustration of the fact that rotating frames of reference are not essential for the purposes of analyzing problems that involve centrifugal force. I can't see much wrong with the section in question, except that I wouldn't even have bothered mentioning the concept of a co-rotating frame at all. But I have to agree with Brews on this issue that plenty of sources have been provided and I really can't see what your problem is. David Tombe (talk) 18:18, 22 July 2009 (UTC)

Inertial frames and CF
In the Newtonian view, centrifugal force is a consequence of rotation, which implies an acceleration of the observer. In Lagrangian mechanics, however, when applied in a routine manner by specifying the generalized coordinates and then writing down the Lagrange equations, the centrifugal force is defined in terms of the $$\dot{q}_k^2$$ terms, which can be non-zero in inertial frames (that is, even when no rotation occurs). Thus, a major distinction between these two pictures of Centrifugal force is their different behavior in inertial frames. Here's a reference:. And here's Hildebrand: “Since such quantities are not true physical forces, they are often called inertia forces. Their presence or absence depends, not upon the particular problem at hand, but upon the coordinates used.”Brews ohare (talk) 16:22, 21 July 2009 (UTC)

This point is made more abstractly for general choices of coordinates in mechanics of planar particle motion where it is pointed out that the space of generalized coordinates is characterized by Christoffel symbols, which describe the "inertial forces" and are present regardless of rotation:


 * $$\sum_{j=1}^n \ m_{ij}(\boldsymbol q) \ \ddot{ \boldsymbol q _j} \ + \ \sum_{j,k=1}^n \ \Gamma_{kji}\dot \boldsymbol {q_k} \dot \boldsymbol {q_j} +\frac {\partial V}{\partial q_i} = 0 \ . $$ … $$i = 1, \ . \ . \ . $$

Willems. Brews ohare (talk) 16:40, 21 July 2009 (UTC)

Getting back to summary style and re-merging some content forks
I made new articles with main links for the absolute rotation and history sections. These were duplications and content forks of similar sections in Centrifugal force (rotating reference frame), badly in need of re-unification. This returns this artilce to summary style, and is a start on that re-unification. The history part still needs to be merged, so I left a tag there. Dicklyon (talk) 17:09, 21 July 2009 (UTC)


 * David, if you want to be useful, work on the history merge. Dicklyon (talk) 17:38, 16 August 2009 (UTC)

Merging the two articles ('centrifugal force' and 'centrifugal force and absolute rotation')
Headbomb, I could never see the point in separating them in the first place. I have consistently argued for one single article on centrifugal force. I support your merger proposal. In fact, I also believe that all the branch articles should be nominated for deletion as the entire topic can easily be accomodated within one single article. David Tombe (talk) 15:04, 16 August 2009 (UTC)


 * The article Centrifugal force was made as a WP:Summary style article for Centrifugal force (rotating reference frame), Reactive centrifugal force, Centrifugal force and absolute rotation, History of the concepts of centrifugal and centripetal forces, Mechanics of planar particle motion, etc. Dicklyon (talk) 17:36, 16 August 2009 (UTC)
 * I think it could work rather well as a summary-style article, and I would much rather see the quality of these articles improved rather trying to move/merge/delete them. I don't see how merging will improve any of these articles in any way. Wilhelm Meis (Quatsch!) 02:37, 17 August 2009 (UTC)

Regarding Dicklyon's reversion
Dick, I made that edit to clarify the fact that it was not Daniel Bernoulli himself who drew that conclusion, but rather it was the opinion of Mr. Meli in the book which he wrote in 1990. I agree that it was somewhat unencyclopaedic to elaborate on that fact, and so the best option would be to remove the explicit statement of Meli's opinion altogether and to leave Bernoulli's statement on its own in order for the readers to make up their own mind. They can check out Meli's book if they like. We cannot have Bernoulli's ideas reinterpreted by Mr. Meli, because we all know that Bernoulli was not alluding to rotating frames of reference, irrespective of what Mr. Meli thinks. Bernoulli was pointing out the fact that the inertial characteristics of the centrifugal force meant that we get a different value for every arbitrarily chosen point in space. David Tombe (talk) 21:59, 16 August 2009 (UTC)


 * Unfortunately David, that view goes directly against wikipedia policy. Meli is a valid secondary source, and his interpretation of Bernoulli's ideas supercedes, for the purposes of the article, any of our own interpretations of Bernoulli's ideas. If you have another reliable, verifiable, secondary source that provides an alternate interpretation of Bernoulli's work, then provide it and we can work it in. However, removal of the statement of Meli's opinion is unacceptable as such removal goes against wiki policies. Including the direct quote is, in my opinion, is what Wilhelm suggested when he advised sticking as close to the sources as possible. --FyzixFighter (talk) 22:53, 16 August 2009 (UTC)
 * Actually, yes, FyzixFighter, that is what I meant. I have long hoped that all the editors here would treat the stated interpretations in reliable secondary sources as superceding their own interpretations of primary sources.  We have long needed the editors of this article to take a step back from the subject and stick with what is Verifiable in Reliable sources.  Thank you for pointing it out. Wilhelm Meis (Quatsch!) 23:57, 16 August 2009 (UTC)

FyzixFighter and Wilhelm, Nobody was stating an alternative interpretation of Bernoulli's statement. It is quite clear from Bernoulli's statement that he was referring to the fact that centrifugal force changes with respect to the point of origin. Bernoulli did not mention rotating frames of reference. Now if we state Mr. Meli's opinion, then we are giving undue weight to Mr. Meli's opinion. So why do we actually need to state Mr. Meli's opinion explicitly in the article without emphasizing the fact that it is Mr. Meli's opinion?

Let's not lose track of what this is about. FyzixFighter holds the point of view that centrifugal force is a fictitious force that only exists in a rotating frame of reference. Nobody is trying to remove that point of view from the article. FyzixFighter could quite legitimately make his point in that respect in the history section in relation to Mr. Coriolis or perhaps even Mr. Lagrange. But why spoil it by introducing it in relation to Daniel Bernoulli when we all know that Mr. Meli has interpreted Bernoulli's statement wrongly. I'm trying to make the history section accurate and it is not accurate as it stands.

The counterbalance would be for me to clarify in the article that it is Mr. Meli's opinion and not Mr. Bernoulli's opinion. But why do we need to go to all those lengths? Why not keep it simple and to the point and state what Bernoulli said? It is playing to the letter of the law that completely ruins many wikipedia articles because there are so many conflicting sources, especially about controversial and changing topics. David Tombe (talk) 00:08, 17 August 2009 (UTC)


 * David's reason for calling out the Bernoulli interpretation as if it's the recent opinion of one guy, as opposed to all the other stuff that's reported with less explicit attribution since it's all from reliable secondary sources, is as he says above, "we all know that Mr. Meli has interpreted Bernoulli's statement wrongly." As far as I've heard here, David is the only editor who believes that the interpretation is suspect, as he pretty much always rejects the modern viewpoint of fictitios force in a non-inertial reference frame.  The only way to be neutral here is to report what Meli said, as a quote, with a footnote to who said it and where and when, which is what we had before.  David should stop jerking us around.  Dicklyon (talk) 03:20, 17 August 2009 (UTC)
 * I'm taking a step back from this issue, for now, and I will let you guys work out how to most neutrally and accurately present the information available in the sources. I'll still watch the page, though. Wilhelm Meis (Quatsch!) 04:00, 17 August 2009 (UTC)


 * Thanks for your help, Wilhelm. I'm going to work on merging this section over to the history article, so watch that, too.  Dicklyon (talk) 04:08, 17 August 2009 (UTC)


 * OK, the question of the Meli quote has now migrated to the other article, History of centrifugal and centripetal forces, per the unopposed merge proposal. Dicklyon (talk) 06:56, 17 August 2009 (UTC)

Dick, The quote has not been neutralized entirely. Alot of people overlook the fact that primary sources are still acceptable under wikipedia's rules if they contain an unambiguous quote. This is especially so if we are dealing with a history chronology. What has been sacrificed here is another important wikipedia policy known as 'undue weight'. We cannot have a history chronology of what the great masters said, overstamped by the modern day opinions of the likes of Meli. We all know that FyzixFighter and Meli are of the same generation, and that they firmly believe that centrifugal force is a fictitious force that is observable only in a rotating frame of reference. But Daniel Bernoulli never said that. So why does a short paragraph on what Daniel Bernoulli said two hundred years ago, have to be overstamped with the opinion of 1990 that 'the idea that centrifugal force is a fictitious force, emerges unmistakenly in a memoir by Bernoulli'? This is a classic case of distorting history in an attempt to bring it into line with the present day. It is against wikipedia policy to do so because it ignores the issue of 'undue weight'. David Tombe (talk) 10:41, 17 August 2009 (UTC)

The Germans on Centrifugal Force
Here is the centrifugal force article from the German wikipedia. This might give a few ideas on presentation. []David Tombe (talk) 20:46, 11 September 2009 (UTC)


 * I can't read German, but I do like the illustration of the rotating cylinder containing a liquid. The fact that it produces a paraboloid surface is very important from an engineering point of view, as that is currently in use to produce extremely large liquid mirror telescopes, such as the Large Zenith Telescope.  I have put this on my to-do list: to borrow the image, add caption and inline text, explain the math, and link to other articles.  CosineKitty (talk) 20:01, 10 February 2010 (UTC)

An interesting and informative article
I stumbled apon this reference, which seems to be a nice general overview, at least after reading the first three or four pages. |a good article

Title: Centrifugal Force - a Few Surprises Authors: Abramowicz, M. A. Publication: R.A.S. MONTHLY NOTICES V.245, NO.4/AUG15, P. 733, 1990 (MNRAS Homepage) Publication Date: 08/1990 Origin: KNUDSEN Bibliographic Code: 1990MNRAS.245..733A

Cheers CoolMike (talk) 18:51, 10 February 2010 (UTC)

Centrifical force
Doubly fictitious is centrifical force. It perhaps deserves some mention in this article. There are still many who believe it is a similar force, or another the word for centrifugal. I just don't know where or how to place it. Perhaps a simple redirect. Thoughts? Anna Frodesiak (talk) 10:12, 24 February 2010 (UTC)


 * I have never seen the word "centrifical" before, and I was unable to find it listed in any mainstream dictionary. On checking a random selection of the instances of its use uncovered by a Google search, I could find none where it was obviously intended to mean anything different from "centrifugal". It would appear to be simply a misspelling, possibly derived from hearing the word "centrifugal" pronounced with the stress on the second syllable rather than the third (both pronunciations are common and correct).
 * &mdash;David Wilson (talk · cont) 13:26, 24 February 2010 (UTC)


 * Maybe an Eggcorn. Actually, I could really go for some eggcorn right about now. Anna Frodesiak (talk) 14:45, 24 February 2010 (UTC)

Subject matter discussion
Okay. So we're discussion a subject matter. And somebody says it doesn't exist. And then I say it does exist, and then you throw me out based on a requirement related to the composition of the article about the subject matter. Does that make sense? I'm not in the article trying to change it. I merely provided a rational method of refuting the statement in the article that centrifugal force doesn't doesn't exist. And I don't know what you're trying to do. So please tell me how else I would be able to provide that information if I got some from your proposed source. And I really don't care about the composition of the article, because I read it to get correct information about the subject matter.WFPM (talk) 14:52, 10 May 2010 (UTC)


 * I really can't make any sense of what you are trying to say. Anyway, this is not the place to discuss the subject matter. Please read the first sentence of the talk page guidelines, then read the guidelines and policies at WP:NOR and WP:RS. Thanks. DVdm (talk) 15:22, 10 May 2010 (UTC)

Okay. Have it your way. And I can see now why it is so hard to get articles corrected.WFPM (talk) 16:45, 10 May 2010 (UTC) If I referred You to Clerk Maxwell's discussion of force vectors in the "Atom" section of the 9th edition of the EB,would that solve your WP:RS requirement?WFPM (talk) 16:58, 10 May 2010 (UTC)


 * I don't find anything in here related to the subject of this article. The word force appears 27 times in the context of electromagnetic attraction and repulsion between atoms. If you intend to draw conclusions from anything in there about the subject of this article, then that is original research - see the section WP:SYNTHESIS. What we need is a reliable source saying what you want to say. So, no, I don't think that "Atom" solves the WP:RS requirement. DVdm (talk) 17:31, 10 May 2010 (UTC)

Well, how about the references in the article, like about "Newton's Bucket" etc. Do the writers of the article read those references? And I particularly like the one about "Acceleration and force in circular motion", where people in a rotating space station are able to stand up and walk on tha outside wall of the station due to the action of the "nonexistent?" centrifugal force exerted on their bodies towards the wall of the station.WFPM (talk) 19:16, 10 May 2010 (UTC) And I don't think you read about Boscovitch's argument that the motions of the atoms are controlled bu the force vectors and not by any physical contact. But thanks for the computer link to the article and I didn't know you could do that. And I am very impressed by the power of the computer to organize and present data. But if you're just worried about the composition of the article, and not about it's subject matter rationale, I don't think you're going to wind up with a good and informative article.WFPM (talk) 19:43, 10 May 2010 (UTC)


 * I don't understand what you mean with this question: "Well, how about the references in the article, like about "Newton's Bucket" etc". What do you mean with "How about..."? DVdm (talk) 19:51, 10 May 2010 (UTC)

The question has always been as to whether there is or is not a real centrifugal force. And Newton used the whirling bucket phenomenon to argue that there had to be a force that moved the water away from the center of rotation until it ran into a force that constrained it. But there wasn't any explainable force within the attention sphere of the bucket, so they got into an argument about relative motion activities, and lost sight of the local problem, which is still as to why the water piles up in the direction away from the center of rotation. And I don't see the reason for the complications. If something accelerates in some direction, it's because something is pushing (applying a force) in that direction. That's part of Newton's laws of motion. But you can keep it complex if you want, by either disregarding the space and motion relationship of the components of the subject matter, or by developing some mathematical formula that leaves out some relationship factor that leaves out something related to the process of the event.WFPM (talk) 20:28, 10 May 2010 (UTC)


 * I'm not asking for your opinions about and reflections upon something that is written, or not written, in the article. As you really should know by now (see WP:NOR), this is not the place to discuss such things. I asked what you meant with the question: "Well, how about the references in the article, like about "Newton's Bucket" etc". I assume that this was a question about a reference in the article, so we can discuss that. But I did't understand the question, so I asked what you meant with "What about..."? DVdm (talk) 20:41, 10 May 2010 (UTC)

Well I assume that the information contained in the article includes the information contained in the references and that it should be compatible with the references as to concept and rationale. But maybe not. So it's not about my information and references versus your information and references, but rather the subjective opinion of the editor about the relative importance of a given subject matter with relation to his point of view. And I thought that the editor's POV was supposed to be neutral about subject matters.WFPM (talk)

And what do you think about the information in the Acceleration and force in circular motion article? does it imply the existence of a real centrifugal force or not?[[User:WFPM|WFPM

I'm afraid I don't understand your intent as to the proper controlling of the message of an article. Are you interested in the correctness of the grammar? Or of the agreed definition of word meanings, (which is important) or the Syntax of the discussion, or of the punctuation, or what else? How about the ability of the article to meet the requirement of Newton's first rule of Philosophy? Which requires the simplest correct and adequate explanation of the phenomenon and nothing more. And since there are many things in the hierarchy of the entities of physical entities and events that need to be explained and understood, that sounds like a good idea to me.WFPM


 * You say that you "assume that the information contained in the article includes the information contained in the references". Ok, so there is no problem with the references then. What I "think about the information in the Acceleration and force in circular motion article" is of no importance. If you have some text to add to the article, then it must be notable, it cannot be original research, it needs a non-fringe reliable source, and it should not put undue weight on the article. Otherwise, please stop discussing the subject matter on this talk page. DVdm (talk) 07:43, 11 May 2010 (UTC)

Well could I put some text into the article asking about the forces involved in those whirling swing devices that they have at the fairs, where they swing out over the audience, and which is obviously an unstable balance between the gravitational force and some force that's pushing the swing out over the audience, and that you say is a fictitious force?WFPM (talk) 14:46, 11 May 2010 (UTC) And after all, the primary purpose of this contraption is to create and demonstrate this so called centrifugal force. And I think that it would be in order for the article to explain it in an understandable manner.WFPM (talk) 15:21, 11 May 2010 (UTC)


 * No, you cannot put some text into the article asking about anything. DVdm (talk) 15:25, 11 May 2010 (UTC)


 * WFPM: To me it seems you wish to argue that centrifugal force is "real", and don't think that the article does that. If we use "real" in the everyday sense, the article does agree that centrifugal force is real. On the ride at the fair, you do feel a real centrifugal force. Of course, as the person swinging on the ride, you are a rotating observer, not a stationary observer.
 * The only way the centrifugal force is not "real" is in a very technical sense, that is, in the sense that stationary observers don't use the concept of centrifugal force in their description of events. The article tries to explain that too.
 * So, there are at least three issues here. First, do you agree with the orthodox interpretation of the article in terms of stationary and rotating observers? Second, do you believe the article to misrepresent the orthodox view? Third, assuming you agree with the objectives of the article, what portions are unclear or misleading?
 * I have a hunch that you do not accept the orthodox view that the stationary observer (the one on the ground) can explain everything they see without using the centrifugal force. As that view is not correct, the article may need to be reworded to make even more clear that position is false. Brews ohare (talk) 16:49, 19 August 2010 (UTC)

I try to tie my concepts to a memorable physical event; so I can keep thinking about it when I have the time and inclination. And the memorable Centrifugal force event that I remember is seeing the people at the fairs sitting in the chairs which were whirling around over my head, and which were restrained by some taut chain tethers. And I know that I could measure the centripetal tensile force existing in the tethers. And if I had to make a sketch of the balance of forces explaining the tension in the tethers, I'd have have to show an inward centripetal force which is counteracting an outward "centrifugal" force. Now if I neglect the mass of the tether apparatus, and just concentrate on the mass of the (constant speed) traveling passenger, I can see that the tether is applying a restraining force to him which is perpendicular to his path of travel, and just capable of diverting his inertia driven straight line travel tendency into a circular path with a retained amount of angular momentum. And after he attains this state of constant velocity circular motion, I note that the affected mass of his body becomes static with respect to its motion related to the centrifugal and centripetal force vectors and that consequently no energy is being supplied to or taken from the system. And at that point, as far as I can see, the existence of both the centrifugal force and restraining centripetal force are real. But if it doesn't foul up the physical calculations, I wouldn't belabour the point.WFPM (talk) 06:05, 20 August 2010 (UTC)

Constitutive law of inertia
This material is not appropriate for the introduction, which is a qualitative section. Also, the term "constitutive law of inertia" and a good deal of the math here appears to me to be unsourced and a bit out of the main stream. To be included, it must be properly introduced and sourced, and a basis laid for a new section on this topic. Brews ohare (talk) 15:06, 18 August 2010 (UTC)
 * I had added it there for the benefit of people like me who find it difficult to process large chunks of text and just need to refresh their memory of what a centrifugal force is. In my opinion, Noll's skew tensor notation is much clearer than the standard multiple curl of vector notation for the same formula.  However, that formula does not appear in any discussion of centrifugal forces within Wikipedia.  Bbanerje (talk) 22:33, 22 August 2010 (UTC)

Bloat
This article was intended to be summary style, but it keeps accumulating bloat. Brews ohare reverted my latest attempt to remove unnecessary junk that was recently added to a section (I was responding to someone's suggestion that a cleanup was needed). Can anyone comment on whether it's helpful to have that level of detail in a summary of another article? Dicklyon (talk) 02:49, 19 August 2010 (UTC)
 * I removed the detailed material that you removed, but with an explanation (immediately above). I left the "Common experiences" portion, which seems to me appropriate for such a preliminary article. Brews ohare (talk) 05:41, 19 August 2010 (UTC)
 * And now you've got that as part of "Context and Usages", which says its main article is "Centrifugal force (rotating reference frame)". Can you repair that at least?  Dicklyon (talk) 05:59, 19 August 2010 (UTC)


 * Now that the latest ado has reached some kind of definitive consequences, I'm in agreement with you, Dicklyon. I think your removal of bloat was warranted and an improvement, and I'd support redoing it (in fact I think I'll go do that right now). There might have been a few references for the Lagrangian formulation that brews added in that it might be worth salvaging, but overemphasis on the lagrangian usage by be a bit undue weight.
 * In line with this, I think there are a few other concerns that I have.
 * The "See also" section needs trimming so it matches the manual of style.
 * The section headings could use tweaking - mainly I'm looking at the 4th item in WP:MOSHEAD and some of the guidelines on article titles.
 * Finally, I still don't understand why we have both this article and Centrifugal force (disambiguation). It seems like both pages are trying to do the same thing. Perhaps I'll make a subsection just for this item since I could see discussion on this getting pretty lengthy.
 * --FyzixFighter (talk) 21:09, 22 August 2010 (UTC)

The James Bond Cartoon
There was alot of fuss about a James Bond cartoon while I was away and I didn't get the chance to state my 2 cents. The cartoon should not be in the main article, but it makes an excellent basis for a talk page discussion for the purpose of improving the article. The cartoon highlights the controversy very clearly. And here is an even better cartoon. Check out card number 12 at this weblink. David Tombe (talk) 19:49, 21 October 2010 (UTC)

Re-merging
Right now we have at least three separate pages (this page, a disambiguation page, and one specific to rotating reference frames) and a lot of overlap in material and in function. For example, this page and Centrifugal force (disambiguation) are performing nearly the same function. Perhaps someone knows the rational for why we have both of them? I'm wondering if we can't re-merge this page and Centrifugal force (rotating reference frame), since a good argument could be made (imo) that the rotating reference topic is the primary topic. That way the disambiguation page can still exist (to help distinguish between this and the Reactive centrifugal force). The only aspect that might not nicely fit is the Lagrangian formulation but which is (afaik) a very limited and slightly esoteric usage. I could very easily see that as a subsection. I could be wrong on this point, in which case it could be spun off into a separate article (Centrifugal force (Lagrangian mechanics) perhaps), but I still think the rotating reference frame should be the primary topic rather than the expanded faux disambiguation page we have now. Thoughts? --FyzixFighter (talk) 19:53, 13 September 2010 (UTC)
 * I would agree with a three way merge, between Centrifugal force, Reactive centrifugal force and Centrifugal force (rotating reference frame). The latter two seem far less encyclopaedic than they should be, with a surplus of examples and large, confusing diagrams needing overlong captions to explain them (and even then they are unclear). If the unencyclopaedic content were pared back it could be merged into the sections in Centrifugal force and I don't think the resulting article would be too large.
 * The DAB page I think should stay for now, though once the articles are merged this could be reassessed, as what would be left might be too trivial - there would only be one page on centrifugal force. But the page at Centrifugal force (disambiguation) has no content and would not get in the way of the merge, so need not be considered.-- JohnBlackburne wordsdeeds 20:23, 13 September 2010 (UTC)
 * For the most part I agree with you John, especially on the paring of surplus (imo, textbook-y) examples. The only difference in opinion I have is I would not advocate merging Reactive centrifugal force back in. The two are sufficiently distinct physical concepts (one's a fictitious force and frame dependent, the other a very real force that exists independent of frame; they will only equal in magnitude in a co-rotating frame) that I think separate articles are warranted. The concept of reactive centrifugal force is also a very common in engineering and one doesn't have to go searching for esoteric sources to find some that clearly make the distinction between the two. IIRC, one of the reasons for spinning it off was that one or two editors were constantly confusing the two and making the claim that they were the same thing. That isn't to say that Reactive centrifugal force couldn't use some paring and de-bloating, but I believe that there could still be enough information there to warrant its own article.
 * I should probably add some merger tags as a courtesy and to encourage others to chime in. --FyzixFighter (talk) 16:30, 14 September 2010 (UTC)

I think you should do away with the disambiguation page, since I can't see what it's for, but leave the summary-style centrifugal force article, and keep the other bloated articles separate (and separately work on de-bloating them). Dicklyon (talk) 04:18, 15 September 2010 (UTC)


 * I would support this merger idea. One single article is all that is required for the topic 'centrifugal force'. David Tombe (talk) 11:42, 21 October 2010 (UTC)


 * It wasn't a merger idea, so it's not clear what you're supporting. Dicklyon (talk) 20:51, 21 October 2010 (UTC)

Dick, the title of this section says re-merging, and from reading the lead that is what the author seems to be advocating, and I am supporting the re-merger. We only need one 'centrifugal force' article. The Germans don't have a multitude of articles on 'centrifugal force'. David Tombe (talk) 00:17, 22 October 2010 (UTC)


 * But your reply to me above seemed to say you were supporting me; sorry I misunderstood. Dicklyon (talk) 05:42, 22 December 2010 (UTC)

So everybody involved in this discussion supports the re-merge, but two months later it hasn't happened yet. Why not? (I support it too FWIW.) Alzarian16 (talk) 20:48, 21 December 2010 (UTC)


 * Well, not quite. I agreed with getting rid of the new disambiguation article, but keeping the summary-style article (this one) and keeping the bigger and more specific articles (the ones I called "bloated") separate.  I went ahead and merged the disambig (by redirecting it here, since there was nothing else to do). Dicklyon (talk) 05:40, 22 December 2010 (UTC)


 * JohnBlackburne and FyzixFighter, do you have a merge plan that would get rid of some of the 48 KB of Brews ohare's bloat from Centrifugal force (rotating reference frame) as you merge? I might consider agreeing to a merge if I didn't think it would just add a lot of junk to what's currently not such a bad article.  Dicklyon (talk) 05:46, 22 December 2010 (UTC)
 * My suggestion would be to merge only the first three sections of Centrifugal force (rotating reference frame) and drop the rest entirely, but I'd guess that others would probably disagree. Alzarian16 (talk) 18:26, 22 December 2010 (UTC)
 * I would just trim the article as it is now: it's something that I've thought of before but never got around too, but even as a standalone article there's too much bloat from Advantages of rotating frames onwards, and too many references for them to be useful. It should be easy to do now without Brews's disruptive objections.-- JohnBlackburne wordsdeeds 19:12, 22 December 2010 (UTC)


 * The Lagrangian section could do with considerable trimming also. I think this is a specialist and somewhat informal use of the term. Martin Hogbin (talk) 18:14, 22 December


 * I'm opposed to the merge. This article is the sister article of coriolis effect and shouldn't be merged with others. It's a completely different topic; the maths is different, and the equation that it comes out of is different one.Planetscared (talk) 17:00, 13 January 2011 (UTC)
 * I get the feeling that you have confused the merge here. The proposal entails a merge of Centrifugal force (rotating reference frame) into Centrifugal force. How are those a completely different topic? Yoenit (talk) 17:39, 13 January 2011 (UTC)


 * I'm opposed, too. I think this is a stale proposal, that we partially fulfilled by phasing out the disambig page.  If someone still thinks that it's important to do more merging, they should speak up right away, or start a new proposal explaining why.  Dicklyon (talk) 19:18, 13 January 2011 (UTC)

Dick, are you against merging Centrifugal force (rotating reference frame) into Centrifugal force? It seems like a good idea to me.


 * Yes, I Oppose the merge, because, as I've explained before, Centrifugal force is a summary-style article that introduces the deeper treatments in Centrifugal force (rotating reference frame), Reactive centrifugal force, Absolute rotation, History of centrifugal and centripetal forces, and other articles. This seems like exactly the right place to have a summary-style article.  Dicklyon (talk) 23:07, 13 January 2011 (UTC)
 * I do not believe that a disambiguation page is desirable. There is only one definition of centrifugal force in widespread modern use and that is Centrifugal force (rotating reference frame). A disambiguation page is in my opinion confusing to the general reader and gives undue weight to specialist, historical, or fringe meanings of the term.  Martin Hogbin (talk) 12:45, 14 January 2011 (UTC)


 * I agree with you that a disambiguation page is not desirable here; that's why I eliminated it. I'm not sure why Wolfkeeper created it in the first place, or why Brews felt a need to bloat it to over 1600 bytes, but now it's gone.  As for your assertion that "There is only one definition of centrifugal force in widespread modern use," that's sort of true, but a lot of disclaimers.  Some dispatch to the other less modern, less widespread, and related points of view is still important, I think.  A summary article is a good way to let the reader know what the different aspects are; for most, it's all they'll need.  Or are you saying that some of the other articles are just junk that should be eliminated?  Dicklyon (talk) 16:17, 14 January 2011 (UTC)
 * I am thinking of how this looks to an average reader who wants to know what centrifugal force is, or maybe a student needing some help on the subject. At the moment they see two articles, suggesting that the term has two, or more meanings.  Personally, I would like to see one article on the standard modern meaning of the with short sections on historical or other meanings.  Martin Hogbin (talk) 22:43, 14 January 2011 (UTC)

Dicklyon, anybody with a reasonable comprehension of the subject would know that there is only one 'centrifugal force', and that a single article could very easily accomodate all of the various perspectives on the matter. What you seem to have failed to grasp is that there is a big difference between,

(1) considering centrifugal force to be a fictitious force as viewed from a rotating frame of reference, and (2) considering centrifugal force to be a radially outward inertial force that arises in conjunction with absolute rotation, and which is revealed when Newton's laws are expressed in a rotating coordinate system such as polar coordinates.

The former involves the idea that centrifugal force even exists when an object is not co-rotating with the rotating frame, while the latter attributes centrifugal force specifically to absolute angular momentum. The two perspectives overlap in the co-rotating scenario, but it is unnecessary to involve a rotating frame of reference when doing planetary orbital analyis. David Tombe (talk) 11:44, 14 January 2011 (UTC)


 * David, a rotating coordinate system is the same as a rotating frame of reference. Fictitious forces and inertial forces are two terms for the same thing.  In the context of a rotating frame of reference (or coordinate system) rotating refers to absolute rotation.  The distinction you make simply does not exist. Martin Hogbin (talk) 22:43, 14 January 2011 (UTC)

Martin, Part of what you are saying is right. I agree with you that centrifugal force is a single topic. I also agree that most modern textbooks introduce it as a fictitious force that is observed in a rotating frame of reference. I also agree with you that that the words 'fictitious' and 'inertial' are used inter-changeably in the modern literature. But you are also overlooking some important factors. When an object is co-rotating with a rotating frame of reference, the centrifugal force will be an inertial effect which can actually be felt pushing outwards. However, within the context of the 'rotating frame of reference' perspective, if an object is stationary and not co-rotating with the rotating frame of reference, it is still deemed to be subjected to a centrifugal force based on the angular speed of the frame of reference. That is where this approach differs from the polar coordinates approach.

When we deal in polar coordinates, we are only concerned with the centrifugal force that arises in connection with absolute rotation, and which can be felt physically pushing outwards. And it is this perspective which is used in planetary orbital analysis where the rotation doesn't in general have a uniform angular speed. In other words, there is a branch of physics in which we consider centrifugal force as an outward radial force, and in which we don't normally invoke the concept of a rotating frame of reference, and in which the centrifugal force is induced by absolute rotation. This perspective needs to have a section of its own in the article.

What I would like to ask you is 'what category do you place this latter perspective in? Is it specialist? Or is it fringe? Or is it historical?' I would say that it is general and historical. It was originally devised by Leibniz, and it is used today in planetary orbital analysis. At any rate, we have identified two different perspectives on centrifugal force. We have one in which it is a fictitious force which is a function of the rotating frame of reference, whether the object is co-rotating or not. And we have another in which the centrifugal force is an inertial force which can be physically felt and which is a product of absolute rotation, and which doesn't require the concept of a rotating frame of reference. Both of these perspectives are sourced, although I admit that the former is currently much more widely sourced. David Tombe (talk) 23:17, 14 January 2011 (UTC)


 * It's essentially unsourced, idiosyncratic, and fringe. Goldstein made it clear enough that radial distance is a coordinate in a rotating coordinate system, not a concept different from the usual.  Dicklyon (talk) 00:06, 15 January 2011 (UTC)

David, you seem completely confused, I suggest that we continue this discussion on your talk page. Martin Hogbin (talk) 02:19, 15 January 2011 (UTC)


 * OK. We'll go there. But based on what you have written above, I am guessing that you have done one of those university courses in applied maths entitled 'rotating frames of reference' in which the coordinate transformations are done, and where centrifugal force and Coriolis force emerge and are introduced as fictitious effects which are a product of observation from the rotating frame. That of course, despite being prolific in modern textbooks, is a specialist approach for advanced mathematicians and it is not the common understanding of centrifugal force amongst the public at large. The public at large think of centrifugal force as being the outward radial pressure which arises when something is spun. And the common understanding is the one that is used in planetary orbital analysis. Anyway, by all means carry on on my talk page. David Tombe (talk) 11:44, 15 January 2011 (UTC)

five different contexts?
I just reverted this edit which changed the description of the two types of centrifugal force, fictitious and reactive, into I'm not sure what. I had a look at the source for the 'five different contexts' but could not find it, and frankly the source is very poor one, a long and poorly written essay which is no substitute for the reliable academic sources already in the article. More generally if there is some source which introduces new material it should be worked into the article alongside existing material, not added to the lede in a way which disagrees with the rest of the article.-- JohnBlackburne wordsdeeds 17:31, 6 November 2010 (UTC)


 * John, it was in the paragraph third from the bottom. It read,


 * Thus Newton uses the term “centrifugal force” in the Principia to describe three very distinct concepts. First, he uses it to refer to a hypothetical repulsive force (such as the force between two electrons), which would result in a hyperbolic path, accelerating away from the source of the “central” repulsive force. Second, he uses the term to refer to the outward force exerted by a revolving object on some framework (such as the force exerted by a roulette marble on the housing). Third, he uses the term to refer to the “fictitious” outward force on a revolving object when viewed from a revolving frame of reference. A fourth context in which the concept of “centrifugal force” may arise is when phenomena are described in terms of curved coordinate systems, such as polar coordinates. Such non-linear coordinate systems are not inertial in the spatial sense, even though they may be static (i.e., not accelerating), as discussed in the note on Curved Coordinate Systems and Fictitious Forces. A fifth usage of the term “centrifugal force” occurs when the inertial forces on an object, relative to a momentarily co-moving inertial frame, are de-composed into tangent and normal components (in the osculating plane). The normal component is called centrifugal force. There is no Coriolis force with this convention, because the particle is always at rest with respect to the co-moving inertial coordinates. Needless to say, all these usages are very closely related, and differ only by context and convention.


 * You cannot leave the article lead stating that there are only two concepts of centrifugal force when there are clearly more. Polar coordinates is one such context. That is the context which is used in planetary orbital analysis. It is not something which is in any doubt. David Tombe (talk) 17:44, 6 November 2010 (UTC)


 * What Newton thought might be of interest historically but physics has moved on a long way since his time, in both what we know and how we describe it. From my reading of that he used it for more than we would today: e.g. the first example of repulsing electrons. But no, there are two concepts as expressed in the article and it summarises in the lede. And that essay hardly seems a reliable source: more a personal essay by someone with some odd views, on a web site created to push his self-published book.-- JohnBlackburne wordsdeeds 17:57, 6 November 2010 (UTC)

John, The article mentioned three concepts in connection with Newton. I had discounted the first concept in my count of five. Newton's other two concepts are exactly the same two concepts that you have already accepted. Ie. the reactive force and the inertial force in a rotating frame of reference. So you should have no problem with the bit about what Newton said. The article then went on to talk about polar coordinates. That is not in any doubt. We formulate the planetary orbital equation in polar coordinates and the radial equation has an outward centrifugal force term. Then he mentioned about normal and tangential resolutions of velocity. I found his remarks about 'no Coriolis force' in this system to be very interesting. I see no grounds for you to either doubt what the author has said, or to deem the source to be unreliable.

And for your information, in my own personal opinion, there is only one single concept of centrifugal force. In my view, four of the five mentioned in the source are one and the same thing. The so-called reactive force is merely a knock-on effect of the inertial force, just as a brick falling on somebody's head is a knock-on effect of gravity. David Tombe (talk) 18:12, 6 November 2010 (UTC)


 * None of this really matters. The Mathpages is a very intereresting work (- i.m.o. it is piece of art -) but it can never serve as an authoritative source as a basis for Wikipedia content. It is someone's personal (and, apart from one chapter, book-unpublished) view. It clearly is an ideal entry for the External links section, and perhaps even for the Further reading list, but the unpublished parts can never be used as a wp:RS, and can certainly never replace a solid textbook source. DVdm (talk) 18:37, 6 November 2010 (UTC)

Dvdm, Is your only concern about a solid textbook source which uses polar coordinates as an illustration of centrifugal force? Are you seriously doubting that centrifugal force is a polar coordinate term in the radial planetary orbital equation? David Tombe (talk) 19:07, 6 November 2010 (UTC)
 * Even if it were properly sourced the introduction is not the place to introduce sourced material. It should be introduced into the body of the article, properly integrated in what is a well established article. As for the content I still find what you added confusing and unclear, in particular what you mean by context. Polar coordinates are just another coordinate system, but there are an infinite number of them, any of which could be used to calculate the force, as they are largely interchangeable – Lagrangian mechanics is one way of approaching this. It's not clear what "normal and tangential resolutions of velocity" have to do with centrifugal force. And the others are what is there already, and in the article.-- JohnBlackburne wordsdeeds 19:45, 6 November 2010 (UTC)

John, It's a simple yes or no question. Do you accept the fact that centrifugal force is a term in polar coordinates which is used in the radial planetary orbital equation without involving rotating frames of reference? David Tombe (talk) 19:53, 6 November 2010 (UTC)
 * Take your questions to the ref desk if you don't understand the topic. If this is about the article I don't see how your question relates to it. Perhaps you could point to the section of the article you think is wrong and suggest a, reliably sourced, way to improve it.-- JohnBlackburne wordsdeeds 19:57, 6 November 2010 (UTC)

John, You didn't answer the question. The section in the article which you are asking about doesn't exist for the reason that some editors in the past have rejected the idea that centrifugal force is a term in the radial planetary orbital equation. I have supplied a source which states that centrifugal force is a term in polar coordinates outside of the context of rotating frames of reference. Do you have any objections to that material being put into the article on the basis of your own beliefs, or is it purely a matter of whether or not the source is reliable? David Tombe (talk) 20:08, 6 November 2010 (UTC)
 * Everything here needs a reliable source, and you have yet to supply one; it has nothing to do with "my beliefs".-- JohnBlackburne wordsdeeds 20:23, 6 November 2010 (UTC)


 * See also this new entry at the Reliable sources/Noticeboard. DVdm (talk) 20:30, 6 November 2010 (UTC)


 * Didn't we have some of this discussion re: the radial equation of planetary orbits a little more than a year ago? "Introduction to Classical Mechanics" Atam P. Arya (1990), pg 231 is a reference that explicitly connects the moving the centripetal acceleration term to the force of the equation to get the radial equation as equivalent to viewing the physics from a non-inertial frame rotating with the planet. Jeremy B. Tatum "Celestial Mechanics" Chapter 16 also clearly places the radial equation in a co-rotating, non-inertial frame. --FyzixFighter (talk) 20:44, 6 November 2010 (UTC)
 * Ah, I see. So this is nothing new, just reopening the same old arguments interrupted only by David Tombe's ban from physics. I suggest that if David Tombe has nothing new to bring to this discussion he stops it now, especially disrupting multiple venues with the same flawed arguments, in case he attracts the same sort of attention that got him banned a year ago.-- JohnBlackburne wordsdeeds 20:59, 6 November 2010 (UTC)
 * I agree. All input from David Tombe is best ignored; it was a large part of the reason for the massive bloat in these articles and for Brews ohare's problem and eventual banning.  He is well known as a physics crank, and has done nothing to move away from that position in his year off. Dicklyon (talk) 18:37, 22 December 2010 (UTC)

Dicklyon, That is quite untrue. My input to the various centrifugal force articles has been negligible, and I have consistently advocated that we only need to have one very short article. As regards the 'crank' position which are are referring to, it is very well depicted by Bond's adversary in that cartoon that you seem so keen to include in these articles. David Tombe (talk) 19:47, 14 January 2011 (UTC)


 * Your several hundred article edits and several hundred talk-page edits in April–July 2008 kicked off and fueled the period of Brews hyper-inflation. Dicklyon (talk) 00:12, 15 January 2011 (UTC)


 * In the cartoon, when 'hat guy' says, "A laughable claim, Mister Bond, perpetuated by overzealous teachers of science. Simply construct Newton's laws into a rotating system and you will see a centrifugal force term appear as plain as day," he is indeed displaying some of your confusion. In one sense, he is entirely correct: "construct Newton's laws into a rotating system and you will see a centrifugal force term appear."  That's what's called a "fictitious force", and I think we all agree that it arises from a rotating reference system.  On the other hand, he is probably just confused about "overzealous teachers of science," likely because he doesn't know what to make of the term "fictitious"; this is the same problem you have exhibited many times.  Mr Bond is also perhaps confused when he says "there's no such things as..."; you can interpret his position as meaning that he understands that he'll be crashed by the rim of wheel accelerating him along a curved path.  Perhaps it's true that these "overzealous teachers" who deny "centrifugal force" actually exist; it would be interesting to find a sourced discussion of that if so.  Dicklyon (talk) 00:26, 15 January 2011 (UTC)

Dick, The centrifugal force(rotating frame of reference) perspective is certainly the most prolific in the modern literature. But it is also specialist. It is for advanced mathematicians. It is a mathematical subject about describing how things are viewed from a rotating frame of reference. It is not about physical inertia. It involves using mutually cancelling fictitious forces in relation to stationary objects which have no inertia. That is not the perspective that Bond's adversary is invoking in the cartoon. Bond's adversary is invoking real physical inertia which crushes bones. Bonds adversary is talking about coordinates fixed in a physically rotating system which induces an outward inertial force. These are two distinct ideological perspectives on centrifugal force. They both need to be treated in separate sections within a single article on centrifugal force. The two perspectives overlap in the co-rotating scenario in which case the fictitious term is describing an actual inertial force.

Mr. Bond's perspective is yet a third perspective which is popular amongst high school students. And then of course there is Isaac Newton's perspective about centrifugal force being a reaction to centripetal force. You have your opinion on which is the correct perspective, and I have mine. But both need to be represented in a single article. And at least we are both agreed that neither Newton's nor Bond's opinions are correct. It seems to be a battle over whether it is the rotating frames of reference perspective or the Leibniz perspective, with myself supporting the latter. David Tombe (talk) 00:42, 15 January 2011 (UTC)


 * David, you seem to have a completely different understanding of this subject from physicists. I suggest that you continue on your talk page with those interested. Martin Hogbin (talk) 02:53, 15 January 2011 (UTC)

Martin, OK. See you there. David Tombe (talk) 11:48, 15 January 2011 (UTC)


 * Right, except nobody is interested. I'll go back to following my advice and ignoring David.  Dicklyon (talk) 05:12, 15 January 2011 (UTC)

Dick, The problem would be greatly assisted if we could actually pin you down to a definite opinion in all of this. David Tombe (talk) 11:47, 15 January 2011 (UTC)

Single Centrifugal Force Article
I am proposing that there should be a single united article on centrifugal force to cater for all the perspectives on the topic. These perspectives are,

(1) That it is a radially outward inertial force that arises in connection with absolute rotation. It obeys the inverse cube law when angular momentum is conserved, and it is observed in planetary orbits and in the centrifuge device. It does not have to be equal to a centripetal force, but in the special case when it is equal to a centripetal force, we will have circular motion. (Leibniz/Lagrangian perspective)

(2) That it is a fictitious force which shows up in the transformation equations from an inertial to a rotating frame of reference, and which is observed to act on all objects from the perspective of the rotating frame of reference, whether such objects are co-rotating or not. (modern university perspective)

(3) That centrifugal force doesn't exist, and that circular motion arises when a centripetal force deflects an object from its straight line inertial path. (modern high school perspective)

(4) That centrifugal force is an equal and opposite reaction to a centripetal force. (Isaac Newton's perspective) David Tombe (talk) 11:57, 24 January 2011 (UTC)


 * I think the current article does a good job of clarifying the different perspectives, this way:


 * (1) No sources support this perspective, so we don't mention it. The inverse cube law comes up in (2).


 * (2) See Centrifugal force (rotating reference frame). We have a section with a main link.


 * (3) I don't see why we need to represent the opinion of someone who would say that something doesn't exist, when we have reliable sources on the thing. I think this "modern high school perspective" is essentially aprochryphal anyway; or it's a confused mixup between the two concepts (2) and (4), which do exist.


 * (4) See Reactive centrifugal force, which is not the same thing as what is most commonly called centrifugal force, but is related. We have a section with a main link.


 * Further, we have a section on historical conceptions, where the relationships of different conceptions can be compared.


 * I think a "unified" article would be an invitation for more of David's pushing of (1), and for other bloat. I'd rather see more effort put into tuning up the articles by trimming off unneeded junk and making them clear.  There is stuff worth keeping in the other articles, and too much to merge into one, I think. Dicklyon (talk) 17:27, 24 January 2011 (UTC)

Dick, As regards your claim that persepective (1) is not sourced, that is where you are absolutely wrong. I supplied some sources recently at WT:PHYS. And then you claim that centrifugal force as an inverse cube law force is dealt with in perspective (2). No it is not. It is dealt with only when studying the planetary orbital problem as per perspective (1) which you seem to be very keen to sweep under the carpet even though it is represented in your favourite cartoon. Modern textbooks which deal with perspective (2) are dealing with the rotating frame transformation equations and they never look beyond the expression mrw^2 for centrifugal force. I have never seen the inverse cube law mentioned in a chapter about rotating frames of reference. And as for your claim that the reactive centrifugal force is something different, no it isn't. In fact, strictly speaking there is no such thing as a reactive centrifugal force because it is a pro-active effect. David Tombe (talk) 18:17, 24 January 2011 (UTC)


 * I agree with Dick's summary of (1)-(4). We have a number of references that show that (1) is the same as (2) (see Swetz, "Learn from the Masters!", pg 269; Linton, "From Eudoxus to Einstein", pg 413; Aiton, "The celestial mechanics of Leibniz in the light of Newtonian criticism"; Arya (1990), "Introduction to Classical Mechanics" (1990), pg 231) Perspective (1) is really only interesting historically, as these references show that (1), as a study of the motion along the radius vector (Leibniz's approach), is essentially a study of motion relative to a rotating frame of reference, ie perspective (2). We also have references that (4) is something different from (2) (see Roche, "Introducing motion in a circle").
 * I don't know if I agree though that there is too much to merge this article and Centrifugal force (rotating reference frame). I apologize for letting the merge discussion go stale - RL issues both fun and not so fun. But I do agree that both articles need extensive trimming - maybe after the trimming it will be clearer whether the two can be merged properly or not. --FyzixFighter (talk) 19:25, 24 January 2011 (UTC)

FyzixFighter, The point which you have overlooked is that (1) and (2) are only the same in the special case when the object is co-rotating with the rotating frame of reference. What perspective (2) does is, it uses maths to patch up the difference between the real inertial effect which can be felt as an outward push on an object that is in a state of absolute rotation, and the situation where an object is sitting stationary and being observed from a rotating frame of reference. In the latter, there is no inertial effect.

Perspective (1) concentrates on the actual inertial effect which can be felt and which can break bones and doesn't have to involve a rotating frame of reference, so we can hardly say that perspective (1) and perspective (2) are the same thing. Perspective (1) does not deal with stationary objects that are being viewed from a rotating frame of reference.

Your logic basically runs like this. There is an article on equines and it doesn't mention zebras. Dick argues that zebras don't exist and that there are no sources which say that zebras exist. You argue that zebras are just a kind of horse and don't need any specific mention as they are covered under horses. And despite the fact that what you are saying is not the same as what Dick is saying, you nevertheless claim to be saying the same thing as Dick. But between the two of you, you are both trying to make sure that zebras don't get mentioned. Then when a source is produced which proves that there is such a thing as a zebra, you produce another source showing that a zebra is an equine and that therefore it doesn't need any special mention within the article. Would we really need to have a source which specifically states that a zebra is a species distinct from a horse in order to be allowed to write an article on zebras? No. But we do have sources which treat planetary orbits without mentioning rotating frames of reference and in which the centrifugal force is an outward inertial inverse cube law force. Do we need to have a special source which states that this is a different perspective on centrifugal force from the perspective which ascribes a centrifugal force to a stationary object which doesn't actually possess any inertia and which merely appears to move in a circle? David Tombe (talk) 20:08, 24 January 2011 (UTC)


 * David, it is quite simple. You are wrong. Your argument is based on a bizarre conspiracy theory of physicists.  This shows that not only do you not understand physics but you do not understand conspiracy theories.  It is time to call it a day. Martin Hogbin (talk) 20:14, 24 January 2011 (UTC)

Martin, Which conspiracy theory are you talking about? Can you not see the difference between,

(a) An object with an absolute angular momentum that is pushing outwards from a centre due to its inertia, and

(b) An object that is sitting stationary with no inertia, but which is being observed to move in a circle from the perspective of somebody in a rotating frame of reference?

Those are two different physical situations. Can you not see the difference between them? Only situation (a) involves an inertial centrifugal force. I know that you think that situation (b) involves a centrifugal force and a radially inward Coriolis force, but this is just mathematical accountancy and doesn't involve any real inertial effects as such. David Tombe (talk) 20:24, 24 January 2011 (UTC)


 * @David - since we do have multiple reliable sources that say (1) is understood today as a specific application of the more general (2), then yes, we do need a reliable source that says (1) and (2) are distinct. Please remember WP:OR, WP:FRINGE, WP:BATTLE, and WP:SOAP, which you have previously been warned about. --FyzixFighter (talk) 20:43, 24 January 2011 (UTC)

FyzixFighter, There is a completely different emphasis. Perspective (1) is about actual motion along the radial vector. It's about actual inertia. It about a force which can be felt. Perspective (2) is about accounting for observations from a rotating frame of reference and it applies centrifugal force to situations in which there is no actual inertia. They are completely different perspectives on the subject, and I can show you multiple sources that deal with the orbital problem without using a rotating frame of reference. David Tombe (talk) 21:12, 24 January 2011 (UTC)
 * The merge proposed in its current form runs the risk of violating WP:SYNTHESIS. If each of the perspectives are so different, why is a joint article preferable? To justify a single article about all the perspectives listed, we would need a single source covering them all, as opposed to lots of sources each discussing one perspective. Details on each perspective could be filled in using other sources, but without the overarching source we wouldn't actually have any evidence that there is a single topic to cover. Alzarian16 (talk) 10:05, 25 January 2011 (UTC)