Talk:Centrifugal force/Archive 8

Particles vs. frames
In discussion of a particle moving in a circular orbit, one can identify the centripetal and "tangential" forces. It then seems to be no problem to switch hats and talk about the fictitious centrifugal and Euler forces. But what underlies this switch is a change of frame of reference from the inertial frame where we started, where centripetal and "tangential" forces make sense, to a rotating frame of reference where the particle appears motionless and fictitious centrifugal and Euler forces have to be brought into play. That switch is unconscious, but it shouldn't be unconscious in an article on centrifugal force.

And what is the parallel in the case of an elliptical orbit? Suppose we identify the forces normal to the trajectory as centripetal forces and those parallel to the trajectory as "tangential" forces. What switch of hats is needed now to make the switch to fictitious centrifugal and Euler forces? As far as I can see, one has to make a switch to a continuously changing frame of reference, whose origin at time t is the center of curvature of the path at time t and whose rate of rotation is the angular rate of motion of the particle at time t. The only way that makes sense is to sit on the particle, but not with a local polar coordinate system, but one that has unit vectors normal to the trajectory and parallel to it. So, as pilot in an airplane, the fictitious forces are useful, but they are not related to polar coordinates. Brews ohare (talk) 12:54, 30 May 2008 (UTC)

I have added this discussion to the article here. Brews ohare (talk) 13:36, 30 May 2008 (UTC)


 * Euler forces are tangential forces causing α = dω/dt? These don't go away in a constantly rotating frame-- they stay the same, since the acceleration of the particle is the same in either frame (just as in the linear case where acceleration is the same if you switch to a different inertial frame at a different linear velocity). Euler forces only appear as ficticious forces if you're in a frame with accelerated rotation rate where α = non-zero. But that's not the setup we carefully made for the centrifugal and Coriolis forces where ω is constant and dω/dt = α = 0. So in a way, the Euler forces are a different animal, and we really have to decide if we're going to stay fixed to a coordinate system or fixed on a rotating object which may not be rotating with a fixed rate. The planetary case is interesting: the Euler force is zero there, NOT because of the fact that the revolution rate doesn't change (as it states falsely in the fictious force Wiki)-- because the revolution rate of a planet DOES change for eliptical orbits! Instead, Mr. Tombe's "law of areal velocity" per Kepler kicks in (a consequence of angular momentum preservation) which causes r to decrease as ω increases, so the product stays constant and thus the Euler term stays zero even IF dω/dt is not zero: this is perhaps what confused Mr. Tombe (he as thinking about Euler forces and calling them Coriolis forces; most of what he said about one was true for the other!). Euler force = 0 even with variable rotation, and this happens any time the force is purely central, as with planets and no drag, or (say) when a skater pulls in her arms, etc. All again because of conservation of angular momentum in a system with no external angular momentum-changing influences. [addendum-- the above is wrong, drat. Euler force is present in central force systems, but it is countered by an extra tangential Coriolis force, so that torque is zero and angular momentum does not change, even though ω does. See below.] S  B Harris 21:01, 30 May 2008 (UTC)
 * Hi Steven: I'm not sure what your point is in this comment.
 * 1) Euler forces - agreed that they relate to angular acceleration. The Euler force has showed up in this article on centrifugal force just for completeness (that is, to include all the fictitious forces related to rotation). The cases where it is zero are duly noted, if I remember rightly. I don't think inclusion of the Euler force is bad thing. Do you agree?
 * Agree if we make it clear that this one is defined differently, and appears only in rotationally accelerated frames, by which we mean the coordinate system itself is rotating AND the rate it is rotating is changing. This is in contrast to the centrifugal and Coriolis forces, which depend only on a constantly-rotating frame (or do they? Are the equations still correct at any t if ω(t) is a function of time? If we have a dω/dt term, do we merely note that the ω terms are ω(t) terms? The way we define them now discusses only constant ω and I think presumes dω/dt=0, but perhaps there's a more general case not discussed. S  B Harris 04:27, 1 June 2008 (UTC)
 * 2) What IS the Euler term? According to Marsden it cannot be zero if the angular acceleration is nonzero.
 * I don't see where he actually says that, but it may be true. The angular acceleration may be nonzero, but the sum tangential forces (those in the direction orthogonal to spin axis and radius vector) on a planet must sum to zero if the torques on the planet sum to zero, which must in turn be the case when the angular momentum does not change in time (which it does not). I see I was even wrong in what I said above: in the planetary motion case, if we have an elliptical orbit and put our coordinate system on the planet so that dω/dt is non zero, then we do have an Euler force Fe = m(dω/dt) X R. The first term direction is along the spin axis (in the direction of the ω vector), of course, and cross that with R and get a vector in the direction of tangent velocity. An Euler force in this direction is at right angle to any R and MUST produce a torque and dL/dt, unless exactly balanced. All I can see to do that is the tangential component of the Coriolis force, which results from the planetary radius increasing and decreasing. Normally that would produce a Coriolus force in the tangential (azimuthal) direction, and yet a planet, in our system of accelerated rotation, only has one motion, and that's up and down the radius vector between us (at the Sun/primary) and it. So it has a (changing) dr/dt, a (changing) Coriolis force on it, and therefore requires another tangential force to explain why it stays on the radius vector, even though ω changes. And THAT must be the Euler force on the planet in this system-- a force arrisingly ONLY from the planet's changing ω. Very odd. But might make a good teaching example, and again still conflicts with the Fictitious force article which pretends that planetary ω is generally constant (only true for circular orbits, of course). The centripetal and centrifugal terms do not balance for a planet in elliptical orbit, however, since the planet is in motion along the radius, and even accelerated (inward/outward) motion thought its "year". But it goes out and comes back, so there's an interplay of unbalanced radial forces throughout the orbit. The centrifugal force in this case changes as a function of time because dr/dt is not constant. It must outpace gravity/centripital for part of the orbit, then they reverse to bring the planet back in. S  B Harris 04:27, 1 June 2008 (UTC)

Maybe you are using an identification based on some terms from the polar coordinate form for the acceleration? For example:
 * $$\mathbf{a}=\mathbf{u}_{\rho} \left[ \frac {d^2 \rho }{dt^2}-\rho\left( \frac {d \theta} {dt}\right)^2 \right] + \mathbf{u}_{\theta}\left[ 2\frac {d \rho}{dt} \frac {d \theta} {dt}+\rho  \frac {d^2 \theta} {dt^2}\right] \  $$
 * where the uθ term can vanish if the sum of the derivatives is zero? I'd submit that it is a stretching of terminology to call this the Euler force, because uθ is not tangent to the trajectory. Do you agree?
 * Yes. I'm using the standard m(dω/dt) X R definition of Euler force. See above.  S  B Harris 04:27, 1 June 2008 (UTC)
 * 3) My view is that the fictitious forces have to be defined relative to the actual normal to the trajectory and tangent to the trajectory, and are not to be inferred by looking at components in a polar coordinate system, even though that coordinate system is great for doing the inverse square-law problem. That is how I understand the relevance to airplane motion. The inverse square-law problem is only obliquely related to the centripetal, Coriolis, Euler forces. Do you agree? Brews ohare (talk) 22:05, 30 May 2008 (UTC)
 * Well, no, because as discussed above, if you go to an accelerated rotational coord system in a system where angular momentum is constant, as you do with a planet, then an Euler force appears, and because it's in a direction to produce torque, you have to get rid of it! So some discussion of where it goes, or what balances it, is needed. S  B Harris 04:27, 1 June 2008 (UTC)
 * Hi Steven: I'm not understanding you well. Part of the problem is that I don't know what you mean by an Euler force - apparently it isn't what Marsden is talking about. Part of the problem also is that all this discussion should be independent of any example like planetary motion, for example, there is no need for angular momentum to be conserved. It is a kinematic discussion: depends only on the trajectory, not on inverse square law, or Kepler's rules or whatever. Brews ohare (talk) 06:37, 1 June 2008 (UTC)
 * Euler force is another force you get when the rotation rate of your frame of reference varies. Obviously if it does that, everything moves, and you need another force to handle it.- (User) WolfKeeper (Talk) 09:14, 1 June 2008 (UTC)
 * I was a bit confused by Sbharris's example above, I think what he means is that if you put the frame of reference origin at the sun, and then rotate the frame with planet, so then the planet is always along say, the x-axis, then you need the Euler force (and the coriolis) because the frame rotation varies over time (and because the planet moves in and out), respectively.- (User) WolfKeeper (Talk) 09:14, 1 June 2008 (UTC)
 * Yes, exactly. If the planet moves in and out on a radial line, that produces a Coriolus force and you need an Euler force to keep it on the line. In the article examples things experiencing Coriolis forces are kept on the radial line by mechanical means. But for the arms of spinning skaters, and (even more obviously) for planets in non-circular orbits, in their frame of revolution, this isn't the case. S  B Harris 21:02, 1 June 2008 (UTC)
 * But I don't think we need to discuss Euler force that much in the article, other than note it exists and link to it.- (User) WolfKeeper (Talk) 09:14, 1 June 2008 (UTC)

Euler Force
In textbook kinematics the Euler force arises as a fictitious force only in nonuniformly rotating frames. The article cites Marsden, Arnol'd and Taylor on the subject, and I believe the extent of discussion in the article is appropriate as it stands. A link to Euler force is provided, although the Euler-force article could use some work. The tendency for planetary motion to creep into the discussion is alarming, as it seems to hold sway as a paradigm of some kind for fictitious forces, which it is absolutely not. For one thing, planetary motion is a very specific dynamical system, and kinematics is more general. Moreover, the everyday experiences with fictitious force are things like centrifuges, gravitron amusement rides, flying airplanes and cornering cars; which don't have much to do with Kepler's laws. If there are some changes or additions to be proposed for the article, maybe they could be unveiled here for specific comment? Brews ohare (talk) 13:10, 1 June 2008 (UTC)
 * I'm just noting that planetary motion tends to arise in discussion of Euler forces, because it's one interesting case of where rotation rate varies and there's a tendency to pick a frame which keeps up with it. Another would be a skater pulling her arms in, in which case she naturally keeps her reference frame even though its rotation rate varies. In her case, you also have to "explain" the fact that she feels no Coriolis force at all. Only the centrifugal force pulling her arms exactly straight outward, as she pulls them in. And the reason is the same as for the planet-- she doesn't change angular momentum, thus the force she exerts must be exactly central from her perspective. The reason being that even as she spins faster, SHE feels no torques, and indeed there are none (not in any frame, since dL/dt = T = 0)! In her frame, the Coriolis force when she pulls her arms in, is balanced by the Euler force which arises from looking at her arms coming in, as she spins up. On the other hand, if she spins at a constant rate (as the person in our office chair) then the Euler force goes away, and only the Coriolis force of our example is left. Perhaps most of this should go in the Euler force article, but some mention and summary of these odd effects might be placed here. S  B Harris 20:04, 1 June 2008 (UTC)

David Tombe Was correct And Wikipedia editors Are Wrong
I am sure that if Mr Tombe had not been unfairly blocked by Mr SZencz for an imaginary infraction of the rules, he would offer the following reply to Mr SbHarris' allegations, made above. I am sure his reply would be something like this: "I don't see any evidence that Mr. Tombe is confused between the Euler force and the Coriolis force. Kepler's law of areal velocity applies to both of them. It eliminates all the tangential forces." As an observer of this discussion it is apparent to me that MR SZencz harbors a personal and long nurtured hatred for Mr Tombe, and that he frequently blocks Mr Tombe when there is an important point in the discussion that may lead to an agreement or any kind of progress. Mr Tombe is blocked to prevent this from actually happening. I think Mr Tombe may actually have a point regarding the deceitful intentions of some wikipedia editors who persist in avoiding justifying their inadaquate opinions. They do this by blocking Mr Tombe so their errors will not be exposed. Now regarding the facts. In a recent discussion Mr Tombe took a position roughly equivalent to the following: "The only sense in which the term centrifugal force can be used with propriety as a force, is obtained by the consideration of relative equilibrium, in which case, if the same centripetal force acted on the body, the centrifugal force would keep it in equilibrium, if the body were at rest, as it would appear to be to an observer moving with it." This answers the debate here in favor of Mr Tombe. It is clear that the same result is obtained whether the fame is in motion or not. This quotation is from Newton's Principia which the editors have apparently not read. Hence the above quotation from an authority settles the matter and the wikipedia editors have given the wrong answer in this article.72.64.41.20 (talk) 17:11, 31 May 2008 (UTC)

This has been deleted several times and that is vandalism. Wikipedia seems to support valdalism when it is directed against editors who insit on being heard. You need to redress your harmful actions toward Mr Tombe, since as this quotation shows, his statements are correct.71.251.190.231 (talk) 23:25, 3 June 2008 (UTC)
 * Who's right and who's wrong overall, I cannot say. I do know that Mr. Tombe is dead wrong in not regarding circular motion as an acceleration which requires a force. It is, and does. As for planets, absent tidal effects they have no torques on them, and this only means that in all frames in which they are viewed, all tangential forces must sum to zero, and only radial forces must be left. That's clear. For the skater, because angular momentum doesn't change, that doesn't quite mean that there are no torques-- only that torques sum out to zero, even thought she spins faster. A physicist friend of mine points out that if a skater were to draw in two weights on strings, they'd end up coming in and rotating faster than she, until they wound up in a spiral orbits, and hit her! Imparting a tangential impact which would THEN cause her to spin-up. The fact that she can do this with her arms, only means that she exerts a backwards torque on the arms to keep them from going forward, while they cause forward torque on her, causing her spinup, and the difference here actually does obey Newton's third law; so it's not quite a matter of tangential fictious forces balancing exactly, as is the case for planets where all unbalanced forces are required to be central (in all frames). In any case, Mr. Tomba, get used to the fact that linearly accelerated frames have one inertial force, rotationally moving frames have two forces (centrifugal and Coriolis) and rotationally accelerated frames have those plus Euler. The artificial circle example is correct, and you should get your mind around it. S  B Harris 23:56, 3 June 2008 (UTC)


 * Sir, Apparently you do not read the discussions, and did not read the above, that answers the issue. As I recall Mr Tombe has attempted to explain this to wikipedia editors but they are so biased against him that they insist on misinterpreting and misrepresenting his views. Then when he attempts to make clear his position, they block him to insure that the misunderstandings continue. There is no tangential force, only two equal and opposite forces in circular motion. One is the centrifugal and the other the centripetal force. Historically the centrifugal force was known first and that knowledge served to enable the calculation of the centripetal force. I suggest you become more objective and actually read the discussions. Carefully read the Newton quote, which exactly explains the physics. Apparently you are interpreting things incorrectly along with other Wikipedia editors.72.64.51.139 (talk) 00:32, 4 June 2008 (UTC)


 * If you are Mr. Tombe, I remind you that you were blocked for WP:CIVIL, and a great deal of the above is a continuation of this dispute via IP, with the same assumptions of bad faith and adding a conspiracy. Mr. Tombe's/you block may be extended if you insist on characterizing editors in this manner.  Please note that I do not judge the subject at hand.  I suggest a time out from editing, either as an IP or as a named account.  Physics will carry on.    Acroterion  (talk)  00:52, 4 June 2008 (UTC)
 * And of course there are cases of circular motion with tangential forces. Types of circular motion where there is angular acceleration accompanied by change in angular momentum, require torques, and thus tangential forces. An example would be a can rolling down a hill at faster and faster velocities. Or a drag-racer tire as it takes off. Or spinning up a gyroscope. Planets are special cases with no torques unless there are tidal forces slowing spins. But of course there are often tides. Our own Moon experiences tidal torque and thus spirals outward. Its angular momentum increases, as the Earth's decreases to result in sum-conservation (resulting in a slowly lengthening day). S  B Harris 01:45, 4 June 2008 (UTC)
 * It seems to me that Tombe loses the right to express opinions when he gets suspended. The above is specifically attempting to represent Mr. Tombes views, then by definition he's either Tombe's meatpuppet or a sockpuppet and, either way, should be suspended also.- (User) WolfKeeper (Talk) 03:05, 4 June 2008 (UTC)
 * Sock yes, meat no. We don't have any rules on meats actually, except that they are frowned on. But there's not much you can do about person B who shows up to agree with person A about a matter of nonWikiality (non-policy), even if recruited. It could have been one more physicist YOU OR I recruited from the department, if you knew he was interested in rotational kinematics. Is he only a meatpuppet if he disagrees with you? The whole idea of "meatpuppet" is actually pernicious, as it ascribes no free will or judgement to person B. That's sort of a pinacle of non-AGF-- ascribing mental slavery to somebody just because you don't like the side they've taken. Unless they're a Hillary Clinton democrat, I suppose, in which case we could maybe look the other way, because all those folks are clearly cultist brainwashed zombie pod-people with puppetmasters and brain-slugs attached.  S  B Harris 08:31, 4 June 2008 (UTC)
 * Well, there is Sock: "A new user who engages in the same behavior as another user in the same context, and who appears to be editing Wikipedia solely for that purpose, shall be subject to the remedies applied to the user whose behavior they are joining." - (User) WolfKeeper (Talk) 09:24, 4 June 2008 (UTC)
 * I mean is this Tombe behaviour or not: "I think Mr Tombe may actually have a point regarding the deceitful intentions of some wikipedia editors who persist in avoiding justifying their inadaquate opinions."?? IMO that's Tombe, or somebody indistinguishable from Tombe.- (User) WolfKeeper (Talk) 09:27, 4 June 2008 (UTC)

How to handle the above anon
''To those who are engaged in discussion with, and about. the anonymous user above:'' User:Acroterion was right to remove this section, and others would have been well advised to support him in that. Our talk page policy allows removal of text that does not contribute to improving the article, and a rant like that certainly qualifies. By debating the physics issues, you make that more difficult. By arguing about blocking the anon, you ignore the fact that it's a non-static IP (Verizon, in fact) and hence difficult to block effectively. In my experience, either ignoring or removing the comments of users whose behavior becomes inappropriate past a certain point is the most time-efficient and effective way of dealing with them. It pains me to see the different responses of the various well-meaning editors here working against each other. Please think, before you make any edits in regard to Mr. Tombe, what you expect to achieve, and whether your edit will really achieve it. -- SCZenz (talk) 12:52, 4 June 2008 (UTC)

Definition of acceleration
I believe that D. Tombe's arguments all fail because they do not admit to the simple definition of acceleration as (see the classic reference by Whittaker §14, p. 14):
 * $$\boldsymbol{a} (t) = \frac{d^2}{dt^2} \boldsymbol{r} (t) \, $$

where r ( t ) locates the moving object relative to a selected point of origin in an inertial reference frame. Given this definition, all the derivations in the various articles centripetal force, centrifugal force, fictitious force, reactive centrifugal force follow by direct, unarguable time differentiation of the trajectory r ( t ) with absolutely zero need for long-winded verbiage. In particular, the acceleration requires only the specification of a path in space and the time at which each position is occupied on the path, r ( t ). With the acceleration so determined, the real and the fictitious forces related to the trajectory r ( t ) are fully determined, with no necessity to delve into the way these forces might be made to arise. Brews ohare (talk) 22:14, 4 June 2008 (UTC)

Kinematics vs. kinetics
As pointed out above, for the discussion in the articles centripetal force, centrifugal force, fictitious force, reactive centrifugal force all that is needed is:
 * $$\boldsymbol{a} (t) = \frac{d^2}{dt^2} \boldsymbol{r} (t) \ . $$

That is to say, these articles deal with kinematics, not kinetics. The origin of the required forces is not an issue. Thus, the same kinematics applies to trajectories r ( t ) in particle accelerators, satellites, and motorcycles, provided only that the same trajectory r ( t ) is traversed in the same manner.

All arguments about where the forces come from that compel obedience to the trajectory r ( t ) have nothing to do with kinematics, but are kinetic in origin. The books cited in the articles kinetics, kinematics make the distinction crystal clear. See, for example, Whittaker: Chapter 1 on kinematics:

D. Tombe has diverted discussion from the limited, uncontroversial topic of kinematics, to wander about in the more complex system-dependent arena of kinetics, leading to issues about specific force arrangements. Forces providing the accelerations dictated by a trajectory r ( t ) differ greatly between planets, particle accelerators and skateboards. That variety found in kinetics is unlike the kinematics of r ( t ), which are system independent. Brews ohare (talk) 22:14, 4 June 2008 (UTC)

Another example
I've added another centrifugal-Coriolis force example at Fictitious_force.

BTW, the animation referred to at mensch.org School of Meteorology site at U of Oklahoma shows the Coriolis force pointing inward for the example of a zero force motion in the inertial system. Brews ohare (talk) 21:58, 5 June 2008 (UTC)

Tangential Forces
The tangential forces (Coriolis and Euler) can be applied to a system, but they don't occur naturally apart from perhaps in electromagnetism which is off-topic, but in the absence of vorticity, they do not occur naturally apart from when the two mutually cancel as in a Keplerian orbit.


 * Trivially wrong.- (User) WolfKeeper (Talk) 19:36, 6 June 2008 (UTC)


 * No Wolfkeeper, it's you that is wrong. David Tombe (talk) 07:06, 7 June 2008 (UTC)

During the last week there was quite a bit of discussion going on about the Euler force and the Coriolis force along with false allegations that I was confused between the two. I wasn't able to reply at the time.

We can apply a Coriolis force or an Euler force to a system if we like. The Euler force will increase the angular acceleration and the Coriolis force will change the direction of a constrained co-rotating radial motion.

In a rotating frame of reference with non-uniform angular acceleration there will be a fictitious Euler force acting tangentially.

In a Keplerian orbit, there will be zero tangential acceleration, although it is possible to see that this zero is the sum of an ongoing equal and opposite Euler force and Coriolis force.

Having said all this, tangential forces are not highly relevant to this article. They could be mentioned in passing, but the article is about a radial force. The centrifugal force is an outward radial force.

More attempts should be made by the editors here to concentrate on differential equations in the 'radial distance' variable.

They then might begin to get a feel for what centrifugal force is all about. David Tombe (talk) 08:29, 6 June 2008 (UTC)

Reply to Brews ohare
Brews, I am fully aware of the difference between kinematics and kinetics. This article doesn't need to involve that difference.

You quoted above an expression for acceleration. That expression is correct. I am not disagreeing with it. But it tells us absolutely nothing that would enable us to solve a motion problem.

To solve a problem in motion, we need an input force. If it only kinematics, we still need an input acceleration.

We always need some kinds of constraints or known accelerations before we can determine a trajectory.

The solution to your general acceleration equation above is "Anything".David Tombe (talk) 08:38, 6 June 2008 (UTC)
 * Yes, the kinematic results apply to any system with the prescribed trajectory r ( t ). But that is all that is needed here. This discussion is about kinematics. All the other stuff, however interesting, is off topic. The time has come David, for less talk and more specifics. Take the rotating identical spheres example, say, pull it all apart and focusing only on this example, without dragging in Kepler's laws, gravity and other miscellaneous irrelevancies, write up the example the way you think it should go. With a particular case in front of us, it will be more likely that some concrete discussion that goes somewhere can occur. Although we have a great tea party going on here, it's not adding to Wikipedia following this endless roundabout. Brews ohare (talk) 14:08, 6 June 2008 (UTC)

Brews, the rotating identical spheres makes a good action-reaction pair example. We'll begin with the general radial equation as it applies to sphere A,

Applied centripetal force + induced centrifugal force = m$$d^2r/dt^2$$

where r is the radius. Since the string joining the spheres is not changing in length, then m$$d^2r/dt^2$$ will be equal to zero and so the centrifugal force outwards on sphere A will be equal to the centripetal force inwards on sphere A, which is given by tension T. Hence T = mv^2/r which equals both the centrifugal force and the centripetal force.
 * David:
 * That is exactly right from the viewpoint of the ball: according to the ball, it is at rest and so no forces are acting upon it. In the inertial observers' picture, they see the ball in circular motion and so subject to an unopposed centripetal force that overcomes the ball's inertia, the radially inward mv^2/r. They see it as being provided by the string tension T, as you state. The ball reconciles its belief in zero net force by invoking the centrifugal force that exactly balances the string tension. So I'd say the ball's report is:
 * "Hey you inertial guys, I'm at rest here. But you guys say I have to provide a centripetal force to stay on my path. I say, baloney: I'm going in a straight line here, good old law of inertia, you know. What you inertial guy's don't get is that all the help I'm getting from the string to stay on a straight line is just to counter this pesky centrifugal force. I don't get where it comes from, it's just a damn nuisance that is always around, causing me to ask for help just to stay at rest."
 * So far, I don't see any departure between you and the article, except possibly the introduction of the frame of reference of the ball itself, which is a reference frame equivalent to that of the rotating observers.Brews ohare (talk) 19:48, 6 June 2008 (UTC)

Every force acting on sphere A will have an equal and opposite force acting on sphere B. Hence the centripetal force (-T) acting on sphere B could be considered as a reactive centrifugal force from the perspective of sphere A.


 * David
 * I'll go along with that. So does the article Brews ohare (talk) 19:48, 6 June 2008 (UTC)

This example is OK, but because it is circular, it masks the general picture. If you were to choose an elliptical example, that would eliminate some of the equalities and also eliminate any confusion that might ensue from those equalities.

That's why I favour a more complicated example such as a Keplerian orbit.David Tombe (talk) 16:23, 6 June 2008 (UTC)


 * David:
 * Simplest cases first. So far as I can see, you have raised no objections to the way the rotating spheres problem is discussed in the article. Agreement reigns serene. Want to try the dropping ball? Or, maybe Crossing a carousel? Whichever shows the least amount of contention. Brews ohare (talk) 20:44, 6 June 2008 (UTC)

Brews, I may well be in agreement with that part of the article. But I don't concern myself with looking at any of these rotational problems from the perspective of Cartesian coordinates or Newton's law of inertia. That may well be one legitimate way of looking at these problems in day to day terrestial situations, but it is not the most general way of looking at them on the cosmological scale or the microscopic scale.

The problem that I am finding with the other editors is that they are incapable of considering a problem entirely in terms of polar coordinates. As soon as the centrifugal force shines out at them too strongly they immediately dive for cover behind Cartesian coordinates.

As far as I am concerned, we only need to consider the radial direction when discussing equations that involve centrifugal force and centripetal force. And just as gravity or tenson in a string are radial centripetal forces, so also is centrifugal force a radial force. We can't get rid of one without getting rid of the other.

Reply to Brews ohare Part II
The other argument I have is when you then consider the two identical spheres when they are at rest and not rotating. In that case, there is no induced centrifugal force and hence no tension in the string. Yet the article talks total rubbish about a net inward Coriolis force. It is absolute rubbish. David Tombe (talk) 07:18, 7 June 2008 (UTC)
 * David:
 * Great, let's deal with this problem. No doubt we agree that the string is under zero tension according to all observers. We agree that the situation for the inertial observer is that the spheres are at rest, and Newton's laws state there is no force on the balls or the string. However, we agree that to the rotating observer, the two spheres appear to be rotating about the center of the string. So please pick up from there and explain how the rotating observer handles Newton's laws for what looks like circular motion. Please pick the article apart and propose an alternative discussion for this case. Brews ohare (talk) 12:55, 7 June 2008 (UTC)


 * David:
 * I'll intersperse remarks. Brews ohare (talk) 12:40, 8 June 2008 (UTC)

Brews, The way I see it is, in a rotating frame of reference, a circular motion artifact is imposed on top of the already existing motion, and this artifact is not catered for by the transformation equations at all.
 * David:
 * Not clear to me what you mean. In the spheres at rest problem, there is no motion, but a rotating observer. The "transformation equations" must refer to the "fictitious force" equations, as there are no other equations in this example. The only purpose of these equations is "to cater for" the "circular motion artifact". What I need here is some detail on how you would explain the rotating observer's observation that the spheres rotate. What math does the rotating observer bring to the table that predict the spheres' motion in his frame? Brews ohare (talk) 12:40, 8 June 2008 (UTC)

I'll side track for a moment to your other example in which an object in the rest frame follows a straight line outwards from the axis of rotation. As viewed from the rotating frame, it spirals outwards.
 * David
 * I believe you have misread this example. It is in the rotating frame that a straight line is followed. So it appears that this example is exactly the "marble in a radial groove" with the marble constrained to travel at constant speed in the groove. Brews ohare (talk) 12:40, 8 June 2008 (UTC)

You might think that we are witnessing Coriolis force but we aren't. We are looking at a circular motion superimposed on top of a straight line motion. That is not Coriolis force. Coriolis force is a force that changes the direction but not the speed of a moving object.
 * David
 * These remarks will change when you re-read the example.

The maths of the rotating reference frame transformations and the maths of polar coordinates is identical. The only difference is that in the former case it is set up to specifically deal with objects in a rotating frame of reference that are exactly co-rotating. In other words, the centrifugal force term applies to exactly co-rotating objects, and the Coriolis force term applies to objects that are constrained to a co-rotating radial motion.
 * David
 * I'd like to keep the conversation focussed on the two examples at hand. That is already confusing enough. Brews ohare (talk) 12:40, 8 June 2008 (UTC)

None of the maths associated with centrifugal or Coriolis force applies to stationary objects as viewed from a rotating frame, or inded to objects that are moving but which have no physical connection with the rotating frame. In either of these scenarios, the rotating frame serves only to impose a circular motion artifact on top of the already existing motion.

The marble on the radial groove on the rotating turntable is the best and most simple example for illustrating both induced centrifugal force and applied Coriolis force, both active and reactive.
 * David:
 * Perhaps this will become clearer to me as you approach the carousel problem more precisely. Brews ohare (talk) 12:40, 8 June 2008 (UTC)

I should have finally added that the polar coordinate derivation shows beyond doubt that Coriolis force is a tangential force. As such, it can never act in the radial dircetion. The idea that the artifact circular motion has a net inward radial force supplied by the Coriolis force is a double nonsense. David Tombe (talk) 06:03, 8 June 2008 (UTC)
 * David:
 * Go ahead and analyze carousel in the manner you find appropriate. Please use the example discussed in the article with constant radial speed so there is a clear context for the discussion. Pick it apart. Explain it your way, but so it's simple to follow, please. For clarity, terms like "circular motion artifact" and other terminology with a specific technical meaning in the discussion should be defined. Point out where the math in the article disagrees with yours, or is interpreted differently. Brews ohare (talk) 12:40, 8 June 2008 (UTC)

Brews, you are correct that I misread the carousel example. I have now read it correctly and I agree with you that the walker does indeed experience a tangential Coriolis force on his feet. If it doesn't trip him up, then it will indeed as you say be the same as the marble in the groove to all intents and purposes.

Now I suspect that you will want to know my views on the inertial observers view on the walker crossing the carousel. The inertial observer will see a spiral as you correctly say. The Coriolis force enables the man to walk in a radial straight line relative to the carousel. If there were no friction, he would go in a straight line relative to the inertial frame.

But it is not the Coriolis force that is causing the circular motion component to the walker's path because he would have that component even if he were stationary on the carousel. The Coriolis force is an extra frictional force on top of the friction that causes the co-rotatin and it restrains him in a co-rotating radial path. The friction on the carousel does two jobs. It keeps an object in a state of co-rotation. Additionally, it will cause a Coriolis force to act tangentially on a person who attempts to walk radially. David Tombe (talk) 16:01, 8 June 2008 (UTC)
 * David:
 * So the carousel is OK? We agree on that one? Brews ohare (talk) 19:18, 8 June 2008 (UTC)

Well Brews, I assumed that we agreed on it. But your colleagues below, Wolfkeeper, PhySusie, and Itub all seem to be saying that the applied force that keeps the object in the co-rotating radial line is not a Coriolis force. David Tombe (talk) 06:43, 9 June 2008 (UTC)

Reply to Brews ohare Part III
So where does that leave our disagreement? It's back to the stationary identical spheres again. As far as I am concerned, there is nothing happening there. The artifact circle imposed on it from the perspective of a rotating observer is not described by the maths of the transformation equations. There is neither Coriolis force nor centrifugal force involved. It is a simple case of superimposition.David Tombe (talk) 16:01, 8 June 2008 (UTC)
 * David:
 * In my view the same procedure that is used for the carousel also is used in the Coriolis force example. I have done a line by line comparison, and see no difference in method. Please go through this analogy yourself and point out where you see differences in method or interpretation.


 * Here are the steps in outline as I see them. Each step results in an equation for each of the two observers (inertial and rotating) for the particular problem (whichever of the two problems one chooses)


 * For each observer:
 * Step 1:
 * Describe trajectory r  (t); For the stationary spheres, $$\mathbf{r_B}(t) = \mathbf{u_R} R $$ for the rotating frame, where uR points to the sphere. For the inertial observer $$\mathbf{r_A}(t) = \mathbf{r_A}(t = 0)\ .$$


 * Step 2
 * Find acceleration $$\frac {d^2}{dt^2}\mathbf{r}(t)\ .$$ For the stationary spheres, $$\mathbf{a_B}(t) = -\omega^2 R\mathbf{u_R} $$ for the rotating frame, where uR points to the sphere. For the inertial observer $$\mathbf{a_A}(t) = 0\ .$$


 * Step 3:
 * Multiply by m to get forces.


 * Step 4:
 * Use equivalence principle to say the forces must be the same for both observers. For the stationary spheres, $$m\mathbf{a_B}(t) = -m\omega^2 R\mathbf{u_R} $$ for the rotating frame, where uR points to the sphere, and the string tension is zero. Therefore, we must conjure up a fictitious force that can provide $$m\mathbf{a_B}(t) = -m\omega^2 R\mathbf{u_R} \ . $$ For the inertial observer $$m\mathbf{a_A}(t) = 0\ ,$$ and zero tension is expected.


 * Step 5:
 * Add fictitious forces to rotating frame so the forces in both frames are the same. We must add a fictitious force $$m\mathbf{a_B}(t) = -m\omega^2 R\mathbf{u_R} \ $$ in the rotating frame. With this force "naturally" present, the force on the sphere is looked after, and the string can have zero tension.


 * Generalization to arbitrary observations in the rotating frame.
 * This single experience with the stationary sphere in the rotating frame is generalized to every situation using the general formula :$$

\mathbf{F}_{\mathrm{fict}} = - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} - m \boldsymbol\Omega  \times (\boldsymbol\Omega \times \mathbf{x}_B ) $$&ensp;$$\ - m \frac{d \boldsymbol\Omega  }{dt} \times \mathbf{x}_B \. $$. That is, from numerous different observations in the rotating frame with constant rate of rotation (among others, the observations on rotating identical spheres at rest in the rotating frame, where centrifugal force shows up, as treated just before this example), there are two forces at work: the centrifugal force, which is not helping out here because it points outward, and the Coriolis force. The Coriolis force is found (from general experience in the rotating frame) to be $$ \mathbf{F_C} = - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} \. $$ To evaluate this formula we need the velocity of the sphere in rotating frame, which is $$\mathbf{v_B}(t) = \mathbf{u_{\theta}}\omega R \, $$ with uθ pointing in the apparent direction of movement of the sphere. Plugging in, we find the Coriolis force is $$\mathbf{F_C} = -2m \omega^2 R \mathbf{u_R} \ ,$$ just what is needed to overcome the outward centrifugal force and provide in addition the needed fictitious force found above, namely $$m\mathbf{a_B}(t) = -m\omega^2 R\mathbf{u_R} \ $$, which is the centripetal force for circular motion. With this force present, the string can have zero tension, as observed, even though the sphere executes circular motion.Brews ohare (talk) 00:26, 9 June 2008 (UTC)


 * Following this recipe for either problem leads to the results described in the respective articles on Coriolis force or carousel. Brews ohare (talk) 20:25, 8 June 2008 (UTC)

Need for observation from a rotating framework
Brews, while I agree with you in the situations in which actual rotation is occuring and actual forces are occurring, I cannot agree with you on your extrapolation of this maths to situations in which no actual rotation is occurring.

When no rotation is occurring, nothing is happening. There is no tension in any strings due to centrifugal force and there are no tangtential Coriolis forces need to maintain a moving object in a rotating radial line.
 * David:
 * Your observation is from the inertial observer's viewpoint. Brews ohare (talk) 12:05, 9 June 2008 (UTC)

And there can never be any need to observe such stationary situations from a rotating frame of reference.
 * David:
 * Hypothesizing a "need" or lack of a need is off-track. The presumption is that a rotating observer is present, and the issue is how they reconcile the apparent motion with Newton's laws. Brews ohare (talk) 12:05, 9 June 2008 (UTC)

If we do so choose to view such stationary situations from a rotating frame of reference, we will obtain a superimposed circular motion. That is all. Nothing more.
 * David:
 * I might agree with there being a "superposed circular motion". Of course, the rotation of the observer does not change the physical situation, if that is what you are driving at. Brews ohare (talk) 12:05, 9 June 2008 (UTC)

The application of the rotating frame transformation equations to stationary objects goes totally against the conditions that were implied in the derivation of those equations.
 * David:
 * I'd have to disagree on this point. The derivation is based upon the observations from a rotating frame, and how they compare with the inertial frame. Brews ohare (talk) 12:05, 9 June 2008 (UTC)

And when you misapply them to a stationary object you end up swinging the Coriolis force around into the radial direction and ending up with a net inward centripetal force when in fact a circular motion demands that the second time derivative of radial distance must be zero.
 * David:
 * Circular motion in any frame requires net centripetal force. The only difference between frames is whether the force is real (like tension in a string) or fictitious (like a centrifugal or Coriolis force). Are you in disagreement with the article on centripetal force as well? Brews ohare (talk) 12:05, 9 June 2008 (UTC)

It is a nonsense. You should stick to studying centrifugal force in the context of actual rotation because that is the only time that the effect will exist. David Tombe (talk) 06:56, 9 June 2008 (UTC)
 * David:
 * The reasons you see it as nonsense are that (i) you insist on seeing things from the standpoint of the inertial observer, and (ii) you refuse to consider the issues faced in application of Newton's laws by a rotating observer whose observations are contaminated by artifacts of their rotation.
 * However silly the problem may appear, the problem is that. And accepting the challenge of reconciling the rotating observer's results with Newton's laws, how would you do it? I've shown above in detail my proposed approach. In its favor, I'd say it leads to an explanation in the rotating observer's own language that is totally self-consistent both with their observations and with Newton's laws. Brews ohare (talk) 12:05, 9 June 2008 (UTC)

Brews, yes but it's wrong. It's wrong for at least four reasons which I'll record below in a few days time. One of them is the fact that the Coriolis force never acts radially.

At any rate, if we ever did need to view a stationary or non-rotating situation from a rotating reference frame, the solution is simple. Superimpose a circular motion on top of it.

It doesn't matter whether Newton's laws can be made to hold or not. His laws were designed to hold in inertial frames. End of story.

Ultimately, you will need to be shown that the rotating frame transformation equations apply exclusively to something like the rotating turntable example which Wolfkeeper deleted out of spite. They do not apply to objects that have no physical connection with the angular velocity in question. David Tombe (talk) 12:25, 9 June 2008 (UTC)
 * David:
 * You can say, of course, that "It doesn't matter whether Newton's laws can be made to hold or not. His laws were designed to hold in inertial frames. End of story." but in my mind that says only that you aren't interested in the problem. If one is interested, then here is the procedure. Brews ohare (talk) 12:50, 9 June 2008 (UTC)

Brews, you have given a mathemaical procedure for superimposing a circular motion on a non-rotating system. It may be correct, but it won't be correct if it involves swinging a Coriolis force around into the radial direction.

At any rate, even if it is correct, it has got nothing to do with centrifugal force. Centrifugal force is all about the induced radially outward acceleration that comes with tangential motion.

The article could be simplified drastically if the ediors here were to realize that. David Tombe (talk) 13:03, 9 June 2008 (UTC)
 * David
 * I don't know how to simplify the article. It is not sufficient for the article to say simply that "there isn't any point in considering this problem". It also is insufficient to make entirely verbal statements: the reconciliation of the rotating observer's observations with Newton's laws has to be actually mathematically demonstrated. How would you do that? Brews ohare (talk) 13:20, 9 June 2008 (UTC)

Brews, considering co-rotating motions in rotating reference frames is what the transformation equatons are all about. But that is only one aspect of the wider issue of centrifugal force.

This article focuses far too much on centrifugal force as viewed from rotating reference frames.

But worse still! It focuses on stationary situations as viewed from rotating reference frames which nobody ever needs to do. And it extrapolates the transformation equations to these situations when those equatons are simply not designed for the purpose.

That is what is wrong with the article.

The article needs to be totally re-written with a simple introduction stating that centrifugal force is a radial outward force that occurs when an object undergoes tangential motion.

Then we can go on and give examples such as the rotating turntable, the rotating equal spheres, the gravity orbit, the carousel, and the centrifuge.

That's all it takes. David Tombe (talk) 13:29, 9 June 2008 (UTC)
 * David:
 * Maybe the "whirling table" example is what you like? Brews ohare (talk) 13:33, 9 June 2008 (UTC)

Reply to FyzixFighter
FyzixFighter, you are making some of the same mistakes as Brews. You seem to think that we can take that four part expansion of acceleration in terms of polar coordinates and read some physics into it. We can't. The polar terms tell us nothing about any particular motion.

But they are nevertheless very useful. We can use the expressions in a properly modelled differential equation that involves real physical input. The radial convective term is used as a centrifugal force in the two body gravity problem.

You seem to think that because it is derived with a negative sign that it has to mean centripetal force. That is not so. The negative sign is a consequence of the outward positive convention for the position vector.

The expression is merely the mathematical form for a force that changes the direction of motion and acts in the radial direction.

When we construct the planetary orbital equation, we end up with a radial gravity force inwards and a centrifugal force radially outwards. We have a scalar equation in the radial length and the two forces equate to the second time derivative of the radial length. You have got too much bogged down in trivia over matters like whether or not the second time derivative of radial length is entitled to be termed radial acceleration or not.

It doesn't matter. Just concentrate on the equation and solve it. And in doing so, you will see that inward radial gravity is working in opposition to an ongoing outward radial centrifugal force. David Tombe (talk) 08:48, 6 June 2008 (UTC)

Things that are wrong with the main article
Using polar coordinates in the inertial frame, the centrifugal force is an outward radial force which is induced as a consequence of tangential motion. However the introduction claims that the centrifugal force does not occur in the inertial frame. This claim is totally wrong.

The introduction uses any term but the most appropriate term "inertial" to describe the centrifugal force and this is for a deliberate reason to support a fringe viewpoint. They will call it "apparent", "D'Alembert", "Fictitious", or "pseudo". Anything but "inertial". This is to suit a particular party who don't believe that centrifugal force is real despite the fact that the outward radial effect can cause pressure and potential energy.

All attempts to draw attention to scenarios that emphasize the outward radial aspect of centrifugal force that is induced by actual rotation are erased, other than those further down the article that were already there before the edit war began.

The emphasis of the article is on the mis-application of the rotating frame of reference transformation equations to objects which aren't rotating and in which no centrifugal force is involved. This is a fringe viewpoint which is not mainstream textbook physics but has been shown to have appeared in a scientific journal. Yet it has nevertheless become the flagship of this article due to a fascination about it on the part of some editors, based on some misinformed view that it represents a principle of equivalence between actual rotation and observing something stationary from a rotating frame of reference. This view is in total contrast to Newton's Bucket argument

David Tombe (talk) 16:27, 8 June 2008 (UTC)

Moved from article
This appeared in the article. The problems I have with it are that it was in no logical place, and it's description of the coriolis force is completely incorrect. Nothing applies a coriolis force.- (User) WolfKeeper (Talk) 16:38, 8 June 2008 (UTC)


 * Wolfkeeper, the problem that you had with it was the fact that it was me that put it there. And you are completely wrong. The wall of the groove applies a Coriolis force on the marble perpendicular to the wall just as PhySusie says below.David Tombe (talk) 06:15, 9 June 2008 (UTC)

The rotating turntable
Consider a rotating turntable with a radial groove. A marble in the groove will experience a centrifugal force which will cause it to accelerate outwards towards the edge. If there is a wall at the edge, it will cause an inward centripetal force to cancel the outward centrifugal force when the marble reaches it, and no more radial motion will occur. The marble in turn will cause an outward reactive centrifugal force to act on the wall at the edge of the turntable.

While the marble is rolling outwards, its direction will be continually changing. This will be due to the Coriolis force that is applied by one side of the groove. The marble in turn will apply and equal and opposite reactive Coriolis force to that side of the groove.


 * The force exerted on the marble while it is moving outward along the groove is perpendicular to the wall of the groove it is moving in. A component of that force acts radially inward, which provides a centripetal force. I don't see the need to introduce a centrifugal force here to explain the motion. PhySusie (talk) 21:13, 8 June 2008 (UTC)


 * This problem is treated in detail as the example crossing a carousel. Brews ohare (talk) 05:10, 9 June 2008 (UTC)

PhySusie, you say

The force exerted on the marble while it is moving outward along the groove is perpendicular to the wall of the groove it is moving in.

That is the applied tangential Coriolis force that I was talking about. Are you disagreeing with Wolfkeeper? Wolfkeeper says that no Coriolis force is applied.David Tombe (talk) 06:12, 9 June 2008 (UTC)


 * The groove applies a force, but it's not the Coriolis force. The Coriolis force is the fictitious force that acts on the marble when you look at it from the rotating frame, and which exactly opposes the real force applied by the grove on the marble. --Itub (talk) 06:25, 9 June 2008 (UTC)

Itub, first of all, it doesn't matter which frame of reference we view the situation from. A marble rolls radially out a groove on a rotating turntable.

But let's for the sake of argument get into the frame of reference of the rotating turntable. You say that a fictitious Coriolis force acts tangentially on the marble, and that it has got nothing to do with the walls of the groove, but that the walls of the groove react to it equally and oppositely.

No Itub, the Coriolis force is the applied force which changes the direction of the radial motion and it is applied by the walls of the groove. If the groove wasn't there, the marble would not co-rotate at all and there would be no forces acting on it.

I assume now that you disgree with Brews's carousel example.

How long are you all going to keep up this united front for?

Wolfkeeper removed that section out of spite and for no other reason and you are rushing in to back him up and forgetting all about the issues that have been agreed above.

The argument between me and you is in relation to the application of the rotating frame transformation equations to non-co-rotating objects.

I carefully selected that edit specially to make sure that it didn't involve that controversy and that it was based on issues that had already been agreed. But Wolfkeeper couldn't resist the temptation to delete it, and so now you are all rallying around him and contradicting what you had said earlier.

You are giving no indication at all that you have any serious interest in this article beyond deleting what I put into it and trying to provoke me into being uncivil so that you can block me again. If I were you, I would take a long hard look at what first brought you into this debate. Because it is not going to end until alot more administrators have been brought in to see exactly what you are doing. You are acting like you are serious scientists with an interest to ensure that this article is correctly written up. But in actual fact, the evidence continues to unfold that you don't really have much of a clue about the subject matter.

You have joined a little team that goes around the articles establishing sole right of authorship. It is a kind of abuse that wikipedia hasn't yet managed to deal with. David Tombe (talk) 06:41, 9 June 2008 (UTC)


 * In fact Itub, I can see exactly what you have just done. You have noticed how PhySusie while attempting to show a united front with Wolfkeeper has inadvertently contradicted Wolfkeeper. And so you have attempted a damage limitation by deciding that the tangential force applied by the side of the groove is not a Coriolis force. You have then invented some fictitious Coriolis force, which although supposedly only fictitious, interacts in a real fashion with the wall of the groove. And to cloud the matter further, you have decided that we need to look at it from a rotating frame to see this fictitious force.


 * Itub, it is obvious that your intervention here was not in the name of helping the article, but rather to give false justification to Wolfkeeper's decision to delete my perfectly helpful edit yesterday.


 * Sadly you have too many administrators helping you out in all of this, but I think that you certainly have exposed yourself for what you are.David Tombe (talk) 07:15, 9 June 2008 (UTC)


 * I don't disagree with Brews's carousel example. In fact, I disagree with PhySusie's statement that there is "a component of that force acts radially inward, which provides a centripetal force". If the groove is radial, the force it applies to the marble is tangential and there is no centripetal force. Which is precisely why the marble moves away from the center. If you look at it from the rotating frame, you can explain the straight-line motion using centrifugal force. If the groove were not there, the Coriolis force would still be there, but it would deflect the marble from the straight-line path (when seen from the rotating frame). This is in fact nearly equivalent to Brews's carousel example, except that in his example the motion is constrained to a constant radial speed by the centripetal force imposed by the walker. --Itub (talk) 09:57, 9 June 2008 (UTC)


 * Sorry - the picture I had in my mind from the description was a spiraling groove, not a straight groove pointing outward. In that case you are correct Itub, there is only a tangential force applied to the marble. Another example of why the paragraph is unclear in its description - at least to me. Regardless, still no need for an outward force acting on the marble. Thanks. PhySusie (talk) 11:26, 9 June 2008 (UTC)

PhySusie, radial means radial. Don't make excuses for your misreading at my expense. And what do you mean by saying there is no need for an outward radial force on the marble? The rotation causes an outward radial centrifugal force on the marble. David Tombe (talk) 12:44, 9 June 2008 (UTC)


 * Sorry David - You're right - you said radial and I misread the description - the fault is mine - I apologize. I still don't see where the centrifugal force is coming from though - what agent is exerting it?  I know that in engineering models like this are used frequently and for good reason - they are intuitively easier and give good results.  However, in physics we don't use models like this because they are inconsistent with mechanics in the bigger picture.  This is why I didn't delete it when I first say it in the article.  I think it might be a useful example with the disclaimer that it is using a model that is useful, but not consistent with physics as it is used today.  Anyway - that is my opinion on the matter.  Again, I apologize David. PhySusie (talk) 17:52, 10 June 2008 (UTC)


 * Whoa:
 * Crossing a carousel is a complete analysis that should settle all these questions, in my opinion. For detail on procedure, see above. Brews ohare (talk) 12:07, 9 June 2008 (UTC)


 * Brews, your carousel example is described with unnecessarily complicated maths. I think your physics is correct in the actual rotation example but you don't need to analyse it separately from two reference frames. Polar coordinates in the inertial frame is sufficient.


 * As for the non-rotating example, it is not relevant. The turntable example was an attempt to simplify the issues without bringng in all that maths. So far three people have engaged in specious criticisms of it. Itub is the only one of the three that has demonstrated that he understands it. His criticisms remain at,


 * (1) The centrifugal force only exists in the rotating frame. I said that this is a nonsense idea. It exists in the radial direction no matter how we view it.


 * (2)The force that causes the object to retain it's co-rotating radial motion and which is applied tangentially by the side of the groove is not the Coriolis force. Once again, nonsense. Under the derivation of the rotating frame transformation equations, the Coriolis force is a source unspecified tangential force acting on a co-rotating radial motion.


 * What is your opinion on the rotating turntable example that Wolfkeeper deleted out of spite? David Tombe (talk) 12:35, 9 June 2008 (UTC)


 * In case it helps you understand the mainstream view that we want to include here according to Wikipedia's policies, here are three more textbooks. says quite explicitly "These forces [Coriolis, centrifugal, and Euler] appear to exist only in a rotating frame of reference".  has an example of movement along the equator and how the Coriolis force is radial in that case.  says "If a body moves perpendicularly to a radius, then its Coriolis acceleration is radial". On the other hand, I have yet to see any textbook saying that anything can "apply" a Coriolis force. The Coriolis force is "felt" due to the rotating frame of reference, but it has nothing to do with being pushed by a groove. That is a contact force, which you might consider a "reactive Coriolis force", but it is not the Coriolis force. --Itub (talk) 13:54, 9 June 2008 (UTC)


 * Itub
 * It seems that some form of this paragraph should be in the article. Would you consider writing same? Brews ohare (talk) 14:15, 9 June 2008 (UTC)

Itub, OK. Let's see were we agree. I totally agree with you that there is no radial centripetal force component of the tangential groove force. I couldn't understand what PhySusie was talking about and so I never mentioned it because I didn't want to cloud up the other argument.

I see now that PhySusie is telling us that she thought the groove was curved. She had absolutely no basis whatsoever to assume that and she's just making excuses at my expense. I said a radial groove. That means a radial groove. And PhySusie is totally wrong in thinking that there is no radially outward force. Of course there is. There is the radially outward centrifugal force. It is sheer delusion to claim otherwise. The rotation causes the marble to accelerate radially outwards along the groove. It was was just another case of denial of centrifgal force that I have come to expect from this united front.

You agree with me on this but only partially. You have limited your agreement once again to the rotating frame of reference. But the radial outward force never disappears. You can describe it differently in Cartesian coordinates but that radial force will always be there. It is not frame dependent. Polar coordinates are a perfectly legitimate way to describe that effect and they are the most universal way to do so on all scales. That centrifugal force is there no matter what frame we view it from.

Let's look at Brew's carousel example. When the walker walks radially to the edge of the rotating carousel, the floor friction will keep him on the radial path and also cause a tripping up effect on him. I suppose you are going to disagree with me on terminologies here even if you agree on the physics. I say that the frictional force of the floor tripping him up at his feet and causing him to keep his co-rotating radial path (if he doesn't trip) is a Coriolis force.

But you say that the Coriolis force is what would occur if there were no friction and he were to carry on in a straight line path in the inertial frame. In other words, you see the artifact tangential deflection in the rotating frame in the unrestrained case, as being the Coriolis force. Is that so?

Is there any chance that this can be discussed scientifically without all these alliances and people pretending to be agreeing with other people?

PhySusie has just added total confusion to a discussion by trying too hard to agree with certain people when it is clear that she had hardly even studied the matter in hand. She brought in extra centripetal forces that weren't there because she misinterpreted the scenario and she did this in an attempt to back up Wolfkeeper but ended up accidently going against him.

I'd rather deal with somebody that argues the physics and isn't all wrapped up in united fronts and alliances.David Tombe (talk) 12:10, 9 June 2008 (UTC)


 * If we assume you're right, that this is all a (bizarre) conspiracy to impose a particular view on the article, then you're self-evidently wasting your time here David.- (User) WolfKeeper (Talk) 16:31, 9 June 2008 (UTC)


 * If we assume that you're wrong, then it's even clearer that you're wasting your time.- (User) WolfKeeper (Talk) 16:32, 9 June 2008 (UTC)

No Wolfkeeper, it's not a conspircay. It's a small group of children who have called in a few friends to help out. You were hooked on a fringe theory associated with mis-applying rotating frame transformation equations to non-rotating situations. When it was exposed to you, you decided that you would just dig in anyway. I doubt if you have ever put any serious thought into the rights and wrongs of the issue.


 * Um... calling in a 'few friends to help out' is a type of conspiracy if it was done covertly. If you can't point to where I called in these 'friends' then it's going to seem to be a conspiracy to you. Since I didn't contact anyone that wasn't already involved I know you won't be able to point to me doing that.- (User) WolfKeeper (Talk) 17:37, 9 June 2008 (UTC)

Nobody is wasting their time. We are all going to ascertain whether wikipedia is corrupt and childish with childish administrators who back up groups of teenage nerds, or whether there actually are adult adminstrators.

The section which you deleted yesterday didn't even touch the controversy mentioned above. It was a scenario which fit the transformation equations exactly. You deleted it out of spite. If the applied tangential force is not a Coriolis force what is it then? Why didn't you just delete the word Coriolis and we could have debated that? Why did you delete the whole section? David Tombe (talk) 16:59, 9 June 2008 (UTC)


 * Um... how about for the reasons I already stated?- (User) WolfKeeper (Talk) 17:37, 9 June 2008 (UTC)

Question for Itub
Imagine an object moving away from a point. Now imagine observing that object from a rotating frame whose axis of rotation goes through that point.

The observer on the rotating frame will see the object spiralling outwards. Where do you see the Coriolis force in any of this? There isn't any Coriolis force. The rotating observer sees a circular motion superimposed on top of a straight line motion.

In order to have a Coriolis force, we need to have a radial motion being constrained to co-rotate. It must therefore be applied.

An example of a Coriolis force would be the tripping up effect that the floor of a rotating roundabout exerts on the feet of a person trying to walk a radial line.

Your transformation equations have a very specific application, and my rotating turntable example embodied those applications exactly. The Coriolis term, based on the derivation, is a tangential acceleration that acts on a particle that has a radial velocity, and no specification is given in the maths as to how that scenario may be brought about. There is nothing in the maths that tells us that a Coriolis force will be naturally induced as viewed from a rotating frame of reference.

We need to find physical scenarios that match the maths, and that was one such physical scenario.

If you have books that say that centrifugal force only occurs in a rotating frame of reference then the authors have sadly got it badly wrong.

In the rotating turntable example, the marble experiences an outward radial acceleration given by the centrifugal term rω^2. That is an absolute fact. It is not dependent upon how we view it. It is an absolute fact. Even if we chose to describe the effect in terms of Newton's law of inertia in Cartesian coordinates, it does not change the fact that a centrifugal force of rω^2 acts radially outwards on the co-rotating marble.

It would help greatly if you were to try and gain some comprehension of the topic before coming along with a few books written by some very misinformed people.

You can not write a scientific article by jumbling together a load of quotes from diverse sources. Alot of the textbooks contradict each other.

You need an overall comprehension of the topic first. Then you write it. Then you provide citations for facts which are challenged.

What are you challenging in the section that Wolfkeeper deleted? Are you challenging the fact that the force that keeps the marble in its co-rotating radial path is a Coriolis force? If it is not a Coriolis force, then what is it? It has the exact mathematical expression for the Coriolis force and it acts in the tangential direction. Anybody with any comprehension of the issue would know that it is an applied Coriolis force. It is exactly the tangential equivalent of an applied radial centripetal force.

From what I can see, you are just fishing around for technical excuses to deny a very simple illustative example of both induced centrifugal force and applied Coriolis force. David Tombe (talk) 16:19, 9 June 2008 (UTC)


 * I comprehend the topic just fine, thanks. But, as I hope you know, since "Wikipedia" can neither decide who is the most expert nor who has the right argument, we always defer to published sources. That is part of the core policies of Wikipedia. If the textbooks are wrong and you are right, there is only one thing you can do: publish yourself in something that we can call a reliable source. Send your paper to the American Journal of Physics explaining why all the textbooks are wrong. Then we can cite you in the article, although still as a minority position until most of the new editions of the textbooks correct their mistakes, or at least we see a trend of articles in the literature concurring with you.


 * That said, I already explained why $$m\ddot{r}$$ is not the "real" force, but I'll paste it here again for convenience. Look at eq. 1.48, derived in.


 * $$F_r = m(\ddot{r} - r \dot{\phi}^2)$$


 * Here Fr is the "real" Newtonian force, which in the case of circular motion (that is, at constant r) is pointing constantly inwards and equals $$-mr\dot{\phi}^2$$. That is, the only force is the centripetal force. However, if we say "wait a second, there is a term here, $$m\ddot{r}$$ which looks just like Newton's equation for r!", we can rewrite equation 1.48 as (introducing the definition F′ for convenience):


 * $$F' = m\ddot{r} = F_r + m r \dot{\phi}^2$$


 * The problem is that F′ looks like a force along r, but it's not the "real" Newtonian force. So curiously enough, the centripetal force term from eq. 1.48 "changes sign" and turns into the centrifugal force term for Newton's force in a rotating frame. I argue that by insisting in treating F′ like a force, defined as $$F' = m\ddot{r}$$, we are effectively "hopping on" to the rotating frame. That is, just changing the coordinate system does not make the frame non-inertial. What makes it non-inertial is pretending that the product of mass and the second derivative of the radius is a "real" force.


 * Finally, regarding your example of an object moving away from a point, seen from a rotating frame centered on the point. There is indeed a Coriolis force, which is necessary to explain the increase in tangential velocity and the increase in the centripetal acceleration of the object as it moves away. The math is the exact counterpart of the carousel example (you can even use the same figure and just swap the colors). --Itub (talk) 16:57, 9 June 2008 (UTC)

Itub, let's deal with the person spiralling outwards as seen from the rotating frame. There is no Coriolis force. There is an additional tangential velocity superimposed unto the already existing radial velocity. That is not Coriolis force. Coriolis force takes away from the radial velocity and adds it to the tangential velocity. Coriolis force actually changes the direction of a radial motion into a tangential motion. There is no natural Coriolis force acting on any motion as observed from a rotating frame. We need to apply a Coriolis force to make a radial motion co-rotate.

If the man walking radially outwards on the roundabout is tripped up by the tangential force on his feet, what do you call that force?

On your other points, there is no point in dragging in a bunch of polar coordinate expressions. We can assemble a differential equation using those expressions once we know the exact physical scenario that we are going to apply it to. In a central force orbit, the centrifugal force is outwards and given by rω^2 and it is added to the inward radial gravity force. The sum is equal to the second time derivative of the radial length. That is straight out of the textbooks. You will find it in Goldstein's Classical Mechanics, but as usual your group blocks any references that don't suit them. I can only suspect that elliptical and hyperbolic motion is too advanced for the editors here.

Finally, on the marble that moves radially outwards on the groove with centrifugal force mrω^2, are you denying that as an absolute fact? Does a force of mrω^2 act on the marble or not?

One final point. The section which Wolfkeeper removed yesterday didn't relate to the issue upon which I disgaree with the textbooks, which is the application of the transformation equations to stationary situations.

So you can't bring up the issue of citations or original research to justify Wolfkeeper's decision to delete that section. He did it out of spite clear and simple. If you were genuinely interested in centrifugal force, you would have restored it. But you are interested in chemistry and you have only come here to back up some friends. Your maiden speech here contained the ridiculous sentence that centrifugal force is not related to rotation. And you clearly don't understand the example of the spirally outwards object if you think that there is any centripetal force involved. You're now worse than PhySusie because at least she had the excuse that she thought the groove was curved. You are now talking about centripetal force where there is clearly no radially inward constraining force present at all.David Tombe (talk) 17:16, 9 June 2008 (UTC)


 * LOL, perhaps you won't believe it, but it was you who called me to this conversation, and I had barely had any interaction with any of the other editors in this dispute before. Sometimes I visit the WikiProject Physics page, and there I saw your "plea for help". At first I thought there was something to your case, but once I started to look at it in detail I noticed that it was you who has an "alternative conception" of centrifugal force, to put it kindly.
 * I won't waste my time responding to all your allegations right now, but I'll answer one direct question you made, even if I have already answered it several times before. Yes, I deny that a force of mrω^2 acts on the marble when you look at it from the inertial frame of reference. The only force in that frame is the groove pushing on the marble (and its corresponding reaction). --Itub (talk) 17:47, 9 June 2008 (UTC)

Itub, OK thanks for answering that question. Now we know exactly what the argument is about.

A marble is induced to roll out a radial groove in a rotating turntable with a centrifugal force mrω^2. That is an absolutely undeniable fact. But you are denying it, as are everybody else but one who has been involved in the debate.

Yes, I'm certainly outnumbered. But if you all wish to deny this very basic and obvious fact, then there is something seriously wrong with the modern education system.

I notice that you mentioned that your denial only extends to the inertial frame. The radial acceleration is either there or it isn't. It is not a frame dependent phenomenon. That is where you have all got it so badly wrong.

I don't believe that you are serious. When you see the marble accelerating outwards radially due to the rotation, you must know that the centrifugal force mrω^2 is an absolute fact.


 * Not in the inertial frame. In the inertial frame there's no acceleration applied radially, it's purely transverse (if the ball has no significant angular momentum and friction and so forth aren't important.)- (User) WolfKeeper (Talk) 11:52, 10 June 2008 (UTC)

But the standard trick amongst all the denialists here is to choose to view it in Cartesian coordinates even though the transformation equations, which are the main theme in the article, are done in polar coordinates.


 * We live in a 3-D world, which cartesian coordinates described very well and most people find are fairly intuitive. Polar coordinates are usually found to be much less so for many problems, although they are good for some problems, like central forces.- (User) WolfKeeper (Talk) 11:52, 10 June 2008 (UTC)

Why do you need to dive behind Cartesian cordinates as soon as you are faced with a centrifuge, or an object moving outwards under a centrifugal force? Ask yourself that question. And SBharris too, because he does exactly the same thing. And Anome too and others. As soon as a real radial centrifugal force looks them in the face, they all dive behind Newton's law of inertia and Cartesian coordinates which is merely another legitimate way of looking at the problem. David Tombe (talk) 07:46, 10 June 2008 (UTC)


 * We "dive behind Newton's law of inertia" because Newton's laws are only valid for an inertial system, unless you add fictitious forces. Tombe's laws, on the other hand, always assume that fictitious forces are real. I'm aware that you can construct alternative definitions for terms such as centrifugal force and still get the same trajectories and have some sort of internal consistency. However, we cannot publish your alternative definitions here. We publish what the textbooks say. --Itub (talk) 08:13, 10 June 2008 (UTC)

No Itub, I'll ask the question again. Look at the marble accelerating out to the edge of the turntable with acceleration rω^2 in the radial direction. This happens BECAUSE the turntable is rotating.

Is there a centrifugal force acting or not? David Tombe (talk) 09:03, 10 June 2008 (UTC)


 * From now on, I won't reply to any of your posts unless they are backed up by sources. Like Starwed wisely said, This discussion shouldn't really be happening at all. Much of it seems to involve arguing from first principles what a centrifugal force is, when what needs to be discussed is how the term is used in the literature. --Itub (talk) 11:40, 10 June 2008 (UTC)


 * I agree, we're only encouraging him by paying attention to his nonsense.- (User) WolfKeeper (Talk) 11:52, 10 June 2008 (UTC)

Itub, basically you know fine well that there is a centrifugal force acting radially outwards on a marble in a radial groove on a rotating turntable.

Sources have got nothing to do with this issue. Wolfkeeper deleted the section on a lie.

You decided to back him up in his wikistalking and you tried to hold out for a while with false arguments. But as soon as you came face to face with the inescapable fact that there is centrifugal force present in the scenario, you immediately played the old Anome trick and decided that we need to have sources before we can accept such an obvious fact.

Anybody who tries to deny the centrifugal force in that scenario is either,

(1) A liar

(2) A fool

or (3) has been told at some time that centrifugal force is fictitious and so has become so brainwashed by that teaching that even when presented with a clear cut scenario which shows that that teaching is not true, still nevertheless clings on and goes into denial. David Tombe (talk) 15:41, 10 June 2008 (UTC)

Another question for the denialists
Imagine being in the company of a group who had a reasonably basic education in physics. They are at a fairground and one of them goes unto a rotating carousel. He goes to the centre and then begins to try and walk a radial line on the carousel. The carousel is rotating quite fast and he is finding it difficult to walk a straight outward radial line on the carousel. Eventually he gets tripped up and falls sideways.

Is it likely that one might hear them all saying that he was tripped up by the Coriolis force? David Tombe (talk) 07:53, 10 June 2008 (UTC)


 * who cares?- (User) WolfKeeper (Talk) 11:42, 10 June 2008 (UTC)

Wolfkeeper, it's a Coriolis force. The transformation equations show the Coriolis force to be a tangential force that acts on a co-rotating radial motion. That is exactly what trips up the person walking radially outwards on a rotating turntable while they attempt to walk a radial line. It is what keeps the marble in the radial groove in a co-rotating radial motion.

You deleted that section out of sheer spite because you are confident that you have got a mob behind you, and you know that your own understanding of Coriolis force has been exposed to be totally faulty. And your understanding of the topic is truly appalling. But it's easy to fool a bunch of fools. David Tombe (talk) 15:47, 10 June 2008 (UTC)

Coriolis force
The new section General case in the discussion of the example of rotating identical spheres (one of Newton's original examples) is about as clear as it all gets. David has agreed with the case where the observers rotate at the same rate as the spheres. He thinks the case where the spheres don't rotate "may be" OK too, just needs simplification. Here we see a case that encompasses both limits with the same approach. The first subsection of the new section is pretty hard to escape − any approach has to account for the tension in the string for both observers. The second subsection shows agreement using the full-blown formalism of Fictitious force. I imagine this will put David's qualms to rest. Brews ohare (talk) 09:33, 10 June 2008 (UTC)


 * Brews, it's not about as clear as it gets. You use maths that is far in excess of what is needed to explain this simple case. You have added in the extra complication of a rotating frame that is rotating at a different angular velocity than the spheres themselves.


 * All we need to do is realize that there will be a tension in the string that is equal in magnitude to the centrifugal force acting radially outwards on the spheres. There is nothing more to it than that. We don't need to look at it from fully or partially co-rotating frames of reference.


 * As for the case of a non-rotating pair, there is no centrifugal force acting and we don't even need to examine the issue at all from any frame of reference, least of all a rotating frame.


 * The problem that we are dealing with is a large number of editors who can't see a centrifugal force acting at all, or when they do, they think that it disappears in the inertial frame of reference. It doesn't disappear. It is described perfectly well in the inertial frame of reference in terms of polar coordinates. David Tombe (talk) 16:02, 10 June 2008 (UTC)

"there is nothing more to it than that" and "we don't even need to examine the issue at all" both indicate that the problem addressed just does not interest you, which is your choice, of course, but the article cannot leave these things out.
 * David

I hesitate to advise you about your conflict with editors. But for all the good it does, I have some advice:
 * (i) Centrifugal force by definition does not exist in an inertial frame of reference, only in non-inertial frames. That is simply definition, and therefore, a convention of language. If you are talking about centrifugal force in an inertial frame, it is an unconventional use of the term, and you should change vocabulary to avoid confusing those with the standard definition in mind.
 * (ii) Whatever you are talking about, it may be clearer in polar coordinates (at least to you), but if the effect is real it must be there independent of coordinate system. So why not try an attack outside of polar coordinates, for example, in vector notation, just to clear the air?
 * (iii) A simpler view of your problems with editors than supposing that they are either stupid or part of a cabal, is to suppose that your explanations of what you are trying to say are just not getting across. I've had lots of experience with this kind of thing as editor of a journal – authors always think they have said things clearly and reviewers are either dumb or ganged up against them. However, in that case, you can choose whatever reviewers you like, and get the same response, simply because the writer is not making the point clearly. Clarity is audience dependent, and you have to listen to know what to say.
 * (iv) I suspect that part of your objections is that you take a very "seat of the pants" viewpoint of the subject (a good thing) and find the mathematical approach a bit anemic, somewhat obscure, and nonintuitive. All that may be very true. You can approach these matters without embroiling yourself in semi-technical discussions involving polar coordinates. Instead, try making the examples in the article more down-to-earth. They aren't actually wrong, just a bit pale. Brews ohare (talk) 18:22, 10 June 2008 (UTC)


 * FWIW David Tombe has apparently just been blocked for a month.User_talk:David_Tombe.- (User) WolfKeeper (Talk) 19:29, 10 June 2008 (UTC)

"Choice of frame of reference"
Is it just me, or is this section excessively discursive?- (User) WolfKeeper (Talk) 18:02, 25 June 2008 (UTC)
 * My take on this section is that it attempts to relate the cerebral mathematical notion of a frame of reference to the visceral differences that appear in different frames of reference. The idea is that in an airplane cockpit, or in an amusement park ride, the most natural and immediate perception is in terms of one's own frame of reference, however "fictitious" that may be in terms of a mathematical analysis in some inertial frame. This paragraph may have become long in response to D. Tombe, who holds a very subjective viewpoint of the subject. His views do require some accommodation, as the subject tends to become a mathematical shadow of real experience.


 * One thing I find missing in the discussion is that analysis in the rotating frame using centrifugal force as a real entry in Newton's laws does bring with it a rather intuitive analysis to the centrifuge problem, for example, and intuition is a great boon to physical problems. My feeling from the article is that it leans a bit toward discounting this intuitive aspect in favor of "coordinate transformations".


 * Maybe you'd like to present a more succinct version? Brews ohare (talk) 22:43, 25 June 2008 (UTC)

Please be careful. Fictitious forces are tricky.
I spotted several mistakes or misleading wording in the article. See my edits, particularly the one about the ball rotating about our head (first section). Paolo.dL (talk) 23:47, 29 June 2008 (UTC)


 * Please be careful yourself. What are the errors you see?Rracecarr (talk) 00:32, 30 June 2008 (UTC)


 * And please discuss changes here on the talk page before making significant changes to the article as you have been doing. Thanks! PhySusie (talk) 00:36, 30 June 2008 (UTC)

Of course I need to be careful as well. What I did is evident. My edit summaries are detailed. Each small change has its explanation. About errors, for instance, compare the old paragraph about rotating ball with the new one. Also, in the first row of the introduction, you say that the centrifugal force is produced by acceleration of a reference system. Most of the people who read this article do not know that rotation implies a centripetal acceleration of the points with time-invariant position in the rotating reference frame. Even more difficult is to convince a layman that the reference system itself accelerates when it just rotates with constant angular velocity about its motionless origin. Of course, we typically represent the orientation of the reference frame using an orthogonal basis (a tern of orthogonal versors), and we see the acceleration of these versors is different from zero and centripetal. But most readers of this article are not mathematicians. Notice that, even in mathematics, I can perfectly describe a rotation of the reference system with numbers that have null second derivative, if I use a polar coordinate system (indeed, when angular velocity is constant, angular acceleration is null). So, if we say in the intro that the centrifugal force is an artifact due to rotation, we just say the truth and make the article more readable.

In the paragraph about the rotating car, this sentence is badly misleading:
 * "the car pushes us to keep us turning, not the other way around"

The truth is that we, at the same time, do push the car outward, and this outward push is a non-fictitious force (i.e. compatible with Newton's laws), with the same dignity as the centripetal force exerted by the car. You would have learned all that if you had read my edits with attention. Please don't revert my edits without first reading my edit summaries and explaining why you decide to revert. Paolo.dL (talk) 08:46, 30 June 2008 (UTC)


 * This edit reads like opinion, is unsourced, and I have my doubts about its historical accuracy. I might be wrong, but from what I've read, I think that the modern distinction between "real" and "fictitious" forces was not made by Newton, but emerged much later. Please see The Relativization of Centrifugal Force Author(s): Domenico Bertoloni Meli Source: Isis, Vol. 81, No. 1, (Mar., 1990), pp. 23-43 Published by: The University of Chicago Press on behalf of The History of Science Society. --Itub (talk) 09:11, 30 June 2008 (UTC)


 * Yes, D'Alembert introduced the inertial forces much later. I meant that Newton's contribution clearly rules out any fictitious force, and clearly explains that a (real) force, to be called that way, must be always coupled with a reaction. Also, as far as I know Newton's work was based on the study of curvilineal motion (elliptical orits of planets) started by Keplero, and his results clearly exclude the existance of a centrifugal force applied on the planets (his first law explained to the world that "inertia" is not a force; the conflict with D'Alembert's interpretation is evident). But you are right, one of my sentences in my edit was questionable on an hystorical standpoint. I'll try and rewrite it later and I'll discuss it here. First, I want to see the answers to my previous posting. Thanks for your comment. Paolo.dL (talk) 09:29, 30 June 2008 (UTC)


 * Paolo
 * This comment about the car-passenger example seems to indicate you have not read the article reactive centrifugal force, which discusses this point in detail. The push on the car is real, and is the reaction to the car pushing on the passenger. That discussion is not pertinent to the centrifugal force article, which deals with fictitious forces. Brews ohare (talk) 09:34, 30 June 2008 (UTC)


 * Oh, I don't need to read that article to know that the push on the car door is real. I was teaching that before Wikipedia was born. And that's exactly what I wrote. I just believe this article should at least not say the contrary, don't you agree? My edit was to fix a sentence that somebody else wrote. Anyway, I believe a brief discussion about which are the real forces is pertinent to an article about apparent forces. Paolo.dL (talk) 10:25, 30 June 2008 (UTC)


 * It is already explained in the passenger/car example that the passenger does really push back on the car. Changing acceleration to rotation in the intro would imply that all fictitious forces are the result of reference frame rotation, which is wrong. Rracecarr (talk) 13:23, 30 June 2008 (UTC)


 * What about the sentence "the car pushes us to keep us turning, not the other way around"? (please read my 08:46 comment above). What about the explanation on the ball rotating rotating aroung our head? Rracecarr, you undid all my edits. I think you owe me a thorough explanation. Paolo.dL (talk) 15:14, 30 June 2008 (UTC)


 * Some of your edits are good, IMO. Your most recent edits to the intro seem fine. However opinions like "A deeper understanding of circular motion, such as the motion of a turning car and its driver, can be only achieved by adopting Isaac Newton's approach" do not belong. Because you did so much so fast, it was not easy to sift through. Rracecarr (talk) 15:54, 30 June 2008 (UTC)


 * But you undid all what I did. I am aware that I edited too many parts in a row. We'll discuss things one at a time, but please let's behave friendly. I hate edit wars. Paolo.dL (talk) 16:54, 30 June 2008 (UTC)


 * I am friendly :-). Rracecarr (talk) 17:57, 30 June 2008 (UTC)


 * Yes, now you are ;-). Thank you. Paolo.dL (talk) 20:44, 30 June 2008 (UTC)

Car-passenger example
Paolo:
 * Wikipedia is not about what you know yourself, but about the clarity of the article.
 * The quoted line is taken out of context. The full quotation is:

How is it that you wish to excerpt a few words out of context to argue over? That does not seem to be a constructive activity. Brews ohare (talk) 15:31, 30 June 2008 (UTC)
 * Put in this context, the statement appears clear to me. It states exactly that the passenger is pushing, and provides a link to further explanation.


 * Brews, what makes you think that I am not concerned with the clarity of the article? We don't need to fight about this. We do agree, can't you see? Part of the text (within parenthesis) says correctly that the push on the car exists, a previous part (i.e. the phrase "not the other way around") says incorrectly that it doesn't. In my proevious edit, I just deleted the incorrect part (i.e. the phrase "not the other way around"). That's it. Paolo.dL (talk) 16:16, 30 June 2008 (UTC)


 * I do not agree that selected phrases arbitrarily taken out of context must stand entirely on their own as completely self-sufficient. That approach unduly limits exposition, although, admittedly, there are those readers that will be misled, who will not process context. Brews ohare (talk) 16:27, 30 June 2008 (UTC)


 * Brews, I am not saying that the entire article is wrong. Only some sentences or phrases. In this case, the second part of that specific sentence that I took out from the context. I just removed a phrase that was incorrect and inconsistent with the rest of the article. Do you agree that this improves the readibility of the paper? Paolo.dL (talk) 16:54, 30 June 2008 (UTC)


 * No, I think I have been quite clear already. Brews ohare (talk) 17:05, 30 June 2008 (UTC)

So you think that "not the other way around" is correct? In my opinion, it means that our body does not push on the car door, which is incorrect. What is your interpretation? Can you explain how this part of the sentence helps the reader to understand the concept on which we agree? Paolo.dL (talk) 18:47, 30 June 2008 (UTC)

Thank you for deleting the incorret phrase, Rracecarr. Now the text is clearer, in my opinion. And you are right, it was redundant. Paolo.dL (talk) 19:07, 30 June 2008 (UTC)

Centrifugal forces require motion
This idea is unsupported and at variance with examples throughout many Wiki articles, for example, Coriolis effect, Fictitious force and of course Centrifugal force. Consequently, adoption of this view is not as simple as changing a few words here and there: it occasions a complete rewrite of most of the examples. Therefore, such a proposal requires extensive discussion on this page, and not a edit war on the main page. If a civilized discussion cannot be entertained on this page by Paolo, I recommend that he be blocked. Brews ohare (talk) 16:41, 30 June 2008 (UTC)

Poalo. Wake up. What they are telling you is that your opinion is not going to be allowed on Wikipedia. From the way they treated David Tombe, it is clear that if you have a physically valid and reasoned logical argument that proves them wrong, they simply block you and delete your edits. They don't allow disagreement no matter how correct and logically reasoned it is. David Tombe obviously knew what he was talking about so they had to block him. Wake up and realise that they will never let you change anything they write. These guys are not nice, and they will never agree with your ideas even though you obviously know more and understand physics much better than they do.72.84.69.15 (talk) 13:54, 3 July 2008 (UTC) —Preceding unsigned comment added by 72.64.53.108 (talk)

First sentence in the introduction
I wrote in the first sentence that the centrifugal force is apparently applied on an object which (by the way, I meant its CM) moves along a curvilineal path. This elementary concept was missing. Now, my edit is far from perfect, because the axis of rotation for curvilineal motion is not explained in Wikipedia. Please help me. I don't think we can refer only to circular motion (as in the article about Reactive centrifugal force). Yes, any curve can be represented as a sequence of small arcs of circumference, but the reader does not necessarily know that. Paolo.dL (talk) 16:54, 30 June 2008 (UTC)


 * The object need not move on any path. It can be stationary in either the inertial or in the rotating frame. Brews ohare (talk) 16:59, 30 June 2008 (UTC)
 * I'd add to this suggestion that the present stance in the Wiki articles has very extensive supporting citations, including references to world renowned authorities (not just random works), and I am very doubtful that support can be found via citation for even a minority view of this topic. In any event, the Wiki articles will stand essentially unchanged, but perhaps with some added commentary if dissenting viewpoints can be documented. A long shot at best. Brews ohare (talk)

Here is my edit summary:

"Curvilinear motion is necessary. Only curvilineal motion generates centripetal acceleration, and inertial forces are defined as Fi=-ma... (a is computed from an inertial RF)"

It does not suffice that the reference frame rotates. The condition to produce an (apparent) centrifugal force FC is that the object rotates as well, about an axis not passing through its CM. That's the only way to produce a centripetal acceleration aCP (notice that you need to observe this acceleration in an inertial reference frame), and we know that FCF= -m * aCP. This is D'Alembert's Principle. Paolo.dL (talk) 17:22, 30 June 2008 (UTC)


 * Simple assertion does not cut it: provide citations. I do not think you have a correct viewpoint, and the Wiki citations support that. Brews ohare (talk) 17:38, 30 June 2008 (UTC)

D'Alembert was the man who first introduced the inertial forces. His purpose was to make the net force acting on a body equal to zero, thus artificially producing a condition of static equilibrium... The article about Reactive centrifugal force refers to circular motion (this is excessively restrictive, but easier to understand; many physics textbooks only describe circular motion and do not generalize to curvilineal). Paolo.dL (talk) 18:16, 30 June 2008 (UTC)


 * Paolo: The question is not about d'Alembert, but about the first sentence in the introduction. An example that contradicts your viewpoint in most respects is rotating spheres. Brews ohare (talk) 18:34, 30 June 2008 (UTC)

That is an example in which centripetal acceleration of each sphere exists due to circular motion, as I wrote. Can I have the opinion of someone else? Paolo.dL (talk) 18:53, 30 June 2008 (UTC)


 * I agree with Brews. Centrifugal force is due to the rotating frame, not due to the curvilinear motion. We just had months of exhausting discussion with an editor who disagreed but provided no sources, which may explain the apparent negativity toward your changes. Please look at the recent conversations in this page and the archives to get an idea. --Itub (talk) 19:11, 30 June 2008 (UTC)

Itub, I understand what you mean. But I believe that the readability of this article is still very low. I'll propose changes in pills, so that I can study them more carefully and you all can easily digest or reject them. I hope we'll agree in the future. Paolo.dL (talk) 20:39, 30 June 2008 (UTC)


 * Paolo:
 * You have not looked carefully at the rotating spheres example. It treats several cases; among them the case where the spheres are stationary in an inertial frame and the case where the spheres are stationary in the rotating frame. Depending upon which example you choose, there is no circular motion in one frame or the other frame. Centrifugal force appears in the rotating frame in either case. That does not seem to be in agreement with your perspective. BTW, the general case also is treated. Brews ohare (talk) 19:28, 30 June 2008 (UTC)

Agreement reached
Brews, I can see now your point. The formula,
 * FCF= -m * aCP

is only valid when FCF coincides with the whole inertial force Fi, which is true when the body is fixed in the rotating reference system, and FCoriolis = 0. Otherwise, even when object has null acceleration in the inertial frame, in the rotating frame we have
 * Fi = FCF + FCoriolis = -FCF

which, as you say, means that the centrifugal force is supposed to be still there, just for the sake of consistency, although it is just a component of the net inertial force, totally cancelled out by (half) the Coriolis force. What a mess, if compared with Netwon's approach! But a correct mess, consistent with the literature. So, you were right. Thank you for the explanation. Paolo.dL (talk) 20:25, 30 June 2008 (UTC)


 * But it is Newton's approach :-) It's just a coordinate transformation.- (User) WolfKeeper (Talk) 23:16, 30 June 2008 (UTC)


 * Of course. :-) Not to mention that this illusory mess does not even spare you the "out of body experience"! To compute the inertial forces you actually need to know the kinematics of the non-inertial frame as observed from the inertial frame. Illusion plus out of body experience... (magic mushroom?) Paolo.dL (talk) 10:27, 1 July 2008 (UTC)


 * Just a figurative way to put the reader in a different frame of reference. A literary gimmick. Brews ohare (talk) 15:44, 1 July 2008 (UTC)

Just to make sure that my words are not misinterpreted: when I wrote "illusory mess", I was referring to the fictitious inertial force and its decomposition into fictitious components. Not at all to the article. I used your gymmic just to say that you need the "inertial viewpoint" anyway, even when you use fictitous forces! I'll think about it later, but perhaps the "out of body experience" cannot be presented as a drawback of Newton's approach. It's inevitable with both approaches. May be this should be made clear somewhere in the article, but we'll talk about the article later, I hope. Paolo.dL (talk) 16:18, 1 July 2008 (UTC)

NPOV & Paolo's edits
Paolo has deleted the following:

My purpose in putting this sentence in the article was to express my reaction to solving these problems myself. That experience is that the use of fictitious forces in Newton's second law is an indication of the reality of these forces to the rotating observer. In such problems as centrifuges, cyclones or aiming artillery, there is no question that these forces are treated as real, and actually solving these problems using these forces is more intuitive and more straightforward than using an inertial frame. One example is the inertial circles in the Coriolis force article, where the paths are circles in the rotating frame with fictitious forces, and are ellipses (a rather more complex problem) in the inertial frame. Another example is aircraft, where the books to train pilots use the fictitious forces all the time in their explanations. Yet another example is centrifuges, where centrifugal force is used to balance against the other forces in the treatment of sedimentation.

In any event, my reaction is that the inclusion of forces in Newton's laws puts the problem on a different, and often more understandable, footing than using an inertial frame. So the problem I pose to Paolo is how he wishes to express these matters, since he objects to the deleted sentence? Brews ohare (talk) 03:59, 2 July 2008 (UTC)


 * I'll study the example about "inertial circles" as soon as I have time (it looks interesting). Right now, I believe it is quite important to prove that the sentence I deleted expressed a questionable opinion, a non-neutral point of view. Here's my edit summary:
 * "The NPOV is: they are not real, sometimes perceived as real, sometimes not even perceived (rotating balls example), but just computed"


 * We do agree that sometimes the centrifugal force exists only to satisfy a "mathematical necessity", and it is not even perceived, don't we? We do "perceive" only the net inertial force (please see above).


 * Simplest example (translating non-inertial frame): We sit motionless in a train at the station. The train is also motionless. Another train starts moving and we see it from the window. We can see neither the station, nor the rails, nor the sky. Only our cabin and the other train. Did it ever happen to you that you can't decide whether the other train is moving one way or you are moving the other way? Let's imagine you decide you are moving (you take the non-inertial point of view). Does it change your perception of forces? Do you feel, because of your arbitrarily selected viewpoint, an inertial force pressing you against or away from the seat?


 * Example 2 (rotating frame): Imagine a man sitting motionless close to a rotating merry-go-round. If he at a certain time decides to take the merry-go-round as his reference frame, does he perceive at that time some new force just because of his new viewpoint? This is similar to the example in which the rotating spheres are stationary in the inertial frame, in which the rope joining the spheres is slack.


 * I conclude that your point of view (reference frame) changes, by definition, your "perception of motion", but does nothing to your "perception of forces". The formula that defines the centrifugal force is independent of the realism of our illusory perceptions, and vice versa. Our perceptions coincide with the results of calculation only in the singular case when we are fixed to the non-inertial frame (car driver, etc.). And by the way, our perception is tricky. It is a gift from God or Nature tuned for living on hearth surface, not on vehicles with shielded windows, airplanes, rockets, space stations.


 * I believe that the neutral point of view on this topic traslates into this guideline: let's never forget the difference between illusory perceptions and mathematics. And I suggest everybody to follow this guideline. This is an important point. I ask all those who watch this page to participate in this discussion. There's another related point, but I will spare you for now, to facilitate discussion. (By the way, have you seen the movie The illusionist?) Paolo.dL (talk) 10:32, 2 July 2008 (UTC)


 * Hi Paolo: I'm not in agreement.
 * First, the moving train example is not relevant: the observer is in a rest frame observing a moving object. He/she is never subject to force themselves simply because an observed object moves. The forces come into play when predictions of paths are involved. The observed moving train has nothing to do with fictitious forces. So this example is not an example at all.
 * Second, there is nothing illusory about fictitious forces. They are simply a different view of real properties of motion. You can be crushed by centrifugal force. Just because you say its inertia, not a force doesn't change the facts. And from a time-honored viewpoint, the simplest explanation is often to be preferred. The simplest explanation often involves fictitious forces, as my above list of examples indicates. Fictitious forces are not mathematics vs. perception, nor physics vs. perception. Brews ohare (talk) 12:36, 2 July 2008 (UTC)

Do you propose to delete the words "apparent", "fictitious", and "pseudo" (=false) that appear in the first sentences of this article? The examples I used are similar to the example in which the rotating spheres are stationary in the inertial frame, in which the rope joining the spheres is slack. Is this example irrelevant? Should we delete it from this article, in your opinion? You cannot be "crushed by a centrifugal force" (which is imaginary)! (not even by a reactive centrifugal force, which is real but acting on something else). You are crushed by the centripetal force (real and acting on you). There are several sentences in this article that explain why the centrifugal force is not real. You seem not to agree. You seem to fail to understand the difference between "perceived as real" and "real". If you don't mind, please read my previous comment again. Trust me, it will help. I insist because I believe that this is not a matter of opinion. Comments by others are more than welcome. Paolo.dL (talk) 14:08, 2 July 2008 (UTC)


 * The most accurate term is probably pseudo- pseudo means something that appears to be something that it isn't. Pseudo forces are very, very real but they're manifestations of other things, frame rotation and inertia mostly. If you apply the theory they make measurable predictions, which can be very important indeed. See: for just how important ;-)- (User) WolfKeeper (Talk) 17:07, 2 July 2008 (UTC)


 * From Cambridge Dictionaries Online:
 * {| class="wikitable"

! Pseudo ! Fictitious ! Apparent ! Real or "existing in fact; not imaginary"
 * "not real; pretended"
 * "invented and not true or not existing"
 * "seeming to exist or be true"
 * "not false; being what it appears to be;"
 * }


 * {| class="wikitable"

!Real force
 * means, to me, force exerted by a real object (I am sure you know how to build a free body diagram...), which in turn is acted upon by the respective reaction and experiences the measurable effect of this reaction.
 * }
 * Of course I agree that inertial forces can make measurable predictions. Never written the contrary. But I cannot accept (except in a joke ;-) that "you can be crushed by centrifugal force". To me, "by" means you can identify the object responsible for the action. I am aware that this may seem picky, but when you teach physics to students the fact that you are able to identify... James Bond's "killer" makes a huge difference ;-). Paolo.dL (talk) 19:05, 2 July 2008 (UTC)
 * Of course I agree that inertial forces can make measurable predictions. Never written the contrary. But I cannot accept (except in a joke ;-) that "you can be crushed by centrifugal force". To me, "by" means you can identify the object responsible for the action. I am aware that this may seem picky, but when you teach physics to students the fact that you are able to identify... James Bond's "killer" makes a huge difference ;-). Paolo.dL (talk) 19:05, 2 July 2008 (UTC)


 * The above table isn't really completely accurate, there's subtle nuances. Fictional means that something is completely imaginary, made up from whole cloth, non existent in the real world. Pseudo means something more like 'sham' which means its real but not what it appears to be. That's why quite a few people prefer to call them 'pseudo forces'. They have most of the properties of real forces, you can add them to real forces, and treat them almost exactly as if they were real forces. It doesn't seem completely unreasonable to consider them to be as real as the Casimir force for example. Is that a real force or is it just a manifestation of quantum mechanics? When something bends in a magnetic field, we say that a force acts, but isn't it really something more like the wavefunction distorted by the virtual particle exchange? Does that mean that magnetic forces are pseudo also? Probably IMO.- (User) WolfKeeper (Talk) 19:39, 2 July 2008 (UTC)


 * Hi Paolo: I am going away for a few days, so this is my last communication for a while. I agree that the words "apparent", "fictitious", and "pseudo" (=false) create the impression of illusion, but that is a defect of these words: they have technical and common usage meanings that are unrelated, which is confusing. However, I don't propose to eliminate these terms from the article, because they do have technical meaning.
 * The two of us do have a different understanding however. You find my statement that you can be crushed by a centrifugal force to be outlandish, while I feel that it is beyond controversy. In my view, a rotating observer with their fictitious forces have just as viable a world view as the inertial observer, and their fictitious forces are just as real to them as gravity or electromagnetism. Moreover, "when in Rome, do as the Romans do", that is, adopting their forces will make your life clearer and simpler. It won't help me understand meteorology better if I abandon the use of Coriolis forces.
 * To me it is simply prejudice if an inertial observer claims a "better" world view. From an impartial standpoint, both views work just fine, and sometimes one is simpler than the other - it depends on the situation.
 * The important thing is to be able to translate one view into the terms of the other. Brews ohare (talk) 14:23, 2 July 2008 (UTC)

That's a problem. I believe your point of view is not neutral. Please read my second last comment (posted at 10:32) again. Trust me, it will help. I insist because I believe that this is not a matter of opinion. I hope someone else will join us in this discussion. Paolo.dL (talk) 14:46, 2 July 2008 (UTC)


 * I'm not sure I understand the disagreement. In the case of person crushed in a large centrifuge, it is a centripetal contact force that actually does the crushing.  In the inertial frame, this force supplies the acceleration needed to keep the person moving in a circle.  In the rotating frame, it balances the centrifugal force.  What's not clear? Rracecarr (talk) 14:56, 2 July 2008 (UTC)

There's only one "world view" where all the laws of motion hold, i.e. where all actions have an "actor". The distinction between real and imaginary actions is by no means a matter of opinion. Paolo.dL (talk) 15:04, 2 July 2008 (UTC)
 * Fictitious (adjective) "invented and not true or not existing" (Cambridge Dictionaries Online)


 * A "world view" is not an equivalent concept to a SCZenz (talk) 15:10, 2 July 2008 (UTC)


 * I agree that the difference between real and fictitious forces is not a matter of opinion. I think Brews does too. But as he says, the fact that Newton's laws have to include fictitious forces in non-inertial frames doesn't mean that such frames aren't useful.  Gravity is imaginary, if you like, considering that it is just the result of the curvature of spacetime. But it is still useful for everyday calculations, and it is still not a good idea to step off a cliff. Rracecarr (talk) 15:18, 2 July 2008 (UTC)

I agree with SCZenz completely. I wrote it several times: the inertial forces are perceived as real, they are a realistic illusion. But they are not real. For instance, describing the examples I gave in my 10:32 posting as inappropriate is non-neutral. (by the way, yes, we are talking about different reference frames).

Rracecarr, I never ever ever wrote that the fictitious forces aren't useful, and by no means meant it. Gravity has an advantage with respect to inertial forces: it is produced by physical objects. You do have a "physical" cause for gravity or for spacetime curvature (whatever you want to call it). Also, Newton's first law is objectively much simpler (hence more elegant) in its non-tampered version (the one valid for inertial frames). However, if you want, we can say that there's a third "world view" (Einstein's one) which is even better than the "Newtonian". Contrary to what Brews maintains, as far as understanding the causes of motion is concerned, these worlds are not at all equivalent.

I would love to know if you all agree about what I wrote in my 10:32 posting (at the beginning of this section), which is my main contribution in this section and keeps being ignored.

Paolo.dL (talk) 15:55, 2 July 2008 (UTC)


 * Your **:32 posting seems to suggest that you see some difference between choosing a reference frame and really being in that frame. I see no such difference.  It seems as though you think that even if the man chooses the merry-go-round as his reference frame, he would still "know" that he wasn't spinning in circles.  I disagree.  You can't have it both ways--if the man chooses the spinning merry-go-round as his frame of reference, he sees himself going in circles.  And yes, he is aware of the centrifugal and Coriolis forces acting on him, the combined result of which is his motion in a circle.  Rracecarr (talk) 16:11, 2 July 2008 (UTC)


 * Please see my post here (the paragraph beginning "What you don't seem to recognize..."  It was aimed at David Tombe whose grasp of the subject was obviously not as strong as yours, but still I think it might make you question the belief that perceptions of fictitious forces are only possible if you are at rest in the rotating frame. Rracecarr (talk) 16:17, 2 July 2008 (UTC)

I am sorry, but this is the second time that you attribute to me what I did not write. I do appreciate your contribution, but this is frustrating, because it took much time for me to write that comment. I have never ever written nor meant that there's "some difference between choosing a reference frame and really being in that frame". This doesn't even make sense to me. Of course, your interpretation may be due to my English (I am not a native speaker, as you probably guessed already), and I sincerely apologize if this is the case. Please let me know.

Anyway, I disagree with you: there is a difference between "perceiving" and "computing". The man does not perceive or experience, he just might be able to compute the two components of the inertial force (if and only if he knows the formulas, and he knows the motion of the non-inertial frame relative to the inertial!). I do believe that "perceptions of fictitious forces are only possible if you are at rest in the rotating frame". I do perfectly know (see previous section) that the computed (and not perceived) components of the net inertial force add up to zero when you move relative to the rotating frame. I will be sincere with you, please do not interpret it as a personal attack: it appears to me that you missed my main point. Paolo.dL (talk) 16:56, 2 July 2008 (UTC)


 * In your simple train example, an inertial observer chooses a non-inertial reference frame in which he is accelerating and feels no force. By contrast, if the observer is stationary in a non-inertial frame (e.g. the accelerating train), he does perceive a fictitious backward force.  In fact, it will feel just like a change in the direction of gravity; the two are physiologically indistinguishable if the train accelerates smoothly and constantly, and the observer is blindfolded. -- SCZenz (talk) 16:46, 2 July 2008 (UTC)


 * Yes, you are almost there! I completely agree. My conclusion was mainly based on what you wrote. Yes, in my train example the man feels (perceives, experiences) no force, yet he is acted upon by an inertial force that he can compute (similar to gravity in free fall). And yes, in the opposite case he perceives the inertial force. I also agree that Einstein proved you cannot distinguish between (uniform) gravitational field and inertial force field. What about my conclusion? Paolo.dL (talk) 17:18, 2 July 2008 (UTC)


 * I do not think I am missing your point. Did you read the post I linked to above? Imagine that situation from the point of view of one of the (moving) pool balls. Rracecarr (talk) 18:47, 2 July 2008 (UTC)


 * Thanks for warning me. I am puzzled. Yes, I have read your post (too quickly prehaps). I'll read it again. Have you read my posting in previous section? Do you agree with SCZenz? I don't have a cue about the reason of our disagreement... Paolo.dL (talk) 19:05, 2 July 2008 (UTC)


 * It is a little hard to tell, but I think we agree perfectly from a computational point of view. We both understand how to perform calculations in inertial frames, and also in accelerating frames.  Our disagreement, if it exists, is more ephemeral--we disagree about under which circumstances a person would perceive fictitious forces as real.  That may not be so easy to settle, because regardless of the math, I can say "they would perceive a force" and you can say "no they wouldn't".  My contention is that you do not have to be motionless in a rotating frame in order to regard that frame as your "true" frame, and therefore to perceive the fictitious forces associated with that frame.


 * A hamster running in a hamster wheel probably lives in an inertial frame, and doesn't care that in the frame of the spinning wheel he is subject to Coriolis and centrifugal forces. The hamster lives in his (inertial) cage, and is aware that the wheel spins.  However, an blind ant living on the wheel probably lives in the rotating frame, and is not conscious of the spinning of the wheel.  The ant is used to the centrifugal force, and to the Coriolis force that arises when she starts scurrying along.  Even if the ant were able to scurry so fast, for a short time, that she was stationary in an inertial frame, I don't think she would suddenly stop believing in the centrifugal and coriolis forces that she was accustomed to.  They still give accurate predictions.  It is a big intuitive jump to switch reference frames.Rracecarr (talk) 19:24, 2 July 2008 (UTC)


 * I am going home now. Just a quick and incomplete answer: I agree the disagreement is not computational. However, your concept that a reference frame can be not regarded "as your true frame" makes no sense to me. I still can't understand what you mean. Either you select that frame or not. There's no other option, in my opinion. Don't worry about answering right now. I'll study everything tomorrow. Thank you for your contributions. Paolo.dL (talk) 19:42, 2 July 2008 (UTC)


 * I exactly agree with that. There is no difference.  I imagined that you thought there was a difference, because I couldn't figure out why else you would say a person would only perceive fictitious forces if they were at rest in the accelerating frame. Rracecarr (talk) 19:46, 2 July 2008 (UTC)

Just to give my opinion on the subject at hand: The article is better of with the sentence in question deleted, and Paolo's edit-summary motivation for deleting it was clear enough for me to understand, at least.

I have just spent an hour or so going through Paolo's recent contributions and the various reactions to them. I think there is a tendency by editors on this article to overreact to new editors making changes that they disagree with, and sometimes revert unnecessarily. (This is understandable, given the amount of trolling and tendentious editing this article receives, but unfortunate nontheless.) It is easy to be overprotective of one's own work, but some of the editors here may do well re-reading WP:OWN. --PeR (talk) 17:01, 3 July 2008 (UTC)

Perception vs reality
Perhaps it would be more fruitful and less subjective than entering an almost psychological realm to consider the examples in this article, which present several problems from both a rotating and inertial viewpoint, so as to identify just what changes might be suggested by Paolo. At the moment, the only change that has been made is to delete my sentence:
 * In particular, these observers include these forces in Newton's laws, which is not just a mathematical necessity, but also an expression of the reality of these forces in the experience of these observers.

which I believe should be reinserted as perfectly accurate, and helpful. Paolo has objected here, as I understand it, to the use of the word "reality", which he insists has his own (rather restricted) meaning. Brews ohare (talk) 17:05, 3 July 2008 (UTC)


 * The objection, as I understand it, is that the sentence presupposes that there is a 1-1 correspondence between the reference frame that a person "experiences" and the one he/she uses for calculations, which is not necessarily true. But, besides that, it is (in my opinion) an unnecessarily complex sentence, and the text reads better when it is removed.


 * Regarding the discussion on whether a centrifugal force "exists", "is real", etc, that discussion has been repeated over, and over here already. Both of the following sentences are considered correct, by different people, or in different contexts.


 * 1) Centrifugal forces exist in reality
 * 2) Centrifugal forces don't exist in reality
 * The same problem exists for terms such as "negative numbers", "cold", "vacuum", or "God".
 * It should be possibly to work constructively on this article without splitting hairs on an the philosophical definition of words like "exist" or "reality" and focus on what makes the article readable, understandable, an scientifically correct.


 * --PeR (talk) 19:59, 3 July 2008 (UTC)


 * Yes, I guess philosophical interpretations should not appear in this article. However, my objection cannot be summarized as you did. As I already wrote, I do not agree about the fact that you can use two reference frames at the same time. Calculations wouldn't work. And I believe that this idea, introduced by Rracecarr and by himself considered unacceptable, brings us nowhere. Perhaps a short clarification about this topic can be of help. When you select a reference frame, you use it both for kinematics and dynamics. You perceive and describe motion (position velocity acceleration) from that frame. And that's the only way to make correct calculations.


 * But something more relevant can be said about this. My objection is about what you perceive, or experience (or "feel", as SCZenz wrote). There's one thing that you typically perceive correctly in both "world views" (reference frames): kinematics. The "perception of motion" is in most cases consistent with the "mathematical representation of motion" (kinematics). You perfectly see it with your eyes. Our terminology is not casual: when you are in a non-inertial frame you are called a non-inertial observer.


 * There's something that you may not perceive at all: forces. Especially fictitious forces (but also gravity in free fall, if you like). As for "perception of forces", it is not true that you always experience a centrifugal force as "very real". And I proved it. (I disagree with RRacecarr: his non-inertial-observer ant on the hamster wheel will not feel any inertial force if it runs at the same speed as the hamster, thus remaining motionless relative to the inertial frame; I believe SCZenz agrees with me about that).


 * A fourth concept: Computation of forces. We luckily agree about how to compute forces. And that they make perfect predictions. If these formulas were so close to our experiece, Archimedes or Euclides would have discovered them before Newton. But computed forces don't necessarily coincide with perceived forces. Paolo.dL (talk) 23:02, 3 July 2008 (UTC)


 * It's rather unfortunate that this article has to be at centrifugal force rather than centrifugal effect. As with the coriolis effect, there's a lot less question that the centrifugal effect is real, whereas somehow the force seems fictitious to people.- (User) WolfKeeper (Talk) 00:46, 4 July 2008 (UTC)


 * I think you have summed up our difference very succinctly. I think we may not want to get too carried away with talking about what people would "perceive" in the article, as that seems kind of touchy-feely for a physics article, which would make the whole point moot.  And I think that there may be no way to definitively settle the issue anyway.  But I do think people accustomed to living in a rotating frame would experience fictitious forces very much as they're written in the equations of motion.  Rracecarr (talk) 01:33, 4 July 2008 (UTC)


 * Being accustomed to living in a rotating frame, I can say that, in my everyday life, I personally make absolutely no distinction between Earth's gravitational pull and the centrifugal force due to its rotation. I "feel" the two as if they were one force.


 * Rracecarr's ant experiences a centrifugal force (and a twice as strong opposite Coriolis force), because that ant's brain uses a synthesis of visual and other sensory inputs, combined with intuitive physics knowledge to generate a feeling of "force". Paolo's ant, on the other hand, has brain which does no synthesis, but feeds the raw sensory input, which is "zero acceleration". I think humans are somewhere in-between, sometimes attributing feelings correctly to forces, and sometimes just feeling the net acceleration. --PeR (talk) 08:21, 4 July 2008 (UTC)

Focus on article
Great suggestion: so far the discussion has been unproductive in improving the article in any of these three dimensions. Brews ohare (talk) 17:00, 4 July 2008 (UTC)

PeR's point is wise: nobody can show that centrifugal forces are real nor the contrary. I wholeheartedly agree. I just pointed out that not I, but the scientific literature consistently describes these forces as fictitious, pseudo and apparent (I believe they also frequently call them imaginary). From Cambridge Dictionaries Online:
 * {| class="wikitable"

! Pseudo ! Fictitious ! Apparent ! Real or existing in fact; not imaginary
 * Not real; pretended
 * Invented and not true or not existing
 * Seeming to exist or be true
 * Not false; being what it appears to be
 * }

This proves nothing. Even though it is expressed in the literature, it is a philosophical opinion. I also gave my own philosophical opinion, relevant to this discussion, but that I certainly don't want to impose, nor to express in the article:


 * {| class="wikitable"

!Real force Paolo.dL (talk) 11:37, 5 July 2008 (UTC)
 * means, to me, force exerted by a real object (I am sure you know how to build a free body diagram...), which in turn is acted upon by the respective reaction and experiences the measurable effect of this reaction.
 * }
 * }

The article should not contain philosophical interpretations
The discussion in the previous subsections is about a sentence by Brews ohare I deleted from the article, and he would like to reinsert. This sentence expresses, in my opinion, a non-neutral point of view. This discussion is aimed to show that Brews cannot show that centrifugal forces are always "experienced as very real", and the results of formulas are far from our experience (or perception, or feeling). Our experience proves nothing. Even our quasi-inertial everyday experience (earth surface), in which fictitious forces are negligible, is so far from the beauty and semplicity of Newton's theoretical approach that for centuries people was convinced that no force was necessary to decelerate an object.

My point is quite simple, yet still not understood: mathematics is very abstract. Abstract means it is far from immediate experience. We would have not needed Newton, D'Alembert, Coriolis, Euler, Lagrange and Einstein, if this were not true. The beautiful coherence of physics is far from our experience. Some of you keep ignoring the difference between "understanding" and experiencing or perceiving. We understand only thanks to the teaching of great masters. A human life would not suffice to understand if books and libraries were not invented.

WolfKeeper wrote about centrifugal effect. Do you mean the "crushing effect" (or appearent gravity) which will kill James Bond in this joke? ;-) As well as our "experience of force", the crushing effect is not always produced. In some cases, centrifugal forces exist without a crushing effect: Coriolis would save James Bond, if he could run as an hamster (or just slide on the internal surface of the centrifuge, as a perpetual skier). My two initial examples showed this, right at the beginning of this discussion. The article contains a third example which shows the same. Rracecarr's hamster-weel example is yet another perfectly equivalent example. When Rracecarr's ant runs at the same speed as the hamster, it will not experience any crushing effect, yet it would be acted upon by exactly the same centrifugal force that would produce a crushing effect if the ant were motionless in the rotating frame. There are still a few editors who disagree about that. This is too simple stuff to disagree. It is even explained on the article! In physics, when people disagree, either they are both wrong or only one of them is right. It was easy to convince me that I was wrong, when I was. I look forward to the moment in which we will be able to write a subsection "final agreement on the difference between perceived and computed forces". Paolo.dL (talk) 12:29, 5 July 2008 (UTC)


 * when people disagree, either they are both wrong or only one of them is right. There's another possibility, which is very appropriate here, they can both be right, and simply looking at things in a different way.- (User) WolfKeeper (Talk) 14:25, 5 July 2008 (UTC)


 * I agree with Wolfkeeper on that point. Different people mean different things by words like "feel", "exist", "real", etc. If a person would say "In my heart I feel that God exists", he may well be telling the truth about what he feels, even though a different person might say the exact opposite and also be telling the truth.


 * I also agree with Paolo's statement in the title of this section.


 * I propose that we accept that there is a disagreement among editors (and presumably also among readers) on whether a fictitious force can be said to "be felt", "exist", or be "real". In consequence, any statement that asserts how the Centrifugal force "feels" can be removed from the article, unless it is supported by reliable sources. (Anyone who would like such a statement to remain in the article can of course find a reliable source to attribute it to.)


 * In my opinion, the article does not need to address the existence/reality issue at all. Saying things like "the centrifugal force is not a fundamental force", or "there is no reaction force associated with the centrifugal force" is much more precise, and therefore also easier to attribute to sources, and less likely to cause debate. --PeR (talk) 17:07, 5 July 2008 (UTC)


 * Ultimately, it doesn't matter unless you can reference it, and only then if it is notable.- (User) WolfKeeper (Talk) 17:19, 5 July 2008 (UTC)

Perceived and computed forces
The examples in the article compare rotating and inertial frames from the calculational viewpoint. In the rotating frame, centrifugal forces are included in Newton's second law in order to find trajectories. In the rotating frame they are indistinguishable in their effect from forces like electromagnetic forces. I do not think Paolo can argue about the inclusion of centrifugal force in Newton's laws. It is obviously what is done.

Going beyond computation, centrifugal and Coriolis forces are indistinguishable in the rotating frame from "real" forces in their effect upon objects: they cause accelerations, tensions, and compressions. Moreover, to the denizen of the rotating frame they are treated as real in designing gun sights for Coriolis corrections, and in describing meteorological events, and in describing forces in an airplane or space station. I hope the article makes this clear as well, but I'm not so sure. I expect Paolo to disagree entirely with this aspect, although I do not understand why he would do so. I suppose he would say meteorologists do not have a neutral point of view, whatever the meaning of that phrase may be. (I suspect it is introduced to provide a Wiki legalistic aspect to the discussion, to avoid any sensible argument. However, in my view, NPOV has zero bearing on the matter.)

All this said, I doubt that any changes in the article will occur. Frankly, any changes that I would make myself would be to accent the reality of these forces, contrary to Paolo's views. Brews ohare (talk) 15:40, 5 July 2008 (UTC)


 * You are making your own discussion. If you had read my comments, you would have understood that I do not disagree at all on what you wrote here. Neutral point of view means the same thing that PeR maintained and that you seem to have accepted: you can neither prove that a fictitious force is real, nor the contrary. The meaning of the word real in this context is a matter of interpretation. Also, by opening a new section any time you post a comment, you interrupt the flow of this discussion. Paolo.dL (talk) 17:37, 5 July 2008 (UTC)

Continuing discussion on second last subsection
I agree with PeR. In a previous subsection, we already agreed about the fact that the reality of fictitious forces is a matter of opinion. In this section, we are discussing something that I do not want to write on the article. But something on which we could easily agree. The difference between "understanding" (or computing) and "feeling" a force is not just an opinion, unless you want to invent your own vocabulary. How can we reasonably maintain that Rracecarr's well-educated ant would be crushed or would "feel" any centrifugal force or centrifugal effect if it could run as an hamster (or just slide along the internal surface of the hamster-wheel, as a perpetual skier)? Paolo.dL (talk) 17:41, 5 July 2008 (UTC)

As I maintained here and here, our disagreement on this particular subtopic is terminological. I already agree with SCZenz. I would agree with all of you if you just could use the words "understands" or "interprets" or "imagines" or "computes" or "predicts", rather than "feels" or "experiences", in the above-mentioned four examples. Is that so hard? I guess you understand me, but you are over-protective. Are you afraid to say I am right? Don't worry, I don't want to explain in the article that Rracecarr's well-educated perpetually skiing ant doesn't feel the centrifugal force in its guts (as well as a man in free fall does not "feel" gravity; he feels weightless, like an astronaut in microgravity; it's too hard and sophistic to maintain the contrary). It is enough for me if you accept not to write the contrary! Paolo.dL (talk) 18:05, 5 July 2008 (UTC)

Validity of Newton's laws
Regarding this sentence from the introduction, I believe that Newton's laws are only valid for inertial frames, by definition. Newton himself was extremely clear about that, as you know. Thus, I believe the "adjusted" laws of motion used for non-inertial frames cannot be called Newton's laws. I guess Newton would strongly disagree. I don't know how they call them (Newton-D'Alembert? Newton-D'Alembert-Coriolis-Eulero?). I do know, for instance, that the laws adjusted for rigid body motion are called Newton-Eulero's laws of motion. Paolo.dL (talk) 17:14, 7 July 2008 (UTC)


 * I think you can simply call them "the equations of motion in a rotating frame." Rracecarr (talk) 17:44, 7 July 2008 (UTC)


 * It is hard to argue that Newton's laws are not in use in a rotating frame when exactly the equations advised by Newton are employed to find trajectories. The sole difference is the addition of fictitious forces, which are treated exactly the same as all the other forces.
 * The important point at stake is the equivalence of the laws of physics, which applies only to inertial frames. That equivalence is violated in rotating frames because the fictitious forces vary from frame to frame.
 * Therefore, the sentences as modified by myself are entirely correct. Brews ohare (talk) 18:05, 7 July 2008 (UTC)

I agree with Rracecarr. You can also call them Newton's laws with the addition of inertial forces, or adjusted for non-inertial frames. The problem is another. It was clearly explained in my edit summary:

Paolo.dL (talk) 18:10, 7 July 2008 (UTC)


 * Clear to whom? Whose laws are you using then? Where did F=ma come from? What are you talking about? We don't talk about different laws of motion in a magnetic field just because the Lorentz force is introduced. I find your viewpoint confusing. Brews ohare (talk) 18:17, 7 July 2008 (UTC)


 * You may not agree, but it was clear. You can't understand because something prevents you from considering that we are talking about Newton's laws, not just "Newton's first and second laws". Would you mind to explain to the world why Newton was wrong when he explained to the world that his three laws were valid only in inertial frames? Paolo.dL (talk) 18:33, 7 July 2008 (UTC)


 * Well, Paolo, it is a resort to Wiki legalism, but I believe you will find the literature refers to Newton's laws in this connection. An example is Finch. Another is Taylor. Their advice is: "Treat fictitious forces like real forces, and pretend you are in an inertial frame".
 * If I understand you, you'd agree with me except for the violation of the third law? That law is violated only with respect to a non- existent originating body to act as a source for fictitious forces, which is not a significant violation, in fact, as all other applications of the third law apply in the rotating frame. Thus, it is a quibble to say that Newton's laws do not apply. Brews ohare (talk) 03:49, 8 July 2008 (UTC)
 * Yes! These inertial forces are like gravitational fields that appear here and there in an accelerated frame, except that they have funny shapes and there's no originating body that feels the "other end" of the inertial/"fictitious" force vectors (as there is for g forces that originate from gravitating bodies). So Newton's third law fails there, but that's not obvious at the free-body; you can't tell that it's not pulling on something, even though something appears to be pulling on it. Otherwise, these forces act as gravitational forces do, and normal objects are affected just as they would be by extra gravitational fields. Again, these fields have funny shapes-- they don't radiate out from points or blobs, so the tidal effects from field gradients are sometimes "inside out." And the simplest inertial force from constant acceleration (what you feel in a rocket accelerated uniformly in line in flat space) has no tidal gradients at all, so it "looks" like gravity from an infinitely large flat surface! But again, the free object end "sees" it as that. And yes, these inertial forces change from point to point, but then so would a complex gravity field generated by a complex shape-- that doesn't mean Newton's laws wouldn't apply. Again, the only violation is at the other end of the force vectors, in the lack of "reaction." The "reaction" forces to all these things are due to other introduced forces that are NOT inertial-- they are all due to the other forces of nature: EM, weak, nuclear. And they have two ends to each interaction and fully follow Newton's third law. So the floor of the rocket pushes electromagnetically/mechanically against the feet, and the feet push back, and that's all totally the same as Newton. It is interesting that even as Einstein decided that gravitation itself might be an inertial force from being dragged though space-time in a non-geodesic path, he was also deciding that inertial forces of any kind needed some kind of supporting "aether" like stuff to make them. How does the universe know to provide you with intertial "drag" if you accelerate linearly thiough vacuum? There must be something "in" that vacuum which is "dragging" you; telling you that you're accelerating. Einstein's new aether was our Higgs field, I suppose. The vacuum can't be totally "empty," or else you couldn't tell you were accelerating "through" it. It's still very weird, when you think about it. In an empty universe (no mass, except you and your vehicle) if you fired your rocket, would you feel inertial force? Einstein thought not, since he thought the inertial aether eminated from distant masses, as a kind of thing that filled the vacuum and cut in or out when you accelerated with regard to it. I think we think, instead, that because of the Higgs field everywhere, acting as aether, you still would feel an accelerational inertial force, even without the distant masses. Yes? S  B Harris 04:51, 8 July 2008 (UTC)

Inertial forces act as predictable force fields. Yes, SBharris, of course I agree, although I would not describe them all as "gravity-like" (e.g., the centrifugal force is not an attraction toward a point, but a repulsion from an axis, as you wrote).

Brews, both your references do not apply to this discussion, because they specifically refer to Newton's second law. Again, I must remind you that the discussed sentence is about "Newton's laws", all of them as a whole, and Newton himself clearly stated that his three laws are valid only for inertial frames. Newton's definition of the word "force" was also based on his third law. You should not undervalue the historical importance of this definition. The inertial forces are also called fictictious, apparent, pseudo or not real just because of this definition.

No physical object applies the inertial force, and no physical object is acted upon by the respective reaction. Contrary to what Brews wrote, that's a blatant and full violation of Newton's third law. The third law is actually the only way to tell inertial from non-inertial frames. I would like to know the opinion of someone else about this particular topic: is this violation a "quibble", as Brews wrote, or there's someone who agrees that Newton's work was based on this "quibble", and his distinction between inertial and non-inertial frames was a significant contribution to the world? I insist: in my opinion, here Brews seems not to agree with Newton himself. Paolo.dL (talk) 17:01, 8 July 2008 (UTC)


 * I don't think Newton's formulation is exactly the same as the modern formulation of Newton's Laws, nor does it have to be. One difference is that Newton believed in "true motions" in "immovable space," not in inertial reference frames. -- SCZenz (talk) 17:10, 8 July 2008 (UTC)


 * SCZenz, this one difference does not seem to me relevant to this discussion. Would you mind to explain? What's the modern version of Newton's third law compatible with non-inertial frames? Paolo.dL (talk) 17:28, 8 July 2008 (UTC)


 * My point was to pull the discussion away from arguments about what a primary source written four hundred years ago says, and suggest that we use modern secondary and tertiary sources instead; Wikipedia prefers the the latter over the former, and this argument is illustrating why: even knowledgeable people can disagree over the meaning of a primary source. I know that many "regulars" on this page like to debate, but I would like to suggest that the passages under dispute be discussed specifically, using appropriate sources to back up proposed wording. -- SCZenz (talk) 17:35, 8 July 2008 (UTC)

Modern sources
Examples of modern sources are: Finch, and Taylor. Their advice is: "Treat fictitious forces like real forces, and pretend you are in an inertial frame". They specifically refer to Newton's laws.

Newton's first law is interpreted as "The motion of a particle not subject to forces is a straight line." That formulation appears perfectly valid in a rotating frame provided fictitious forces are included.

The discussion in the article concluding: "Newton's third law applies in all other respects even in rotating frames." reduces any objections to use of the third law in a rotating frame to a quibble over the reaction of non-existent sources to fictitious forces. SB Harris has commented on this point in this discussion.

I just see no traction for Paolo's objections, and am at a loss to see how they impact the article. Brews ohare (talk) 18:28, 8 July 2008 (UTC)


 * Neither of the cited books use the phrase "Newton's laws for inertial frames". I would object to this particular phrase, for the exact reason that Paolo states in his edit summary. I see no disagreement between this objection and the books. The quote "Treat fictitious forces like real forces, and pretend you are in an inertial frame" is a good one, and should be included (with attribution) in either this article or in fictitious force. Note that they don't say "Newton's laws are valid" or anything equivalent to that, because it is not true that every force has an associated reaction force. --PeR (talk) 19:40, 8 July 2008 (UTC)


 * Hi PeR: No problem with the statement quoted: "Treat fictitious forces like real forces, and pretend you are in an inertial frame". I have added this quote in the introduction. I am not sure why the phrase "Newton's laws for inertial frames" comes up: the sentence in the article is "[Fictitious forces] do not appear in Newton's laws of motion when these laws are applied in an inertial frame of reference." It does not say this, but it might be extended to suggest that Newton's laws can be used in a non-inertial frame if fictitious forces are introduced. But, if you accept the sentence Treat fictitious forces like real forces, and pretend you are in an inertial frame; doesn't this last sentence mean exactly: Use Newton's laws with added fictitious forces for the non-inertial frame? I get the impression that you are on both sides of this issue.
 * As for "every force has an associated reaction force", clearly the exception to that rule has been clearly enunciated? Below is the article:
 * However, because fictitious forces acting on an object do not originate from the action of other objects, there is no originating object to experience an associated reaction force: a violation of Newton's third law. This specific violation is a curiosity of fictitious forces. Newton's third law applies in all other respects even in rotating frames.
 * Do you have any issue with this paragraph? Brews ohare (talk) 22:39, 8 July 2008 (UTC)


 * Well, yes, I do have an issue with that paragraph. It fails miserably on the Flesch-Kincaid Readability Test. So do many paragraphs in this article, often because they have been lengthened as a consequence of hair splitting discussions, such as the one on the definition of "exist", or whether the term "Newton's laws" should be interpreted as "the laws, as formulated by N." or "the laws, as formulated in modern textbooks".)


 * I don't think I'm on both sides of the issue, because I think it is a non-issue, and therefore it doesn't have sides. In my opinion, there is absolutely no point trying to convince the other editors on this article about the definition of one term or another. It's the readers' interpretations that matter. Look at the textbooks you cite. They do a good job of explaining the issue, without requiring detailed definitions of the terms discussed here, and while keeping a reasonable readability index. --PeR (talk) 09:56, 9 July 2008 (UTC)
 * Alas, alack. A camel is a horse designed by a committee. The Flesch-Kincaid Readability scores for two wordings are shown below:


 * Fictitious forces do not originate from other objects. Therefore, there is no originating object to experience a reaction force. Absence of a reaction violates Newton's third law. This specific violation is a curiosity of fictitious forces. Newton's third law applies in all other respects, even in rotating frames. Ease=41.9 Grade=9.7


 * However, because fictitious forces do not originate from other objects, there is no originating object to experience an associated reaction force: a violation of Newton's third law. This specific violation is a curiosity of fictitious forces. Newton's third law applies in all other respects, even in rotating frames. Ease =30.2 Grade level= 13


 * As you can see, adding some punctuation and subordinate clauses is frowned upon in this index. I don't think the version with better score is better written myself. Brews ohare (talk) 14:15, 9 July 2008 (UTC)

Inertial frames
It is not the role of the the third law to distinguish inertial frames from others. That is accomplished by the principle of equivalence of inertial frames, which is to say:see Einstein
 * The special theory of relativity is based upon the following postulate, which is also satisfied by the mechanics of Galileo and Newton.
 * Postulate of Relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws also hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.

This statement from the Special Theory is a generalization from Newton's laws of mechanics to all physical laws, but is an implication of Newton's laws so far as mechanics is concerned. It may be that further discussion of this point is needed. At present it comes up in the article where it says that fictitious forces do not exist in inertial frames. The example of rotating spheres also emphasizes this point. The idea is that fictitious forces change from frame to frame (and disappear altogether in inertial frames) so they do not satisfy the above Postulate of Relativity. Brews ohare (talk) 19:09, 8 July 2008 (UTC)

I have added a paragraph to improve upon this discussion of inertial frames. Brews ohare (talk) 20:30, 8 July 2008 (UTC)

Euler force
I just commented out the following sentence from the intro:

When a particle undergoing general planar motion is viewed from its local frame, which is attached to the particle and aligned with its path, no Coriolis force acts on the particle (the velocity of the particle in its own frame is zero); the only fictitious forces are a centrifugal force normal to the path and a tangential Euler force related to changes in speed of the particle along its path.

I had modified it for style from its earlier version:

For general planar motion, viewed from a local frame, attached to the particle and aligned with its path, there is no Coriolis force (the velocity of the particle in its own frame is zero), and only a centrifugal force normal to the path and a tangential Euler force related to changes in speed of the particle along its path.

Honestly, I had never heard of an Euler force before this article, but the sentence doesn't seem right, and it is not supported by references. What about a particle undergoing uniform acceleration in a straight line? No centrifugal force, and, as I read the definition of Euler force, none of that either. Rracecarr (talk) 15:17, 9 July 2008 (UTC)


 * Good revision.
 * According to local frame the acceleration is
 * $$ \mathbf{a}(t) = \frac{dv}{dt} \mathbf{u_t}(s) - \frac{v^2}{\rho}\mathbf{u_n}(s) \ $$
 * which refers the motion to the osculating circle of radius ρ. For a straight line, the radius of curvature is infinite. So the centripetal force in 1/ρ is zero (the centrifugal force is the negative of this, because F = 0 = Ffict + FCentripetal). The normal straight-line acceleration is the first term. It can be interpreted as the Euler force for infinite radius of curvature, as a kind of limiting case. To establish this terminology, we can look at circular motion, where speed is v = ωR and the Euler force is R dω/dt = dv/dt = ds/dt tangential to the path.
 * I'd suggest reinstating your revision above. I think it is a good thing to point out there are more than simple frames that rotate around fixed axes and that the fictitious forces vary with the type of frame, not just its angular rate of rotation. Maybe a more elaborate discussion of this issue is needed? For example, what is the generalization to Euler angles? Brews ohare (talk) 15:38, 9 July 2008 (UTC)


 * I see that straight line acceleration can be thought of as angular acceleration in the limit as the radius goes to infinity. I hadn't thought of that.  However, the article on Euler force says it arises from changes in the rate of rotation of a reference frame, which could lead people to believe that if the rotation rate of the reference frame is identically zero, there is no fictitious force.  I think this should somehow be clarified if the sentence goes back in.  Rracecarr (talk) 16:04, 9 July 2008 (UTC)


 * Yes, I see. It is not this addition to Centrifugal force that has to be changed however. The Euler force article is grossly oversimplified and misleading. Brews ohare (talk) 16:16, 9 July 2008 (UTC)

Introduction is lengthy and not focussed on centrifugal force
I appreciate the enthusiasm and expertise of this team. However, in my opinion, the introduction in the last days became too lengthy (it was already unusually long about a week ago). For instance, IMO the interesting quotation "Treat the fictitious forces like real forces, and pretend you are in an inertial frame" does not belong in this introduction, but in some part (not necessarily the introduction) of the article on fictitious forces. Also, this sentence is either unclear or obvious: "this specific violation is a curiosity of fictitious forces. Newton's third law applies in all other respects even in rotating frames". In all other respect? What do you mean? If you mean that real forces exist in non-inertial frames as well, this information is already given before.

I agree with PeR: these edits reflect into the article some parts of our hair splitting discussions. And this is done even before these discussions reach a conclusion. The main purpose of hair splitting discussions is to avoid misleading terminology, cut questionable sentences, make the article clearer, reach an agreement about style, not to impose explicit reference to the points on which we eventually agree. Paolo.dL (talk) 16:06, 9 July 2008 (UTC)


 * It is kind of you to appreciate the team. However, the complications of this article mainly stem from the inability of the team to understand each other, leading to unnecessary verbiage and elaboration. I suspect that attempts to clean up these excesses will simply repeat the same process of hair-splitting.
 * Perhaps movement of some of the stuff in the intro to a new paragraph or two would help? Brews ohare (talk) 16:20, 9 July 2008 (UTC)


 * Perhaps you refer to other sentences. Anyway, the article cannot be used to end or prevent discussions. As for the above-mentioned two sentences, I propose to just remove them from this article, not due to previous discussions, but because:
 * both of them are not needed here (although the first is needed elsewhere), and
 * the second is unclear (and if I can understand its meaning, also redundant). Paolo.dL (talk) 19:27, 9 July 2008 (UTC)


 * I was suggesting some global changes. As for the two items you have selected for deletion, I could agree that they might go elsewhere in the article, but not that they should be deleted. I also fail to see what is unclear about the second item. Maybe you could propose how you understand them, or what questions they leave in your mind? In particular, I feel that the bare statement "However, because fictitious forces do not originate from other objects, there is no originating object to experience an associated reaction force: a violation of Newton's third law." leaves the reader wondering whether the third law is violated altogether in a rotating frame. Hence, the reassurance: "This specific violation is a curiosity of fictitious forces. Newton's third law applies in all other respects, even in rotating frames." Brews ohare (talk) 19:40, 9 July 2008 (UTC)


 * I interpret it as follows:
 * "violation is a curiosity of fictitious forces" says that it is specific to fictituous forces (this would be very redundant information)
 * the peculiar use of the word "curiosity" probably means that in your opinion this violation is a "quibble" (and this would be an irrelevant and questionable point of view).
 * "Newton's third law applies in all other respects even in rotating frames" uses vague language to mean that it applies to non-fictitious forces (this would be also very redundant information).
 * Waiting for comments by other editors. Paolo.dL (talk) 20:02, 9 July 2008 (UTC)


 * The word curiosity in this context means only something strange, interesting and unusual. That to distinguish it from encounters with other forces. Redundancy can aid clarity. Brews ohare (talk) 20:26, 9 July 2008 (UTC)


 * Redundancy is needed only when you are not clear the first time you explain a concept. And you should always be clear the first time. In this case, the concept is simple and perfectly explained in the previous sentences. On the contrary, the redundant sentence is not clear, as I already explained above. Paolo.dL (talk) 22:09, 11 July 2008 (UTC)

Changed paragraphing
I've tried shortening the introductory portion by introducing new paragraphs. No change of content. Just organization. See what you think. Brews ohare (talk) 23:09, 9 July 2008 (UTC)


 * You probably mean you introduced new sections and subsections. There are now at least two sections and sentences everywhere which deal generically with fictitious forces. This is not the article about fictitious forces. Perhaps, it is a good idea to have a section in this article about fictitious forces. But just one (with reference to the main article)! In my opinion, the other sections should just focus on centrifugal force. I also suggest you to check whether the article on fictitious forces contains the same information or not.
 * The last paragraph in the intro is a mess. You can do much better. Paolo.dL (talk) 22:33, 11 July 2008 (UTC)


 * Centrifugal and Coriolis forces often appear together, and some statements about centrifugal force actually apply to all fictitious forces. So it seems (i) hard to avoid including some other fictitious forces, and (ii) unnecessarily restrictive to make particular statements about centrifugal force that are more generally valid. Brews ohare (talk) 00:01, 12 July 2008 (UTC)