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Archives

This is not a forum for general discussion of centrifugal force. Any such messages will be deleted. Please limit discussion to improvement of this article.

1 Co-rotation
2 Radial motion
3 Physically real centrifugal force
4 Archiving about a megabyte
5 Re-unification of the article
6 Why does Wikipedia insist on using Ω for angular velocity?

Co-rotation

Dick, you have got it all wrong. You are trying to account for a zero effect in terms of the sum of two mutually cancelling illusions, both of which are merely a product of faulty interpretation of mathematics. There is no centrifugal force acting on anything unless there is actual rotation occurring. The rotating bucket of water clearly demonstrates this very basic fact. The angular velocity term in the centrifugal force is for the frame of reference, which essentially means that it is for particles that are co-rotating with the frame, which essentially means that it is for the particles themselves. That is enshrined in the derivation. So at what point does the final result suddenly become liberated to apply to all particles, irrespective of their state of actual rotation? And as regards Coriolis force, the derivation means that the Coriolis force is a tangential force. It is impossible to have a Coriolis force accounting for a radially inward centripetal force. Finally, the central force equation tells us that in order to have a circular motion, the outward centrifugal force must be exactly balanced with the inward centripetal force. If we were to use the Coriolis force for the centripetal force, as you have suggested, it would be twice the size of the centrifugal force and so it would result in a net inward force. A rotating frame of reference is only what its name suggests. It is not a physical entity in its own right. Centrifugal force on an object is already either present or not. A rotating frame of reference merely causes a circular motion artifact to be imposed on the already existing motion. And that artifact cannot be described mathematically with a net inward radial force, never mind a net radial inward force supposedly being supplied by a tangential Coriolis force. You have got it all very badly wrong. David Tombe (talk) 12:43, 4 November 2008 (UTC)

David, I'm just trying to explain what the sources say; if they have it all wrong, we still need to report it the way they do it. But it's not wrong. You are obviously focused on something quite different from the "fictitious force" called centrifugal force when you say of the rotating frame "It is not a physical entity in its own right. Centrifugal force on an object is already either present or not." Quite false; the centrifugal force we are speaking of is "fictitious"; it is NEVER actually present on an object in an inertial frame; it is entirely frame dependent. If you're speaking of something else, it's probably the reactive centrifugal force. Dicklyon (talk) 14:59, 4 November 2008 (UTC)

Dick, I'm not talking about something else. I'm talking about centrifugal force. And there is no longer any need to mention sources or citations because it is clear that you refuse to look at sources and citations that don't suit you. Centrifugal force is the outward radial force in planetary orbital theory. I have directed you to Goldstein's 'Classical Mechanics' where this is written in plain English, but you have somehow managed to take a different meaning out of it. As for this 'reactive centrifugal force' that you keep talking about, anybody with a full comprehension of the subject would understand that there only is one universal centrifugal force. Splitting the subject up is a clear sign of a lack of understanding. David Tombe (talk) 01:31, 5 November 2008 (UTC)

David, I've looked at Goldstein, and it's clear there that the outward centrifugal force is the fictitious force due to the way he rotates the frame to make a one-dimenional problem; just like all the other sources. In the corresponding inertial system, there is no outward force, and if you have a source that says there is, please mention it again; I don't think I could ignore such a thing, but if I've overlooked, I'd sure like to hear about it. Dicklyon (talk) 06:56, 5 November 2008 (UTC)

Dick, The Goldstein doesn't even mention frames of reference in relation to the planetary orbital equation. The equation in question is either 3.11 or 3.12. It is dealt with in plane polar coordinates referenced to the inertial frame. He makes the equation into a single variable equation in r by substituting Kepler's areal constant into the centrifugal force term. The centrifugal force then becomes an inverse cube law force. It is then that he states that it is equivalent to the fictitious one dimensional problem. And so it is. It is a one dimensional radial scalar differential equation in r. I can't see how you deduce that the outward centrifugal force is fictitious. But that doesn't matter anyway. The point here is that centrifugal force exists in the absence of a rotating frame of reference, and the angular velocity in the centrifugal force belongs to the particle. And you continue to ignore the statement that Goldstein made at the top of page 179, which I have quoated at least twice above. David Tombe (talk) 07:22, 5 November 2008 (UTC)

David: you are resorting to exhortation, with neither argument nor sources for support. It seems likely that you agree that the Wiki article is totally correct if one accepts the premise for the vector form of the various fictitious forces, namely:

$\boldsymbol{F} - m\frac{d \boldsymbol{\Omega}}{dt} \boldsymbol{\times r} - 2m \boldsymbol{\Omega \times} \left[ \frac{d \mathbf{r}}{dt} \right] - m\boldsymbol{\Omega \times} (\boldsymbol{\Omega \times r})$ $= m\left[ \frac{d^2 \boldsymbol{r}}{dt^2} \right]\ .$

Thus, to impact acceptance of the article, you must discredit this vector formulation, which you have attempted so far by attacking its interpretation, and suggesting its use is limited to the case of co-rotation. (You may recall Fugal also attempted to discredit it, suggesting that this equation applied only to Cartesian coordinates.) Next, I will critique your suggestion.

The derivation in Fictitious force uses three variables: (i) the vector x_A (t) between the origin of the inertial frame A and the moving object, (ii) the vector x_B (t) between the origin of the rotating frame B and the moving object, and (iii) the vector joining the origins of the two frames X_AB (t), which may move relative to one another. The vector x_B (t) between the origin of the rotating frame B and the moving point is free to take any form, and is not restricted to a co-rotating particle. If you think differently, one way to proceed is to show where in the derivation the co-rotation restriction snuck in, unannounced.

So far you have suggested that this restriction to co-rotation occurs with the introduction of Ω. As you have pointed out, the introduction of Ω occurs in the subsection Rotating systems with the introduction of the time dependence of the unit vectors in the rotating frame:

$\frac {d \mathbf{u}_j (t)}{dt} = \boldsymbol{\Omega} \times \mathbf{u}_j (t) \ ,$

There is no restriction upon x_B (t) introduced here, because the unit vectors apply to the frame, not the particle, and x_B (t) describes the location of the particle wrt the origin of the frame, irrespective of the directions of the frame's unit vectors. The location of the origin of the rotating frame also is unaffected by the frame's rotation: only the directions of the frame's axes change in time. The introduction of Ω above does not affect the frame's origin. Hence, independent of the above equation, the particle motion still is the same arbitrary function of time with the same arbitrary trajectory, but of course the coordinates of x_B (t) in the rotating system change in time, both because the particle moves, and because the axes change orientation in time. In particular, the particle can be chosen to co-rotate or not, as the occasion demands.Brews ohare (talk) 14:45, 4 November 2008 (UTC)

Brews, you have already answered the question for me. The angular velocity in the analysis applies to the frame. This means that it applies to fixed points in the frame and not to moving points in the frame. I can't see how you could interpret the meaning otherwise. David Tombe (talk) 01:26, 5 November 2008 (UTC)

David: You don't get the point here. Yes, the angular velocity belongs to the frame. But x_B (t) = r (t) belongs to the particle, which therefore can have any motion whatever, unrestricted by the selection of rotation by the frame. That means the relation

is unrestricted, and applies regardless of any general motion of the particle, not to only co-rotating particles. Please re-read what I have said above. You have not let it sink in. Brews ohare (talk) 06:28, 5 November 2008 (UTC)

Brews, I haven't overlooked anything. The velocity of the particle relative to the frame is free at the beginning of the derivation, and it doesn't possess any particular angular velocity at that stage. At the end of the derivation, after dr and dθ have gone to zero in the limit, the vector triangle shrinks to an infinitessimal right angle triangle and the particle will have been restricted to co-rotating radial motion. It is only under those conditions that the centrifugal force term and the Coriolis force term can take on their familiar mathematical form, while being restricted to the tangential and the radial directions respectively. David Tombe (talk) 07:32, 5 November 2008 (UTC)

The restriction of Coriolis force to the tangential direction is "familiar" because you are accustomed to Goldstein's treatment, in which the frame rotates to keep a planet a given direction, to reduce it to a 1D problem. The math actually works fine in the much more general situation, with Coriolis force not restricted in direction. Dicklyon (talk) 07:43, 5 November 2008 (UTC)

Dick, Goldstein doesn't mention rotating frames of reference. He deals with the planetary orbital equation in polar coordinates referenced to the inertial frame. The radial planetary orbital equation contains an outward centrifugal force term. The tangential planetary orbital equation equates the sum of the Coriolis force and the angular force (Euler force) to zero, and is hence equivalent to Kepler's second law. There is never a radial Coriolis force under any circumstances in the two body problem. And furthermore, a rotating frame of reference cannot even create the illusion of a Coriolis force because it cannot create a rotating radial motion. David Tombe (talk) 09:21, 5 November 2008 (UTC)

David: You say that a limiting procedure (which appears simply to relate to taking a derivative) in which dr and dθ go to zero introduces a restriction limiting the possible forms of r(t) in the equation:

I fail to see any part of the derivation where a restriction on the form of r(t) arises. Straightforward application of the chain-rule of differentiation is used, and it does not require any "special" treatment of limiting procedures beyond the customary derivative considerations. Explicit introduction of polar coordinates (r, θ) is not necessary at all. The functional form of r(t) is left entirely general, and that is the interpretation in all the references as well. Brews ohare (talk) 15:50, 5 November 2008 (UTC)

Brews, you must go to the root of the derivation, which is a vector triangle. See figure 1 in this web link, [1] The familiar expressions for centrifugal force and Coriolis force only arise when that triangle shrinks to zero in the limit as dr and dθ tend to zero. When that occurs, centrifugal force will be a radial force and Coriolis force will be a tangential force. The derivation involves exactly the same principles of vector calculus as are involved in the derivation of these same terms in polar coordinates. And in the latter derivation, the tangential nature of Coriolis force is overtly recognized in the final expression. It is all one single topic.David Tombe (talk) 02:51, 6 November 2008 (UTC)

This is a re-hash and not responsive. There is no need for polar coordinates, and the only principle involved is the chain rule of differentiation, which imposes no restriction whatsoever upon the functional form of r(t). Brews ohare (talk) 03:50, 6 November 2008 (UTC)

The maths does not stand on its own. It applies to a vector triangle in the limit as dr and dθ tend to zero, in which case the centrifugal force will be radial and the Coriolis force will be tangential. David Tombe (talk) 07:50, 13 November 2008 (UTC)

Radial motion

Here is an illustration showing the futility of using mrǿ² as a "force". Suppose in frame S a particle moves radially away from the origin at a constant velocity. The force on the particle is zero by Newton's first law. Now we look at the same thing from frame S' , which is the same, but displaced in origin. In S' the particle still is in straight line motion at constant speed, so again the force is zero.

Two coordinate systems differing by a displacement of origin. Radial motion with constant velocity v in one frame is not radial in the other frame. Angular rate $\dot \theta = 0$ but $\dot \theta ' \ne 0$

What if we use polar coordinates in the two frames? In frame S the radial motion is constant and there is no angular motion. Hence, the acceleration is:

$\boldsymbol a = \left(\ddot r -r {\dot \theta}^2 \right ) \hat{ \boldsymbol r} + \left(r \ddot \theta +2 \dot r \dot \theta \right) \hat {\boldsymbol \theta} = 0\ ,$

and each term individually is zero because $\dot \theta = 0, \ \ddot \theta =0$ and $\ddot r =0$ . There is no force, including no $r \dot \theta ^2$ "force". In frame S' , however, we have:

$\boldsymbol a ' = \left( \ddot {r } ' -r ' \dot {\theta } ' ^2 \right) \hat { \boldsymbol r } ' + \left( r ' \ddot \theta ' +2 \dot r ' \dot \theta ' \right) \hat {\boldsymbol \theta } ' \$

In this case the azimuthal term is zero, being the rate of change of angular momentum. To obtain zero acceleration in the radial direction, however, we require:

$\ddot r '= r ' \dot {\theta}' ^2 \ .$

The right-hand side is non-zero, inasmuch as neither r' nor $\dot \theta'$ is zero. That is, we cannot obtain zero force (zero a') if we retain only $\ddot r$ as the acceleration; we need both terms.

Aha, I imagine you saying, of course we need the centrifugal force $r \dot \theta ^2$ to balance the $\ddot r$ force. Woops! Now we need a $\ddot r$ force? Well, put aside the $\ddot r$ force, and focus on the centrifugal force for a moment.

How can a physically real centrifugal force be zero in one frame S, but non-zero in another S' identical, but a few feet away? Even for exactly the same particle behavior the expression $r \dot \theta ^2$ is different in every frame of reference, no matter how trivial the distinction between frames. It's zero in S and non-zero in S' . In short, if we take $r \dot \theta ^2$ as "centrifugal force", it does not have a universal significance: it is unphysical.

Beyond this problem, the real impressed net force is zero in Cartesian coordinates. (In a Cartesian system in S' , $\ddot x' = \ddot y' = 0$ ; there is no real impressed force in straight-line motion at constant speed). If we adopt polar coordinates, and wish to say that $r' \dot \theta '^2$ is "centrifugal force", and reinterpret $\ddot r'$ as "acceleration" (without dwelling upon justification), we have the oddity that straight-line motion at at constant speed requires a net force in polar coordinates, but not in Cartesian coordinates. This perplexity applies in frame S', but not in frame S.

Assuming agreement :-) about the absurdity of this situation, that a proper formulation of physics is geometry and coordinate-independent, one must say that $r \dot \theta ^2$ is not centrifugal force, but simply one of two terms in the acceleration. This last view as two terms in the acceleration is frame-independent: there is zero centrifugal force in any and every inertial frame. It also is coordinate-system independent: we can use Cartesian, polar, or any other curvilinear system: they all produce zero. Brews ohare (talk) 00:40, 12 November 2008 (UTC)

The example above on radial motion in one frame as viewed from an adjacent frame shows that mrǿ² cannot be called "centrifugal force", real or fictitious, as it doesn't behave like the radial component of a force unless coupled with the $\ddot r$ term. This illustration is a definitive counterexample discrediting the mrǿ² = centrifugal force argument, and settling this matter once and for all. Brews ohare (talk) 04:42, 12 November 2008 (UTC)

How about adding such a discussion to one of the articles; possibilities are mechanics of planar particle motion, polar coordinates or this article. That would serve to show the invariance of the Newtonian approach and the expediency of the Hildebrand approach cooked up for mathematical convenience. Brews ohare (talk) 18:19, 12 November 2008 (UTC)

I put the argument in polar coordinates. Brews ohare (talk) 01:26, 13 November 2008 (UTC)

Is there an article in Wiki somewhere presenting the invariance of physical law under change of coordinate systems, for example, translated or rotated coordinate systems have the same laws? The articles Tensor field and Vector field seem to dwell on the mathematics, not mentioning the physical interpretation. Brews ohare (talk) 19:06, 12 November 2008 (UTC)

An example is General covariance, which mentions the "geometric, coordinate-independent formulation of physics". The article Lorentz covariance explains the math (but not the point), Galilean invariance refers to inertial frame (a bit overly technical, I'd say) Special relativity never makes the point. Any suggestions? Brews ohare (talk) 19:27, 12 November 2008 (UTC)

Brews, Once again, this is not about terminologies. We now all know that the equation,

$\ddot r = r\dot\theta^2-GM\frac{1}{r^2} \$

holds. I'm not interested in terminologies. If there is a circular motion, then the left hand side will be zero. That means that the first term on the right hand side will have to be equal and opposite to the centripetal force. Hence circular motion cannot exist on a centripetal force alone. That is all there is to it. If you want to deny this and carry on applying the rotating frame transformation equations to particles that are stationary in the inertial frame, then that is up to you. But it is total nonsense. David Tombe (talk) 00:09, 13 November 2008 (UTC)

Apparently arguments that make sense to me can be dismissed by you as "total nonsense" without discussion. The above discussion does not involve "rotating frame transformations" nor "particles stationary in an inertial frame". I have engaged your brand of "total nonsense" with what seems to me to be sensible argument. You don't even read the argument, never mind reciprocate with discussion. But then, that's up to you. Brews ohare (talk) 00:38, 13 November 2008 (UTC)

Brews, Your argument above was unnecessary. The equation,

$\ddot r = r\dot\theta^2-GM\frac{1}{r^2} \$

contains all that you need to know about centrifugal force for the purposes of an encyclopaedia article. Ever since this debate began in early 2007, there has been a systematic effort to deny that equation. Centrifugal force is a radially outward force that arises in connection with rotation. It's as simple as that. David Tombe (talk) 03:14, 13 November 2008 (UTC)

Centrifugal force is a radially outward force that arises in a rotating reference frame in connection with rotation. It's as simple as that. Brews ohare (talk) 03:49, 13 November 2008 (UTC)

BTW, your equation, whatever its content, does not address my above "unnecessary argument", which refers to a force-free motion. Brews ohare (talk) 03:53, 13 November 2008 (UTC)

Brews, centrifugal force is a radial effect. A rotating frame of reference cannot bring about a radial effect, even as an illusion. Any centrifugal forces as seen from a rotating frame of reference are already in existence to begin with. The rotating frame merely masks the cause, which is the actual rotation. The equation which I have given is the equation which explains what centrifugal force is all about. It uses polar coordinates referenced to the inertial frame of reference. And it is silly to argue about what the first term on the right hand side is. It is centrifugal force. Your argument was merely a decoy to avoid having to face up to the radial planetary orbital equation and the fact that centrifugal force is not something which depends on rotating frames of reference for its existence. David Tombe (talk) 04:54, 13 November 2008 (UTC)

David: Not pertinent to my argument, which does not use a rotating frame at all. It is not a decoy, but a very simple case of straight-line motion, and doesn't even need gravity. If your approach doesn't work here (it doesn't, I'd say), it cannot be expected to work at all. Brews ohare (talk) 06:54, 13 November 2008 (UTC)

Brews, My approach is the standard textbook planetary orbital approach. Who said anything about it not working? I'm trying to show you that centrifugal force exists independently of rotating frames of reference. David Tombe (talk) 07:11, 13 November 2008 (UTC)

Physically real centrifugal force

And Brews, Just in case you think I'm ignoring your argument, I'm not. You make out a case for a physically real centrifugal force having a different value in relation to two different origins. That is not a problem. In reality, a particle will have a different centrifugal force relative to every other particle in the universe and the effects will all add together. I've already tried to explain that to you. It means nothing to consider centrifugal force relative to an imaginary origin, just as it means nothing to consider the gravitational force relative to an imaginary origin. David Tombe (talk) 07:32, 13 November 2008 (UTC)

David: You aren't ignoring the argument, just not responding to it. It's like talking to a politician about raising taxes. He'll somehow make that a question about apple pie and motherhood.

Real forces transform like vectors. Your version of centrifugal "force" does not.

Your statement "In reality, a particle will have a different centrifugal force relative to every other particle in the universe and the effects will all add together." is completely off the wall. It sounds like you are saying bodies originate centrifugal force by virtue of their motion, and, I suppose, at a given point in space all these contributions to the net centrifugal force add vectorially? Where are your citations for this one? Brews ohare (talk) 16:00, 13 November 2008 (UTC)

I'm not sure what "physically real" is intended to mean here. Centrifugal force is a "fictitious force", in that it only comes up in rotating reference frames as a way to "pretend" that it's a normal reference frame. The "r" coordinate is the 1D coordinate of a frame rotating with a planet, which is why r-double-dot is related to a centrifugal force term, even though there's no such force on the planet. Dicklyon (talk) 16:19, 13 November 2008 (UTC)

My meaning of "physically real" is that for the rotating observer the centrifugal force is placed on the force side of Newton's law of motion and treated like a real force. That means it behaves like a vector, adds vectorially to other forces, and should the rotating observer switch origins or orientation of his coordinate system, the centrifugal force transforms like a vector. Brews ohare (talk) 16:22, 13 November 2008 (UTC)

OK, I agree that with that definition, the centrifugal force due to frame rotation is "physically real"; I still think "fictitious" is a more informative descriptor of it, and more common in the literature. Dicklyon (talk) 17:50, 13 November 2008 (UTC)

Hi Dick: Of course your are right about that. I didn't intend to introduce a new descriptor. My objective originally was to discredit the referral to $r \dot \theta ^2$ (or $\boldsymbol {\omega \times}\left(\boldsymbol{\omega \times r }\right)$ with $\boldsymbol \omega = \dot \theta \boldsymbol \hat k$ ) as a "force" because it has incorrect transformation properties when the origin of coordinates is shifted. The value of $\dot \theta$ changes with the origin of coordinates, so an observer sees a different "force" at every moment if they walk across their rotating reference frame.. The standard force $\boldsymbol {\Omega \times}\left(\boldsymbol{\Omega \times r }\right)$ transforms properly because Ω and r really are vectors. I moved this discussion to Change of origin. Brews ohare (talk) 18:10, 13 November 2008 (UTC)

Archiving about a megabyte

I've archived over 900K of what I claim is largely pointless drivel mostly two people that are treating the wikipedia talk page as a chat page; there's another 100+k that is less than a month old.

Over a megabyte...- (User) Wolfkeeper (Talk) 04:31, 13 November 2008 (UTC)

Deleting more chat here. This is not a forum for discussing centrifugal force, and unreferenced chat is just that. If people want to talk about information they want to add from reliable and verifiable sources, great. That's what this page is for. dougweller (talk) 10:39, 13 November 2008 (UTC)

Dougweller, you obviously haven't read the contents of what you deleted. It was exactly to do with improving the article. It was all about reducing the topic of centrifugal force to one single article. The discussion was about whether there was only one universal centrifugal force or whether there were two or three centrifugal forces. At the moment, there are too many forks. Regarding the note that you left on my talk page, did you leave a similar note to everybody else involved? David Tombe (talk) 10:47, 13 November 2008 (UTC)

This section is about archiving, it is not about forks, how many forces, etc. (although some spaces have made it a subjection, I'll change that). I'll warn them if I think there is a problem. In any case, if you want to argue for 1, 2 or 3 forces, you need sources, not just assertions. Good, mainstream sources. dougweller (talk) 10:57, 13 November 2008 (UTC)

Well I'll be only too glad to wait for these sources to be produced, saying that there is more than one kind of centrifugal force. Can you please meanwhile delete the forks and warn them that they will need good mainstream sources which state that there is more than one kind of centrifugal force? David Tombe (talk) 11:03, 13 November 2008 (UTC)

What bit of 'this section is about archiving, it is not about forks" etc. is giving you a problem? Anything else directly related to the article should be in another section. dougweller (talk) 11:50, 13 November 2008 (UTC)

I thought you were talking about the whole page originally. David Tombe (talk) 12:01, 13 November 2008 (UTC)

Re-unification of the article

Are there any good reliable sources which say that there is more than one kind of centrifugal force? If not, and I don't believe that there are any, I suggest that the forked articles Reactive centrifugal force and 'Centrifugal force in polar coordinates' should be merged into one single article on centrifugal force. David Tombe (talk) 12:04, 13 November 2008 (UTC)

Reactive centrifugal force is just the other end of centripetal force. As your equation shows, it is not the same as centrifugal force, which is what this article describes. I don't know of any other kind; is there another article we need to deal with? Dicklyon (talk) 15:58, 13 November 2008 (UTC)

A quick search gave this reference, Introducing motion in a circle, John Roche, Phys. Educ. 36 No 5 (September 2001) 399-405 [2]

In it Roche states (on page 402):

"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."

Paraphrasing the rest of the section - the first is the fictitious force that arises in rotating reference frames, the second is the reactive centrifugal force (though he calls it an inertial centrifugal force). I'm pretty sure I've also seen this kind of distinction made in a physics dictionary/encyclopedia. --FyzixFighter (talk) 17:03, 13 November 2008 (UTC)

Three citations are provided in the article Reactive centrifugal force. Brews ohare (talk) 17:50, 13 November 2008 (UTC)

Good, we have articles on the physics and engineering centrifugal forces, and the other interpretations are "false" according to all reliable sources we have seen. Goldstein uses a rotating frame when he writes an equation in r, so his comes under the physics interpretation, even if he wasn't explicit enough about saying so that he confused David. Dicklyon (talk) 17:53, 13 November 2008 (UTC)

Dick, you have just said that Goldstein uses a rotating frame, when he doesn't. You have then said that he wasn't explicit. Too right he wasn't explicit. Your statement that Goldstein uses rotating frames is absolutely untrue. Then you have concluded that Goldstein's lack of explicitness has confused me. Dick, you are the one that is totally confused. You haven't adopted a consistent position since you entered this debate. And FyzixFighter has kindly provided us with a physics journal article as evidence of 'reactive centrifugal force' even though it calls it 'inertial centrifugal force'. I suppose he wasn't being explicit either. And because that author claims that there were a cluster of false interpretations in the literature, Dick Lyon takes that author's opinion to trump all those other authors and further concludes that all reliable sources therefore claim that all other sources are false. No wonder there will never be a reasonable article written here. On explicitness, not one of the three citations on the Reactive centrifugal force article are in any way explicit that there is any such distinct concept. David Tombe (talk) 18:53, 13 November 2008 (UTC)

David, please don't twist what I said. I didn't suggest that that author trumps others; rather, that he is consistent with all others that we have examined here, including Goldstein. In Goldstein, the direction along which he measures r is rotating with the planet; I don't know how else it can be interpreted, but if you have other sources that mention an interpretation, we could examine them. Dicklyon (talk) 19:07, 13 November 2008 (UTC)

David: You say "not one of the three citations on the Reactive centrifugal force article are in any way explicit that there is any such distinct concept."

Mook says: "What is sometimes called a "centrifugal force" is a reflection of the force you are exerting on the ball to keep it in a circular path. Similarly the Sun will feel such a reactive, centrifugal force from each of the planets that it holds in orbit.."
Signell says: "centrifugal force: the reactive force to the centripetal force, to which it is equal and opposite."
Mohanty says: "The centripetal acceleration of magnitude V²/r acts radially inward. Note that the reactive centrifugal force on the [control volume] acts outward."

The underlines are mine. I'd say these authors clearly refer to a reactive centrifugal force. Did you actually look at these references, or simply make an off-the-cuff denial? Brews ohare (talk) 19:23, 13 November 2008 (UTC)

David, if you read the journal article, you would see that what Roche calls the inertial centrifugal force is the same thing that others call the reactive centrifugal force. Also, as for the 1D problem, there are several sources that are explicit that this equation describes the motion in a corotating frame - see Professor Tatum's Celestial Mechanics course notes at the University of Victoria (bottom of the 1st page, top of the 2nd page), also Motion in a central-force field, J.S.S. Whiting, Phys. Educ. 18 No 6 (November 1983) 256-257. So while Goldstein might not be explicit in the 1950 edition, others are explicit. --FyzixFighter (talk) 19:57, 13 November 2008 (UTC)

FyzixFighter, I'm going out of this debate now, but you are welcome to e-mail me through the mechanism. It's best discussed behind the scenes. I'll just respond quickly to your comments. In my way of looking at it, the effect in question would simply be centrifugal force. Anyway, in case you don't want to bother with e-mail, you remember the argument about the force between bar magnets? You said it was F =qvXB. The dilemma was, how do we get a potential energy from a Coriolis type term that clearly has no potential energy? Goldstein, as you can see does it using Lagrangian and obtains grad(A.v). But if you check out Maxwell, that is actually centrifugal force and it exists in addition to F =qvXB. You were trying to explain an effect using the wrong term because the right term has been lost. For attraction it is of course Gauss's law which is still one of the Lorentz force terms. Finally, try looking at that radial equation without getting bogged down with terminologies. Then ask yourself 'can a circular motion exist on centripetal force alone?'. I'll not be replying again on this page again for the foreseeable future. David Tombe (talk) 20:11, 13 November 2008 (UTC)

FyzixFighter: I added a link to Tatum's notes in the article. The other two references are not available to the general reader without a license (or $50) so I didn't include them. Brews ohare (talk) 20:27, 13 November 2008 (UTC)

Why does Wikipedia insist on using Ω for angular velocity?

Several articles in Wikipedia use the uppercase omega symbol (Ω) for angular velocity. Every physics book I have ever read uses lowercase omega (ω). Kinematic variables are always written in lowercase; for example: displacement (s not S), velocity (v not V), and acceleration (a not A). The same is true for rotational kinematics: angle (θ not Θ), angular velocity (ω not Ω), and angular acceleration (α not Α).

What is the origin of this anomalous use of Ω? —Preceding unsigned comment added by 74.64.99.52 (talk) 17:30, 16 November 2008 (UTC)

I raised the same question recently. It seems that the lower case is used for angular velocity of particles whereas the upper case is used for the reference frames contained within rotating rigid bodies. From what I can make out, the topic of 'rotating frames of reference' evolved from rigid body rotation, but I couldn't be absolutely sure about that. At any rate, the use of the higher case omega seems to represent an emphasis on the idea that the angular velocity belongs to the frame of reference and not to the particle. This was the issue in question in the recent debate. Personally, I would prefer to use the lower case as I see the angular velocity as belonging to the object. David Tombe (talk) 19:51, 16 November 2008 (UTC)

David's description of use of upper case Ω is accurate. Take a look at the cited references, for example, Taylor, Landau & Lifshitz, and Arnol'd. However, this choice is not universal. Brews ohare (talk) 20:22, 16 November 2008 (UTC)

In my experience the upper case is used for vector angular rotations, where the vector points along the rotation axis and the length is the rotation speed omega. It's done like that to distinguish it from the scalar.- (User) Wolfkeeper (Talk) 20:26, 16 November 2008 (UTC)