Talk:Centrifugal force (rotating reference frame): Difference between revisions

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	== The condition "does not exist in an inertial frame" doesn't fit the objectives of physics ==

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	] added a comment to an existing post, way at the top of this talk page. I copy ]'s comment here: <br>
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	: The scope of this article extends beyond the first month of high school physics. What high school physics teachers should say is "The centrifugal force does not exist ''in an inertial frame of reference''". But then they would have to explain what a non-inertial frame of reference is, and that is usually saved for the university courses. --] 09:02, 11 January 2007 (UTC)
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	The condition "does not exist in an inertial frame" is blurry, and it does not qualify as a physics statement. Physics is about the entities that are frame-independent. That is: independent from the way we assign numbers to certain states. For example, for temperature there is the scale of Fahrenheit and there is the scale of Celsius. Each scale assigns different numbers to the melting point of ice and the boiling point of water, and this difference is irrelevant for physics considerations. Calculations can be interconverted between units of Fahrenheid and units of Celsius. Likewise, calculations can be interconverted from mapping motion in an inertial coordinate system or a rotating coordinate system. Either way, inertia exists, independent of how a particular motion is mapped. Inertia exists, and when an object is forced into non-inertial motion, the object's inertia manifests itself.
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			== Not to be confused with ==
	This is a matter of principle: the building blocks of physics theories are entities that are independent of the way that motion happens to be mapped.

			There are various warnings not to confuse various forces: ], ], ], ]. There is however no discussion of the distinction between these various phenomenon. --] (]) 20:46, 2 July 2012 (UTC)
	Summary: <br>
	Independent of whether motion is mapped in a inertial coordinate system or in a rotating coordinate system, one can recognize the role that inertia of objects is playing in the physics taking place. What teachers should teach is that inertia exists, and how it plays a part in physics taking place. --] \| ] 13:50, 11 January 2007 (UTC)

			== More properly an effect than a force? ==
	:: Cleonis, you and I have iterated this discussion ad nauseam already on my talk page and in other places. I agree with everything that you say above. Fictitious forces do not exist in the sense of fundamental interactions, and often physics teachers don't explain inertia in the best way.
	:: However, the question was whether the page should be replaced with a short text referring readers to the centripetal force page, because of what the anon's physics teacher had said. This I disagree with. The ''concept'' of fictitious forces does exist, as a useful mathematical tool, when dealing with non-inertial reference frames. As an analogy, ]s do not exist from a certain philosophical perspective, but the ''concept'' of negative numbers is very useful in mathematics, and hence it is a good idea to keep that page as it is rather than replacing it with a text stating that they don't exist, and then pointing readers to the ]s page. The same is true for this page. --] 12:21, 12 January 2007 (UTC)

			I suspect that the lead would be better if reworked à la N.M.J. Woodhouse, who writes (p. 7) in his ''Special Relativity'' (Springer-Verlag, 2003),
	:::I suppose this relates to ambiguity in the verb 'to exist'. Often in physics a discussion may arise as to whether something actually exists. For example, from a human perspective, we may well get the impression that there is some cold-suction action, where a particular cold actively ''sucks'' warmth away. From a physics point of view, there does not exist an active suction from cold being exerted on warm regions. So I prefer to be very cautious with the verb 'to exist'. If a calculation would be set up in which a fictitious cold-suction-force is applied, I'd still emphasize that no cold-suction force exists. In the case of applying a mathematical tool, there is no need to assert that it "exists" (inviting the ambiguity of that verb), it suffices to assert that the tool is regularly applied, and that it is very useful.
			:"In problems where the rotation matters, for example in the analysis of Foucault's pendulum, it is helpful to treat a terrestrial frame as if it were intertial, but to introduce correction terms, the 'fictitious' centrifugal and Coriolis forces, to take account of the rotation. But these are not real forces, and the frame is not really inertial."
	:::Ambiguity cannot be eliminated entirely, but every opportunity where it is easy to avoid ambiguity should be used. --] \| ] 14:21, 12 January 2007 (UTC)
			Indeed, even ] is a redirect to ''Coriolus effect'', and that article makes it clearer than this one does that the force is only apparent. I'd have just changed it myself, but wondered if there were a good argument for retaining the nonparallelism of treating one of the two forces as though it were somehow less fictitious than the other.—] (]) 20:57, 19 February 2013 (UTC)

			:My two cents here - I think there is a distinction between "effect" and "force" in these instances. My feeling from the literature that I've read is that the effect refers to the apparently anomalous deflection of the path of a particle while the force is the pseudo-force or fictitious force that is introduced to explain the deflection. As for an argument for retaining the nonparallelism, this is what we find in the literature, ie the terms "Coriolis effect" and "Coriolis force" are used with about the same frequency and sometimes it seems inter-changeably. The choice also seems to be dependent on the context - in meteorology we find "Coriolis effect" (and my guess this is true for the everyday person), while in the physics literature "Coriolis force" is more common. I don't think the same can be said for "centrifugal force"/"centrifugal effect". Just to get a general idea of how common the terms occur in the literature I searched for each phrase in google books:
	:::: Heat transfer works just the same with signs reversed. In fact, on the temperature scale which ] originally used, increasing numbers represented colder temperatures. Absolute temperature is a rather recent invention.
			:* Coriolis effect : ~44,500
	:::: One could say that the centrifugal force does not exist in the same sense that "cold" does not exist. But I think you're right in that one probably does best in avoiding the word "exist" altogether. --] 21:38, 13 January 2007 (UTC)
			:* Coriolis force : ~138,000
			:* Centrifugal effect : ~16,700
			:* Centrifugal force : ~1,260,000
			:That's almost two orders of magnitude difference for centrifugal between effect and force, while for Coriolis the two are roughly equal (okay, a factor of about 3 but less than an order of magnitude). So imo I don't care whether the other article is "Coriolis effect" or "Coriolis force", but I strongly favor keeping this one as "centrifugal force" per the usage frequency in the literature. That being said, if the intro needs to be clearer on it being a fictitious force then that should be fixed. --] (]) 05:33, 20 February 2013 (UTC)

			:I agree with FF. If you want it more parallel, go the other way. And I'd avoid the notion of "only apparent", since we already have a well-define notion of "fictitious force" that says exactly what it is. ] (]) 05:49, 20 February 2013 (UTC)
	::::: So do we have a consensus to rewrite or remove all assertions that such-and-such concept does or does not "exist"? ] 00:49, 14 January 2007 (UTC)

			== Acceleration Derivation ==
	:::::: It does seem that there is such a consensus; asserting the usefulness, without using the verb 'to exist'. For the example of heat transfer it means that it would be asserted that what exists (according to our theories) is 'entropy'; heat will flow from the warmest regions to any less warm regions. --] \| ] 11:17, 14 January 2007 (UTC)

			In the derivation section, I'm noticing that the last two lines of equations in the "acceleration" section do not seem to follow from one another. When I evaluate the d/dt(+w x r) term in the next to last line, it does not give the factor of two in front of the Coriolis term. I believe the error is leaving out part of the first derivative operator: that is, in that equation, instead of the operator "d/dt" we should have "d/dt + w x" as the operator. (also see the rotational reference frame wiki page for that derivation, in which the derivation correctly gets the factor of two into the Coriolis term)
	==Centrifugal Force does not exist==
			I would just go ahead and add it, except I'm not at all familiar with the proper coding for inserting equations into wikipedia, and am very new here in general <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 02:13, 6 March 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
	I learned that in the first month of high school physics. The length and scientific precision of this article suggests the veracity of this falsehood. This article should explain where the misconception comes from, why it is incorrect, and then point readers to the centripetal force page.

			: It is correct. Don't forget that
	: The scope of this article extends beyond the first month of high school physics. What high school physics teachers should say is "The centrifugal force does not exist ''in an inertial frame of reference''". But then they would have to explain what a non-inertial frame of reference is, and that is usually saved for the university courses. --] 09:02, 11 January 2007 (UTC)
			::<math>\frac{\operatorname{d}\boldsymbol{r}}{\operatorname{d}t}=\left + \boldsymbol{\omega} \times \boldsymbol{r}\ ,</math>
			:and of course likewise
			::<math>\frac{\operatorname{d}}{\operatorname{d}t} \left=\left + \boldsymbol{\omega} \times \left \ ,</math>
			:so that is where the second term comes from.
			:'''Note''' - this derivation could need a source. - ] (]) 12:47, 6 March 2013 (UTC)

			== It's the rotation of the ''direction of the velocity vector'' that matters, not of the frame. ==
	Centrifugal repulsion exists radially between any two objects that possess mutual tangential motion. That is an indisputable fact. It manifests itself if we try to restrain it. Maxwell used centrifugal force in the hydrodynamics of part I of his 1861 paper 'On Physical Lines of Force' in order to account for electromagnetic and ferromagnetic repulsion. He also used it to account for diamagnetic attraction and repulsion in what was effectively the Archimedes' Principle of magnetism.

			Yep. We have here a misleading article title, and misleading wording that implies that a ''reference frame'''s rotation results in centrifugal force/pseudoforce. Rather, it's the ''centripetal acceleration'' of the frame (or object) that results in such forces. The centripetal acceleration of the frame (stated in an inertial frame) is proportional to the rate of change of the ''direction of the velocity vector'' (also stated in the same inertial frame). Thus, if the rate of rotation of anything matters, it's the rate of rotation of the direction of the velocity vector, ''not'' the rotation rate of the frame.
	I was also taught at university that centrifugal force does not exist. This false teaching is based on the simplistic argument that when we release an object that is being constrained to move in a circle, it will fly off at a tangent and not radially. In actual fact, it flies off both tangentially and radially. There can be no doubt that centrifugal force is a very real force but that it has been dropped out of modern physics. The Coriolis Force is also a real force that manifests itself in electromagnetism as '''F''' = q'''v'''X'''B'''. David Tombe 4th February 2007 (] 20:40, 3 February 2007 (UTC))

			I grant that, in most usual cases (such as ball-on-string), the most common frame is attached to the object (ball) and is also rotating along with the object. The rotation rate of the frame in these cases is the same as the rotation rate of the direction of the velocity vector, ''but that's only incidental''. It's the rate of change of the direction of the velocity vector that makes for the centrifugal forces here. If the frame was still attached to the ball, but was chosen to rotate at twice or three times the rate of the velocity vector, or if it was chosen to not rotate at all, it would not effect the magnitude of the centrifugal force, nor would it effect the actual direction of the centrifugal force. Such an independently-rotating frame would have different ''numbers'' representing the direction of the centrifugal force, but the actual direction (or magnitude) of the centrifugal force at any particular moment would not vary with rotation rate of the frame.
	== Centrifugal force in statics ==

			We should not muddle-together the ''movement'' of a frame (such as in a circle about a point) with ''rotation'' of the frame. They are two different things that can be independent. If we don't keep that in mind, it leads to fallacies.
	I originally created this section about a year ago as part of an attempt to make what the article now describes as "fictitious centrifugal force" its main topic and then explain how in limited cases the "reactive centrifugal force" also makes some sense. It appears that my point was rather poorly made, and that the section has survived to this day mainly because no subsequent editors have felt they understand it well enough to remove it. In the context of how the article looks now, I think the section is confusing and misplaced; I'd like to delete it all. Has anybody secretly grown so fond of it that they would complain if I did? ] 00:46, 14 January 2007 (UTC)

			] (]) 17:32, 31 May 2015 (UTC)
	:I think the opening sections already cover what is addressed in the section 'centrifugal force in statics', and that the opening sections do a better job.

	:Anyway, the scope of statics is objects that are in equilibrium. To test the load-bearing capacity of a suspension bridge, a large amount of heavy vehicles is parked halfway the length of the span of the bridge. Another part of testing a bridge is to find out whether winds can trigger an oscillation of some parts of the suspension bridge. That is dynamics. Calculations/modeling in statics do not involve inertia, calculations in dynamics do. --] \| ] 11:39, 14 January 2007 (UTC)

	:: So removed. For what it's worth, the intended relevance of "statics" was a situation where one wants to design a complex system that rotates (i.e. where all the constituent parts are supposed to follow the same constant rigid rotation) such as a centrifuge or a flywheel, and we must find out whether the various contact forces and internal stresses will suffice to supply the necessary centripetal forces. This can be done most easily in a rotating frame where nothing moves and the various shortcuts of statics are thus available, if only we add in artificial loads from the centrifugal force. ] 01:11, 17 January 2007 (UTC)

	::: Of course, in the case of rotation of solid bodies the analysis reduces to statics.

	::: Interestingly, it's quite rare that the analysis reduces to the statics case. For example, in the case of helicopter blades, a major concern is that when the rotating helicopter blade bends upwards, it's center of gravity moves closer to the rotation axis, resulting in an increase of the blade's velocity. More blade velocity gives more lift, which tends to increase the upward bending. When the frequency of the blades flapping up and down coincides with the rotation rate, this mechanism of self-reinforcing vibration can cause the helicopter blades to shatter. Rotor designs must incorporate dampening to dissipate the energy of vibrations. Any device with rotating parts is prone to developing self-reinforcing vibrations.
	::: Generally, what needs to be modeled is rotation with a variable rate of rotation. When a calculation is set up for helicopter blades with an oscillating rotation rate due to vibration, the coordinate system that will be used is a coordinate system with a ''constant'' rotation rate, hence the centrifugal term will be constant. The amount of reactive centrifugal force will oscillate, since the rotation rate of the blade oscillates. Whenever rotation is accompanied by vibration, the centrifugal term and the reactive centrifugal force are distinct.
	::: Summerizing: <br> Generally in using rotating coordinate systems, the centrifugal term and the reactive centrifugal force do not coincide, they coincide only when the rotating body can be considered vibration-free. --] \| ] 02:14, 17 January 2007 (UTC)

	== Maxwell on Real Centrifugal Force ==

	The reason that I deleted your insertion

	"It should be noted however that when proposing this 'hydrodynamic' description (that was built upon in work published in the seminal papers 'On Faraday's Lines of Force' and 'On Physical Lines of Force') Maxwell was not intending the fluid to be thought of as real:<ref>'On Faraday's Lines of Force', reprinted: The Scientific Papers of James Clerk Maxwell, Editor
	- W.D. Niven, Cambridge University Press 1890 Vol. I, p160 </ref>
	-
	- <blockquote>
	- It is not even a hypothetical fluid which is introduced to explain actual
	- phenomena. It is merely a collection of imaginary properties which may be
	- employed for establishing certain theorems in pure mathematics in a way
	- more intelligible to many minds and more applicable to physical problems
	- than that in which algebraic symbols alone are used.
	- </blockquote> "

	was because the web link for Maxwell's 1861 paper 'On Physical Lines of Force' was made available for anybody to read. Anybody reading part I of this paper would know that Maxwell believed absolutely in the reality of the fluid aethereal medium. To say otherwise is a total misrepresentation of the truth. You then finished with a quote but didn't tell us who made the quote.

	Maxwell was quite clear on the fact that a sea of aethereal vortices exists and that these vortices must be surrounded by electrical particles. If these vortices aren't real, and yet they explain the mechanics of magnetism, then what are they? Why would they be any less real than the elements of the periodic table? David Tombe 7th February 2007 (] 18:34, 7 February 2007 (UTC))

	: I went further than that and removed the entire section. To the best of my comprehension it tried to argue that the fact that Maxwell had an ether-dynamic interpretation of electrodynamics somehow implies that one must consider centrifugal force a ''fundamental'' force (except that it muddled the concept further by speaking about "real" forces, a word with a host of varying possible meanings) – a conclusion that mainstream physics unanimously rejects. In order for an argument otherwise to be relevant Misplaced Pages material, the very least we can accept is a solid citation showing that such an argument has been made in a respected peer-reviewed professional journal. (I might add that the major schism among editors of this article appears to be whether the "reactive" or the "fictitious" meaning of "centrifugal" is the most important, but ''neither'' of the camps would accept ''either'' of the concepts as describing a fundamental force). ] 22:40, 7 February 2007 (UTC)
	:: Oops, I misread the conclusion of the deleted section; one of the negations must have slipped me. My apologies for misrepresenting it. I still think that the section was confusing, of doubtful relevance and definitely out of place as early in the article as I found it, so I'll not self-revert – but if it were to be rewritten with a clearer emphasis about what the story can tell us about the ''centrifugal force'' concept and less emphasis on what Maxwell personally believed (or didn't) about the physical nature of the electromagnetic field, I might not be opposed to having it appear later in the article, after the basic concepts have been well presented. (This is not meant to contradict the ] policy, so proper sourcing would still be necessary). ] 22:58, 7 February 2007 (UTC)


	Maxwell's 1861 paper is highly relevant regarding the topic of centrifugal force. The original archive paper has been provided in the form of a pdf web link. The paper consists of four parts. Part I is the relevant hydrodynamical part.

	Maxwell operates on the basis that space is pervaded by a sea of tiny aethereal whirlpools. Maxwell does the mathematics for such a sea of whirlpools, and at equation (5) he arrives at an expression for some of the important aspects of magnetism. Central to this hydrodynamical analysis is the fact that centrifugal repulsion force acts between spinning objects.

	Anybody who has ever studied polar coordinates, knows that any two objects with a mutual tangential velocity will have a mutual radial repulsion which takes on the mathematical form of the centrifugal force. Maxwell uses this concept to show that ferromagnetic repulsion, electromagnetic repulsion, as well as diamagnetic repulsion and paramagnetic attraction can all be explained by focused centrifugal force in the equatorial plane of his sea of whirlpools.

	Unless you are a logical positivist, this ought to be conclusive evidence that centrifugal force is real and that the sea of aethereal vortices is also real.

	The 1861 paper is there to be read by anybody who can then make up their own mind.

	The reason that I deleted the extra insertion was because whoever made the insertion made it look as if it was part of the original article, and it had the effect of undoing the point. Whoever made that insertion was trying to have us all believe that Maxwell did not actually believe that the sea of whirlpools was real. The insertion was completely untrue and the matter can be easily checked out simply by reading the preamble of part I of Maxwell's 1861 paper. Had the person making the insertion simply stated that they themselves didn't consider Maxwell's sea of vortices to be real then that would have been a different matter. But they tried to put across the idea that Maxwell didn't believe it.

	Maxwell did believe it and he went to considerable pains to give a mechanical explanation of magnetism using the concept.

	But the key point as regards the principle topic 'Centrifugal Force' is that centrifugal force can explain magnetic repulsion. That is an indisputable fact. David Tombe 8th February 2007 (] 05:43, 8 February 2007 (UTC))

	: Two points. I did reference my quote as being from 'On Faraday's lines of Force' by Maxwell himself, Maxwell also refers the reader to this paper in 'On Physical Lines of Force'. Secondly Maxwell dropped this mechanical explanation in favour of a field description in 'A Dynamical Theory of the Electromagnetic Field' (A move towards Field descriptions is his real legacy), so I wonder how much he did believe it? What he did or did not believe is not for us to say, I was just illustrating that the point wasn't as clear cut as made out.

	Regarding: "If these vortices aren't real, and yet they explain the mechanics of magnetism, then what are they? Why would they be any less real than the elements of the periodic table?", that is an interesting point. The atomic model of a nucleus and electron shells, which the gives the arrangement of the periodic table it's logic, is just a model which fits the observables. One shouldn't really think of a particle orbiting a center - except that it's a handy tool for describing the situation (just as Maxwell's vortices). The reality of actually what these things are is not necessarily the same as the model used to describe them.

	I still think all this Maxwell stuff is an interesting afterthought on the topic of Centrifugal Force, it really should be relegated to the bottom of the article - most people will be looking for other information on this page.

	Richard Allen ] 13:29, 9 February 2007 (UTC)

	== Fictitious Centrifugal Force ==

	Every fictitious centrifugal force as viewed from a rotating frame of reference will correspond to a real centrifugal force. Mutual radial repulsion due to tangential velocity is an absolute fact, dependent only on the existence of a real frame of reference to give meaning to the tangential velocity.

	This is in contrast to fictitious Coriolis force. Fictitious Coriolis force is truly fictitious and it occurs only in a rotating frame of reference.

	The difference between fictitious centrifugal force and fictitious Coriolis force arises from the fact that centrifugal force is a radial deflection due to a tangential motion, whereas Coriolis force is a tangential deflection due to a radial motion. As such, a rotating frame of reference masks the cause of a real centrifugal force but leads to an apparent Coriolis force.

	In order to obtain a real Coriolis force we would need to have curled space. According to Maxwell's sea of molecular vortices, we ought to have curled space leading to a real Coriolis force. This is almost certainly the origins of the electromagnetic '''F''' = q'''v'''X'''B''' force, where '''B''' is related to the vorticity. David Tombe, 9th February 2007 (] 10:36, 9 February 2007 (UTC))

	: David - You are totally mistaken about the nature of centrifugal force. There is no radial repulsion at work, only inertia. The "force" the is felt by a object undergoing a forced rotation is actually a ''centripetal'' (or inwards directed) acceleration. So while it feels like you are being pushed outwards, in fact you are being accelerated inwards. Only inertia is needed to explain your wanting to go "outwards" in the accelerated frame of reference of the rotating object.

	: I hope that you find this explanation helpful. However, I must in any case kindly ask you to stop introducing misconceptions into Misplaced Pages. You may mean well, but in fact you are disrupting this encyclopedia. Please research your topic and be sure that you know what you are taking about before editing in Misplaced Pages in the future. --] \| ] 16:09, 9 February 2007 (UTC)

	Centripetal force is not relevant in this discussion. Centripetal force is only a 'requirement' force needed to accelerate an object in a circle. Centrifugal force is not specifically related to circular motion. Centrifugal force exists radially between any two objects in the universe that have got a mutual tangential velocity. I don't understand why you have such difficulty seeing this simple fact.

	In conjunction with the radially attractive force of gravity, centrifugal force leads to either elliptical motion, circular motion, parabolic motion, or hyperbolic motion depending on initial parameters.

	You misrepresented me above. I made it quite clear that we only feel centrifugal force when it is restrained, just as in the case of gravity. Ie. we feel the reaction surface that is pushing against it. I wasn't getting confused with centripetal force at all.

	You are completely wrong when you say that inertia is what causes the tendency to move outwards. The tendency to move outwards is a fundamental fact of the geometry of space which occurs when two objects possess mutual tangential velocity.

	If you think that the tendency to move outwards is caused by inertia, can you please tell me exactly what inertia is and how it causes this tendency to move outwards. I might then ask how inertia causes an object to vear to one side in the case of the sister Coriolis force.

	It strikes me that alot of the contributors to this article need to do an applied maths course in orbital mechanics.

	And yes, I was meaning well. I was trying to simplify the article for you because it appears to have been written by people who's qualifications are limited to having swung a bucket of water over their heads.

	Centrifugal force is always real. A rotating frame of reference cannot create a centrifugal force fictitiously that then proceeds to bump somebody against the inside of their car door. David Tombe 9th February 2007 (] 17:28, 9 February 2007 (UTC))

	*The centrifugal force is ficticious - all kinds of ] will confirm this, and none will not. Not only that, but ] allows us to include uncontraversial stuff that anyone can verify - ''grapes are a fruit'' doesn't require sourcing, neither does ''the Centrifugal force is ficticious''. Beyond which, other factual errors (like requiring two objects to have a centrifugal force, when a single object will experience it (try rotating a bucket of water) cast unsourced assertions into serious doubt. ] 18:11, 9 February 2007 (UTC)

	:The point is that this is an article in the wikipedia, and hence is subject to the wikipedia's policies. There's no notable point of view that you have been able to quote David to support these additions, and thus it cannot stay in this article, whether it is right or wrong.] 18:19, 9 February 2007 (UTC)

	:: I agree with WilyD and Wolfkeeper. You have to make a case for your viewpoint, and show that it is held by others and not just yourself. Misplaced Pages is dedicated to documeenting human knowledge. It therefore makes no different if you are right of wrong (although I have no qualms about saying that you are totally wrong). Instead what matters are 1) your disagreement with commonly held scientific opinion, and 2) a total lack of any evidence that it is held by a notable group of people. --] \| ] 19:45, 9 February 2007 (UTC)

	What evidence do you need to show that two objects with mutual tangential motion possess a mutual radial repulsion? It is a self evident geometrical fact. It is basic undergraduate level applied mathematics. Take a position vector and differentiate it twice with respect to time. You will arrive at a general acceleration vector that is split into two components. The radial component contains a direct component and a centrifugal component. The centrifugal component is equal to the velocity squared divided by the distance. Then there is the tangential component that is divided into the Coriolis acceleration and the angular acceleration.

	This is not controversial theory. I'm sorry to see that WilyD felt it necessary to mention the bucket of water. This tends to confirm exactly what I said above. Have any of you guys taken an applied maths course in vector algebra or orbital mechanics, or are your qualifications limited to having swung a bucket of water over your heads?

	Why is it that a very simple topic such as centrifugal force always has to be studied in conjunction with rotating frames of reference? Why do we have to go into that hall of mirrors? It opens up endless permutations. We could talk about the fictitious effects on a real motion as viewed from a rotating frame of reference, or we could talk about the fictitious effects on a fictitious motion due to viewing the object from a rotating frame of reference. We could talk about a fictitious circular motion being caused by a fictitious centripetal force which is itself caused by a fictitious outward centrifugal force in tandem with a fictitious inward Coriolis force that is twice as strong. But why bother?

	We can sit and debate whether the man is flung against the inside of the car door, or whether the car door comes against the man.

	The reason that I simplified the article was because it was an incoherent confusion of real centrifugal force and fictitious centrifugal force.

	I really don't know what makes WilyD so sure that centrifugal force is never real. I would suggest to WilyD that before he goes around censoring left right and centre, that he should think long and hard about that bucket of water that he mentioned. The water above his head defies downward gravity. I don't see anything fictitious about that. The question only remains to quantify this effect. It is clearly an exclusive product of the fact that the water has got tangential motion relative to the fulcrum. There is no need to introduce inertia. It is a purely kinematical fact.

	Have any of you censors ever actually studied planetary orbital theory? The haste with which you deleted my references to hyperbolic, parabolic, and elliptical motion suggests to me that you all possess a fear of the unknown. David Tombe 10th February 2007 (] 03:03, 10 February 2007 (UTC))

	: David Tombe wrote above:
	:: ''Take a position vector and differentiate it twice with respect to time. You will arrive at a general acceleration vector that is split into two components. ... a direct component and a centrifugal component.''
	: I strongly advise taking that same position vector but expressing it in ] instead of ]. In that case you will end up with second derivatives of zero! The truth is that your "general acceleration vector" arises from the ]s for the polar coordinate system. Inertial motion, which is the local extension of a path through space and time in the same direction at each event in the particle's path, naturally occurs along geodesic paths. If the Cartesian coordinate system is being used in Newtonian physics, this is tanatmount to the particle continuing "in the same direction" as originally stated by Newton. However, if other coordiante systems are used, then the matter of what the geodesics are has to be taken into account. In the process of doing so, your "real centrifugal force" just plain vanishes.

	: As for the motion of the planets, you need to learn about Newton's theory of ], which is an inward directed force (effectively a certripetal force) that keeps the planets in orbit. Beyond that, please realize that applied math is all fine and dandy, but only if you apply it properly. --] \| ] 04:44, 10 February 2007 (UTC)

	Yes, Newton's inverse square law force is an inwardly directed radial force. In the special case of a circular orbit, Newton's inverse square law force does indeed act as the centripetal force.

	Now have you ever looked at the general situation for elliptical, parabolic, and hyperbolic orbits? The method is to consider the total forces involved. The tangential components of the general acceleration vector vanish because of Kepler's law of areal velocity (ie. zero curl). This leaves us with only the two radial components, ie. the Newtonian inverse square law force inwards, and a centrifugal force outwards. The centrifugal force is equal to the tangential speed squared, divided by the distance between the two planets. We are left with a complicated differential equation of which the solution is either an ellipse, a parabola, or a hyperbola, depending on initial parameters.

	If the gravitational force is very weak compared to the centrifugal force, then we will have hyperbolic motion. If the gravitational force is negligible, then that hyperbola effectively becomes a straight line.

	It is this straight line solution that we see around us all the time. Every two objects with mutual tangential velocity will possess a mutual radial repulsion. In our everyday cartesian/Euclidian view of things, this will show up as straight line motion. However, if we adopt the broader spherical universal vision, then those straight lines will actually be highly eccentric hyperbolae.

	At the end of the day, the radial expansion between two objects moving tangentially is a reality irrespective of whatever coordinate system we use. It is the cause of pressure in a gas.

	Let's now, for the sake of argument, enter into your rotating frame of reference, which according to the experts is the home of fictitious centrifugal force, and the only centrifugal force. Let's look at a centrifuge. The centrifuge throws objects to the edge and it even accords with Archimedes' Principle. That is a very real effect. The tangential motion that causes this effect is masked out by the rotation of the centrifuge, and hence from the perspective of the centrifuge, it becomes obvious that we now have a radially outward force. Mathematically, this centrifugal force is built into the transformation equations.

	But that is no reason to deem the force as 'fictitious'. That radial motion is a reality no matter what frame of reference we look at it from. As soon as the centrifuge begins to spin, a tangential motion is set up between the particles and the fulcrum, and a radially outward acceleration occurs.

	Not so with the Coriolis force. It is only fictitious. This is because the circular motion of the rotating frame of reference actually yields a tangential effect, whereas the radial effect of the centrifugal force has to be there anyway. The rotating frame of reference cannot create a radial effect.

	I would have liked to have been able to talk about situations where the Coriolis force becomes real, but sadly it seems that that would be a forbidden topic because it involves concepts, such as curled dynamic liquid space, that have not been considered by the ruling physics party. David Tombe 10th February 2007 (] 06:40, 10 February 2007 (UTC))

	:I'm enclosing a Misplaced Pages link on 'Orbital theory'. If we scroll down to the section entitled "Analysis of orbital motion" and look at the first equation, we will see that the last term on the right hand side is the centrifugal force. This is the general equation for orbits in a gravitational field and we can clearly see that centrifugal force is involved as a real effect.

	Yet I am being accused of breaching Misplaced Pages policy by using unorthodox ideas. The accusations are being made by people who clearly haven't got the first clue about orbital theory. WilyD is going around arrogantly censoring everything that I write and claiming it to be pseudoscientific blabber. WilyD storms in claiming that all sources will confirm that centrifugal force is fictitious. Yes, a physics department might confirm it, but an applied maths department might not. It is clearly a contentious issue that hasn't been resolved. It ill becomes WilyD to assume that it has already been resolved in favour of 'fictitious only'.

	This 'Orbital Theory' web link confirms what I have been saying all along. There is another school of thought which knows that centrifugal force is real. The right hand doesn't know what the left hand is up to. If anybody is in doubt, then please show me a differential equation that leads to conic section orbits, but doesn't involve the centrifugal force.

	It is time that WilyD was told to stop the vandalism. David Tombe 10th February 2007 (] 07:46, 10 February 2007 (UTC)).

	: As far as I can see, there is only one vandal here, namely the anon who calls himself "David Tombe". ] 14:22, 10 February 2007 (UTC)

	:: Also, please note that you currently seem to be in violation of the ]. Continuing in this fashion is rather likely to get you blocked. ] 14:32, 10 February 2007 (UTC)

	Count Iblis and Henning Makholm. You panic at the sight of the words ellipse, parabola, and hyperbola. You obviously haven't got a clue about planetary orbital theory. The centrifugal force is one of the input components of the differential equation which leads to these conic solutions. Why not begin by looking at the Misplaced Pages article on 'Orbital Theory'. . Or look at equation (15) in this St. Andrew's University web link David Tombe 10th February 2007 (] 14:43, 10 February 2007 (UTC))

	== Inertia ==

	Hi Edward. I was reading a little bit about your background and I see that General Relativity is your speciality. This means that you would be well into debates on topics like inertia and the equivalence between gravitational mass and inertial mass. At the moment however, I would prefer to concentrate on the issue regarding whether or not inertia is actual relevant in centrifugal force, irrespective of what inertia actually is, or how it could be relevant.

	I can already see that you are influenced by the Newtonian concept that a body continues in a straight line unless acted upon by a force. I certainly don't disagree with this fact.

	However I don't adopt the Newtonian concept that this motion is explained by inertia. I adopt an attitude more akin to that of Einstein, but without the special relativity. I see space itself as determining the motion of particles. Just like Boscovich, I believe that it can all be explained kinematically without any involvement of force or inertial mass. However, I'm satisfied enough with Newton's definition of force and mass but I don't think that they are necessary when analyzing planetary orbital motion.

	From what I can see, mutual tangential speed leads to radial repulsion and that is a geometrical fact. Inertia doesn't come into it. David Tombe 10th February 2007 (] 06:59, 10 February 2007 (UTC))

	== Edit War ==

	An edit war has been declared so I will not revert again for the meantime. I wish however to draw attention to one of the first paragraphs in the original edit. I will quote it here,

	''"A real or "reactive" centrifugal force occurs in reaction to a centripetal acceleration acting on a mass. This centrifugal force is equal in magnitude to the centripetal force, directed away from the center of rotation, and is exerted by the rotating object upon the object which imposes the centripetal acceleration. Although this sense was used by Isaac Newton, it is only occasionally used in modern discussions. "''

	This is an appalling inaccuracy. It implies that centrifugal force is only something that occurs in conjunction with centripetal force, and that it is confined to circular motion situations.

	I have tried to explain that centrifugal force has got a much wider application and that it acts in planetary orbital theory to yield, parabolic, elliptical, and hyperbolic orbits. This raw fact appears not to have been to the liking of the guardians of this article. Am I to conclude that you are all at best physicists who have never done the orbital mechanics courses in applied mathematics?

	The original article was very schoolboyish. I would hope that you would all go away and study the differential equation for a planetary orbit and take note of the presence of a very real centrifugal force. David Tombe 10th February 2007 (] 15:32, 10 February 2007 (UTC))

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Not to be confused with

There are various warnings not to confuse various forces: Centrifugal force, Reactive centrifugal force, Centripetal force, Centrifugal force (rotating reference frame). There is however no discussion of the distinction between these various phenomenon. --Kvng (talk) 20:46, 2 July 2012 (UTC)

More properly an effect than a force?

I suspect that the lead would be better if reworked à la N.M.J. Woodhouse, who writes (p. 7) in his Special Relativity (Springer-Verlag, 2003),

"In problems where the rotation matters, for example in the analysis of Foucault's pendulum, it is helpful to treat a terrestrial frame as if it were intertial, but to introduce correction terms, the 'fictitious' centrifugal and Coriolis forces, to take account of the rotation. But these are not real forces, and the frame is not really inertial."

Indeed, even Misplaced Pages's own article on Coriolis forces is a redirect to Coriolus effect, and that article makes it clearer than this one does that the force is only apparent. I'd have just changed it myself, but wondered if there were a good argument for retaining the nonparallelism of treating one of the two forces as though it were somehow less fictitious than the other.—PaulTanenbaum (talk) 20:57, 19 February 2013 (UTC)

My two cents here - I think there is a distinction between "effect" and "force" in these instances. My feeling from the literature that I've read is that the effect refers to the apparently anomalous deflection of the path of a particle while the force is the pseudo-force or fictitious force that is introduced to explain the deflection. As for an argument for retaining the nonparallelism, this is what we find in the literature, ie the terms "Coriolis effect" and "Coriolis force" are used with about the same frequency and sometimes it seems inter-changeably. The choice also seems to be dependent on the context - in meteorology we find "Coriolis effect" (and my guess this is true for the everyday person), while in the physics literature "Coriolis force" is more common. I don't think the same can be said for "centrifugal force"/"centrifugal effect". Just to get a general idea of how common the terms occur in the literature I searched for each phrase in google books:

Coriolis effect : ~44,500
Coriolis force : ~138,000
Centrifugal effect : ~16,700
Centrifugal force : ~1,260,000

That's almost two orders of magnitude difference for centrifugal between effect and force, while for Coriolis the two are roughly equal (okay, a factor of about 3 but less than an order of magnitude). So imo I don't care whether the other article is "Coriolis effect" or "Coriolis force", but I strongly favor keeping this one as "centrifugal force" per the usage frequency in the literature. That being said, if the intro needs to be clearer on it being a fictitious force then that should be fixed. --FyzixFighter (talk) 05:33, 20 February 2013 (UTC)

I agree with FF. If you want it more parallel, go the other way. And I'd avoid the notion of "only apparent", since we already have a well-define notion of "fictitious force" that says exactly what it is. Dicklyon (talk) 05:49, 20 February 2013 (UTC)

Acceleration Derivation

In the derivation section, I'm noticing that the last two lines of equations in the "acceleration" section do not seem to follow from one another. When I evaluate the d/dt(+w x r) term in the next to last line, it does not give the factor of two in front of the Coriolis term. I believe the error is leaving out part of the first derivative operator: that is, in that equation, instead of the operator "d/dt" we should have "d/dt + w x" as the operator. (also see the rotational reference frame wiki page for that derivation, in which the derivation correctly gets the factor of two into the Coriolis term) I would just go ahead and add it, except I'm not at all familiar with the proper coding for inserting equations into wikipedia, and am very new here in general — Preceding unsigned comment added by 222.221.253.76 (talk) 02:13, 6 March 2013 (UTC)

It is correct. Don't forget that

{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}=\left+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ ,

and of course likewise

{\frac {\operatorname {d} }{\operatorname {d} t}}\left=\left+{\boldsymbol {\omega }}\times \left\ ,

so that is where the second term comes from.

Note - this derivation could need a source. - DVdm (talk) 12:47, 6 March 2013 (UTC)

It's the rotation of the direction of the velocity vector that matters, not of the frame.

Yep. We have here a misleading article title, and misleading wording that implies that a reference frame's rotation results in centrifugal force/pseudoforce. Rather, it's the centripetal acceleration of the frame (or object) that results in such forces. The centripetal acceleration of the frame (stated in an inertial frame) is proportional to the rate of change of the direction of the velocity vector (also stated in the same inertial frame). Thus, if the rate of rotation of anything matters, it's the rate of rotation of the direction of the velocity vector, not the rotation rate of the frame.

I grant that, in most usual cases (such as ball-on-string), the most common frame is attached to the object (ball) and is also rotating along with the object. The rotation rate of the frame in these cases is the same as the rotation rate of the direction of the velocity vector, but that's only incidental. It's the rate of change of the direction of the velocity vector that makes for the centrifugal forces here. If the frame was still attached to the ball, but was chosen to rotate at twice or three times the rate of the velocity vector, or if it was chosen to not rotate at all, it would not effect the magnitude of the centrifugal force, nor would it effect the actual direction of the centrifugal force. Such an independently-rotating frame would have different numbers representing the direction of the centrifugal force, but the actual direction (or magnitude) of the centrifugal force at any particular moment would not vary with rotation rate of the frame.

We should not muddle-together the movement of a frame (such as in a circle about a point) with rotation of the frame. They are two different things that can be independent. If we don't keep that in mind, it leads to fallacies.

Montyv (talk) 17:32, 31 May 2015 (UTC)

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