Talk:Centrifugal force/Archive 2

"Centrifugal force" is not a force
A centripetal force acts to keep the object in circular motion, and a reaction force is imposed on whatever is providing the centripetal force.

"Centrifugal force" is not a force - it is just inertia. 210.50.105.53 09:00, 13 Jun 2004 (UTC)

"Physics teachers are keen to teach that the real force is centripetal force and that centifugal force is the reactionary force which balances it. Conversion of angular momentum into linear momentum is used in a number of ways, the most obvious is perhaps a sling."

What does that mean? Maybe the second part is right, but the first part is (hopefully) incorrect. 210.50.105.53 09:11, 13 Jun 2004 (UTC)


 * My dictionary (Webster New World, 1968) says that "Centrifugal force" is a force. Duk 16:11, 25 Sep 2004 (UTC)

(William M. Connolley 11:24, 18 Oct 2004 (UTC)) Is it a force...? Firstly, your dictionary isn't going to help. Its harder than that. See-also the talk (and text) at Coriolis force. If Centrifugal force is just inertia, is gravity the same? Unless you can define a force in such a way as to make the question meaningful, I think the answer is going to be "depends on your POV".

(Rsduhamel 20:53, 28 Nov 2004 (UTC)) Saying centrifugal force doesn't exist is like saying there's no such thing as a Sparrow Hawk because it's official name is American Kestrel. Centrifugal force is what people call the sensation of an outward force exerted by a spining object. It's just what people call something that feels real to them. I think the article explains it well. If we are going to say centrifugal force doesn't exist then let's stop calling a Sunrise a Sunrise and call it what it really is ("My, what a beautiful Earth rotation we're having this morning.").


 * Prof. Enrico Lorenzini (of Harvard) and Prof. Juan Sanmartin (of the Polytechnic University of Madrid) have an interesting discussion on this in the Dec 2004 issue of Scientific America;


 * In response to a snide letter objecting to them using the term to describe a force; they reply "... yes, professors shy away from teaching first year physics students this term ... yes it is a valid concept when used within a rotating frame of reference..." (paraphrased). Duk 03:13, 29 Nov 2004 (UTC)


 * I think the professors that avoid using the term to an audiance of first year physics students are right. A rotating reference frame isn't a valid concept. However, it is quite useful physics shorthand. In teaching physics I would never use the phrasing that 'the comet Levy-Shoemaker was ripped apart by tidal forces', but in conversation between experienced physicists I would readily use 'tidal forces' as an abbreviation. Cleon Teunissen 09:42, 24 Jan 2005 (UTC)

Newton's third law of motion
Cleon Teunissen 16:23, 12 Jan 2005 (UTC) Newton's third law of motion deals with conservation of linear momentum.

If you have two objects exerting a force on each other, for example a repulsive force, then as soon as you let them go they will fly away from each other, but their common center of mass will remain in the same spot (or will continue in the same straight line, if it was moving in a straight line.)

Newtons third law of motion does not refer to objects that remain solid.


 * (William M. Connolley 19:43, 12 Jan 2005 (UTC)) I dislike the distinct in the article between "action forces" and... something else. I doubt it means anything. I think CT is right that the reference to Newtons 3rd law is wrong. This needs thinking about...


 * Cleon Teunissen 22:08, 12 Jan 2005 (UTC) As I mention in my proposal for revision: the Newtonian description of the dynamics of circular motion is highly counter-intuitive. To many people, the newtonian description feels wrong. I think that is the main issue.

Rewrite of the article, 30 jan
I have rewritten the article. The first section is written for people with no phyisics background at all. The first section aims to stay as close to everyday experience of motion as possible. As the article goes on, the level increases. The final sections assume that the reader has a lot of physics knowledge. Cleon Teunissen 07:04, 30 Jan 2005 (UTC)

How circular motion is to be understood
202.156.2.82 wrote:
 * The centrifugal force may be understood as arising from the tendency of the stone to move in a straight line, or a path tangential to its position on the circle.

I have removed this remark because it leads to an inconsistency. If there would be a centrifugal force then the centripetal force would be prevented from maintaining the circular motion. The circular motion is maintained, so there is only one force at play: centripetal force.

Because of inertia a force is required to make an object deviate from moving in a straight line. Manifestation of inertia opposes the centripetal force, but it does not prevent the centripetal acceleration.

Without inertia, objects would be instantly accelerated to lightspeed. Because of inertia acceleration is proportional to the exerted force. The bottom line: inertia is not a force. Inertia involves opposition to change, but inertia never prevents the change. --Cleon Teunissen | Talk 14:49, 22 Apr 2005 (UTC)

Centrifugal Force *is* a force
I'm dismayed to see the amount of damage that has been done to physics literacy by the "Fictitious Force" falacy.

Centrifugal force is just as "real" a force as the one a wall exerts on you if you bang your head against it. And that's what should be done to the so-called educational "experts" who, at some point, decided that there were such things as fictitious, fake, or phantom forces.

How all this started, as best I can determine, is this: an effort was made in middle school curriculum development to "correct" the understanding of the forces that give rise to circular motion. "They" (you know, Them) decided it was misleading to describe that pail on a rope as pulling on the rope, when in fact it was the rope that was pulling on the pail. And that's fine as far as it goes. It is a change in point of view. It describes circular motion as caused by the acceleration of an object, changing its direction of motion from linear to circular, due to the application of a centripetal force. It's true, it's a good way to describe it, and it probably does help in gaining an understanding of circular motion; or would have, except for what happened next.

Somehow, while the new concept was making its way into the hands of middle-school educators, somebody overreacted. Rather than switching the emphasis from the centrifugal to the centripetal force, the thought pendulum swung too far, and people began teaching that there was no centrifugal force. That's rubbish.

Newton's Third Law tells us that unmatched forces do not exist in the universe. In any force interaction between two objects, the forces exist in pairs. Each force of each pair is the same magnitude as, and opposite in direction to, its partner. Furthermore, it does not matter whether any motion occurs as a result of the interaction, or not. The 3rd law holds perfectly whether you are pushing on a brick wall or whether you are pushing on a shopping cart (accelerating it). The force back on your hand by the object is the same as the force of your hand on the object. The cart accelerates not because there is something wrong with the 3rd law, but because the sum of all the forces acting on it (your hand is but one) is non-zero.

If centrifugal force did not exist, it would be the only known example of 3rd law failure. Thankfully, that's not the case. Centrifugal force and Centripetal force are a 3rd-law force pair, just like any other. It's certainly true that centripetal force is the force that maintains circular motion. And it's a wise way to approach teaching the matter. But it's a simple physical fact that when the rope pulls on the pail, the pail does pull back. It has no choice. Forces exist in pairs.

And that's the way centrifugal force should be taught. It is the Newton's 3rd law reaction force to the centripetal force. That doesn't make it false, fake, fictitious, or phantasmic. It's real. All reaction forces are real. If they weren't, rockets would not take off, and you wouldn't hurt your head if you banged it on the wall.

It does not help anyone's understanding of physics to imply that there are phantom or magic forces around us. And the damage done by teaching that centrifugal force does not "really" exist when it can obviously be directly experienced by anyone, fosters a distrust of empirical evidence.

Beyond that, it's just wrong.

The wiki article needs to be fixed, but I hesitate to take a crack at it myself, because it's not a simple edit.

Anyone have suggestions? --68.239.184.113 17:08, 31 July 2005 (UTC)

I will try to answer this.

The thing to recognize, I think, is that inertia is real. Inertia is always there, it is omnipresent. And paradoxically, because it is never absent, inertia tends to be overlooked.

We have that a force is required to change the velocity of an object. Newtons literal formulation of his third law looks very much like statics, but in presenting his dynamics newton used his third law in a form that today is known as conservation of momentum. If we have object floating in space, and object A is exerting a force on object B, then both will accelerate, in opposite directions. The center of mass will not start moving.

So it is a bit awkward to use Newtons third law as a law of statics.

We do have a law of statics that looks the same: if a force is being exerted, and that does not result in acceleration, then the thing being pushed against is pushing back.

Now, inertia.

Can we say that inertia is pushing back? Well no, for if inertia would be pushing back then there would be no acceleration, and inertia does not prevent acceleration. So it would lead to an inconsistency if we would decree: inertia is pushing back.

Inertia seems a bit like friction, but it is also very different. When there is friction and you can exert only so much force, then the velocity reaches a "ceiling". A car's engine can exert a lot of forward force, but at several hundred kilometers per hour there is so much drag that the car cannot go faster.

But with inertia it is a different story. There is inertia, but there is no "ceiling" to velocity (at least not until you go at a relativistic speed)

Because of the existence of inertia, we have the property that the amount of acceleration is proportional to the force. Twice as much force means accelerating twice as hard.

In all, friction relates to velocity, but inertia is a level higher, inertia relates to acceleration.

It is important to recognize the tremendous importance of inertia. But remarkably it is not listed among the fundamental forces of nature: gravitation, electromagnetism, weak nuclear force, strond nuclear force. But then, it would lead to an inconsistency to declare by decree that inertia is 'a force'.

The four fundamental forces have in common that they are interactions between pairs of object. It is a force when momentum is exchanged between two objects, for example in a gravitational slingshot

Inertia, important as it is, is not an interaction between two objects; you cannot use inertia by itself for a slingshot.

In the general theory of relativity, the description of inertia and the description of gravitation are unified at a most profound level. In that sense, general ralativity has acknowledged how fundamentally important inertia is. In general relativity inertia is described as an interation between matter and space itself. You cannot call it friction, but space does oppose change of velocity. (Acceleration is opposed by inertia, but not prevented. Even the slightest force will get the largest object moving, it just takes more time with a weaker force.)

So it is best to recognize centrifugal force for what it is: inertia. When an object is being moved in a circle, it is constantly being accelerated towards the center. The acceleration towards the center is opposed, but not prevented, by inertia.  --Cleon Teunissen | Talk 18:51, 31 July 2005 (UTC)

I'm sorry, but there's still a good deal of misconception here. Let's address this in Newtonian terms, with non-quantum, macroscopic objects like pails and ropes.

For background, let us agree that inertia is not a force. Inertia is, for all intents and purposes the same thing as mass. To determine the inertia of an object, it is sufficient to know its mass. It depends upon nothing else. So let us drop the word inertia and speak of mass.

Force is the product of a mass and an acceleration. This is Newton's second law. $$(F=ma)$$ Although he originally framed it as a change in momentum, we can, through a simple mathematical theorem show the two to be equivalent. The SI unit of force, the newton, is defined as the force necessary to accelerate a kilogram at a rate of 1 m/s^2. So a newton is 1 m·kg·s^-2. Force is therefore dimensionally different from mass, and cannot be compared to it (i.e, added subtracted or added). We will avoid using them interchangeably, or otherwise confusing them.

Mass (inertia) does not "push". Force pushes; mass resists pushing. It resists in the sense that a larger mass under a given force does not accelerate as much.

Newton's third law says that whatever force I exert on an object, the object will always exert an equal and opposite force on me. Note well the use of the word "always". There are no exceptions. In particular, there is no exception for static vs. kinetic situations.

Consider a 1 kg mass glued to the table. If I apply a 1 N force to it, it will push back with a 1 N force. Newton is vindicated, at least in the static case.

Now consider a 1 kg mass in space. If I apply a 1 N force on it, it will still push back with a 1 N force. It will also begin to accelerate away from me at a predictable 1 m/s^2 rate (and I from it, at a somewhat slower rate), so I will have to use some ingenuity to continue to apply that constant 1 N force. As a thought experiment, I might use a tiny, relatively massless, calibrated, 1 N rocket engine, carefully adjusted to act on the center of mass. The rocket applies a 1 N force to the mass; the mass applies a 1 N force to the rocket. Newton is vindicated again. At the end of the day, if the rocket hasn't run out of thought-fuel, the forces are both unchanged, but of course the mass is now quite far away and moving at a high speed.

Note well, that the reason the first mass did not accelerate, in fact did not move, was not because the 1 N forces matched. All reaction pairs match, all the time. The reason the mass did not move was because the 1 N force I was applying to it was not the only force applied to it. There was an additional force applied by the glue and table. The mass did not move because the total forces on the mass summed to zero.

Similarly, the reason that the mass in space did accelerate was not because the reaction force did not match the applied force. Of course they must be equal and opposite, or the 3rd law fails. The reason it moved was because the 1 N force I applied to it was the only force applied to it. Absent some other force, such as friction, this motive force was unbalanced, and the mass accelerated in the direction of the force applied to it.

Just as in the static case, the reaction force is irrelevant in determining the motion of the object, since it was not exerted on the object, but rather by the object.

So, some of your statements are incorrect:

You said inertia seems sowhat like friction, but we've already dispensed with that idea. Inertia is mass, friction is a force. The two are not comparable. You said, "if a force is being exerted, and that does not result in acceleration, then the thing being pushed against is pushing back." In fact, it means no such thing. The object must always be pushing back equally, whether it accelerates or not. What the lack of acceleration truly means is that there must be one or more other forces on the object, such that vector sum of all of these is zero. The push back is irrelevant, since it is not a force applied to the object. The push back on me will, of course, determine how I move, when summed with all the other forces acting on me, but that's relevant to my motion, not the object's. This is why free-body diagrams only show the forces on a single object at a time, and not the forces they exert.

Your statement,"if inertia would be pushing back then there would be no acceleration," is incorrect for the same reason. Inertia does push back, precisely equal, precicely opposite, to the applied force. This does not mean that inertia is a force, or even proportional to the force. It is neither. The force with which the object pushes back does not depend on its mass. Be it a gram or a megagram, the reaction force will be equal and opposite to the applied force. What will differ is that the gram will accelerate much faster away from you than the megagram will. Thus it seems that the megagram is pushing back "harder". It is not. They both push back according to the 3rd law, just as hard as you push on them. The difference is that the gram, when pushed on, rapidly leaves. Once it does so, it is no longer possible for you to exert a force on it, unless you follow it, and continue to push on it with the same force, which means you have to accelerate to keep up with it. But if you succeed, the forces remain equal and opposite.

The same is true of an object in circular motion, with one important difference. Since you are applying the force perpendicular to the object's motion, it does not move toward or away from you, but curves around you at a constant radius. The object does not leave the area, so you can continue to pull on it. You exert a constant centripetal force on it, which results in a constant centripetal acceleration. The force, by the 2nd law, is equal to the product of the mass of the object and the centripetal acceleration. Since there is no other force on the object, the vector sum is nonzero, and the object must be under constant acceleration, which it is. Its speed does not change because there is no component of this acceleration parallel to its velocity.

And just as in every other case, there is a reaction force, applied not to the object, but by the object. It is exerted on the rope (or in the case of a circular orbit, by gravity, on the planet). It does not affect the motion of the object because it is not exerted on the object; it is exerted on whatever is pulling on the object. By the 3rd law, this force is equal in magnitude, and opposite in direction to the centripetal force. It is called the centrifugal force.

Centripetal (center seeking) acceleration is inwardly directed, and caused strictly by the inwardly directed centripetal force. There is no disagreement on that. Since it is the only force on the object, it accounts for the only acceleration of the object. The centrifugal force does not affect it, not because it's fictitious, but because it's exerted on a different object!

The perfectly real and non-fictitious centrifugal (center fleeing) force is outwardly directed, and equal in magnitude to the centripetal force. It does not affect the motion of the object, but might well affect the motion of the rope, unless something pulls on the other end of it with equal force.

In the case of orbital motion, it is the very real centrifugal force that causes the planet to wobble as the moon revolves around it, such that the pair, viewed as an isolated syatem,revolve around their common center of mass.

And there is nothing in the least bit fictitious about any of it.

--Jeepien 02:31:43, 2005-08-01 (UTC)

P.S. There are also two problems with your final paragraph above. You say that centrifugal force is actually inertia, which we had agreed was impossible, as mass and force are dimensionally distinct quantities. You also say that the centripetal acceleration is "opposed but not prevented" by inertia. This is similarly confusing because it encourages the reader to assume that there is some outward-directed something "opposing" the acceleration toward the center. In fact, there is but a single force acting on the object, and it alone (and unopposed) is fully responsible for the acceleration of the object. This is, of course, the centripetal force.

By saying that it is opposed in some way, you are dancing on the edge of the pit of the very fallacy you are seeking to debunk. There is nothing opposing the centripetal force on the object. If there were, its acceleration would be less than that predicted by $$F=ma$$. It isn't, because there is no force pulling outward on the object, not even a "phantom" one. And certainly not a "centrifugal" one.

Remember, the centrifugal force does not pull outward on the object (and therefore cannnot oppose the centripetal force), for the simple reason that the centrifugal force does not act on the object in the first place. It is the force exerted by the object upon whatever is constraining it to a circular path.

As long as we keep this straight, we can allow the centrifugal force to be real (after all, the pail does pull outward on the rope, and we can feel this force and measure it with a scale). But it does not pull outward on the pail. The only force upon the pail is inward, as confirmed by its strictly inward acceleration in accordance with the second law.

This entire muddle, which is all too common in textbooks, well-meaning popularized science explanations, and even on some college .edu web sites, boils down to a confusion between Newton's second and third laws. In his second law, all the forces on a single object are considered, and determine the change in momentum of the object. In his third law, pairs of forces between pairs of objects are considered, and two forces are never exerted on the same object, so they can not be said to cancel, or balance or otherwise oppose each other.

It is easy to tell whether someone is a victim of this confusion. Propose the following to them: "Since by the 3rd law, all forces occur in strictly balanced pairs, all acceleration is impossible." If they are tripped up by that, or begin to deny that the 3rd law applies universally, they are victims. If they can easily point out the fallacy, they have their concepts straight.

--Jeepien

The siginificance of Newton's Third Law
Jeepien Wrote:
 * It is easy to tell whether someone is a victim of this confusion. Propose the following to them: "Since by the 3rd law, all forces occur in strictly balanced pairs, all acceleration is impossible."   If they are tripped up by that, or begin to deny that the 3rd law applies universally, they are victims.  If they can easily point out the fallacy, they have their concepts straight. --Jeepien 02:31:43, 2005-08-01 (UTC)

Hi Jeepien, I think you and I do not really disagree. I may use rather different metaphores but I doubt there is a real difference.

It seems to me that Newton's third law is the key element here. Newtons third law is intimately connected to the principle of relativity of inertial motion. In the Principia the third law's formulation is very reminiscent of statics, but in its application in mechanics it is about interactons between pairs of objects.

The law of equilibrium of forces in the context of statics is of course quite unrelated to newtons third law of motion. If an object is glued to a table then the glue transmits (if stressed) the counterforce of the table. The table can be bolted to the floor, etc etc

When an observer and an object are both free-floating in space and the observer pushes an object, then according to newtonian mechanics you will both accelerate,(away from each other) but the common center of mass of the two of you will remain in inertial motion. Strictly speaking none of these assertions of Newtonian mechanics is provable, but it all works so well it would be absurd to demand more corroborating evidence. Does the object push back? Srictly speaking we don't know, what we see is that Newtons third law holds good.

Any violation of Newtons third law is at the same time a violation of the principle of relativity of inertial motion. The principle of relativity of inertial motion makes asserting Newtons third law inevitable.

Newtons's third law does not trip me up. In fact, I use Newton's third law to provide a distinction between force and non-force. Force is what happens in physical interactions between pairs of objects. Inertia involves an interaction, but there is only a single object, so important as it is, inertia is not to be categorized as a force

I will have another good look at what you wrote, to see if I should stop using particular metaphores. --Cleon Teunissen | Talk 10:22, 8 August 2005 (UTC)

Inertia and Mass
clearly, the expressions 'ínertia' and 'mass' are interchangable. The amount of mass is measured by measuring the ratio of amount of force and the resulting acceleration (m=F/a).

Is there anything we can say about the origin of inertia? Not all particles have mass. Photons have no mass, and they are instantly accelerated to lightspeed. Particles with inertia on the other hand, have an interesting property: the acceleration is proportional to the applied force.

That is somewhere between the extremes: if an object would have infinite inertia, then every finite amount of force would not move it. If an object has zero inertia, then it instantly jumps to lightspeed. But inertia is somewhere in between that: acceleration is proportional to the applied force.

There is an interesting analogy with the phenomenon of inductance. A current circuit with a coil with self-induction in it will not particularly resist current strength; it will conduct a wide range of current strengths. If the current circuit is super-conducting it will conduct current without the necessity to keep applying a voltage. Suppose some voltage is applied, a voltage that tends to increase the current strength. The very first change in current strength leads to a change of the magnetic field of the coil. The change of the magnetic field induces an electric field, and this induced electric field opposes the applied voltage. Inductance opposes change of current strength, but does not prevent change of current strenght, for the mechanism can only come into action when there is some change of current strength. In operation it is a self-tuning mechanism.

When there is a coil with self-induction in a current circuit, then the current strength is by good approximation proportional to the applied voltage. By contrast, without the coil with self-induction, applying a voltage on a superconducting conductor causes an immediate jump in current strenght.

It is not clear how far the analogy between inertia and inductance extends, but I find it an interesting analogy. --Cleon Teunissen | Talk 10:59, 8 August 2005 (UTC)

The force that is exerted on the other object

 * Centripetal (center seeking) acceleration is inwardly directed, and caused strictly by the inwardly directed centripetal force. There is no disagreement on that. Since it is the only force on the object, it accounts for the only acceleration of the object.  The centrifugal force does not affect it, not because it's fictitious, but because it's exerted on a different object --Jeepien 02:31:43, 2005-08-01 (UTC)

This is a quite astute remark. I see now how my words can seem to teeter on the brink of the fallacy I seek to debunk.

When I am swinging around a weight on the end of a rope, then the tension in the rope is just regular tension. So the weight is exerting a centrifugal force on ME, and if I am to remain stationary I must brace myself. The weight, unattached to anything but the rope, is being accelerated.

The frequent fallacy is that when an arrow for a centrifugal force is added to a diagram representing forces it is all too often added to the center of mass of the swinging weight. It is my habit to never add any arrow for a "centrifugal force" in any diagram, because its not a force, and the diagram is supposed to represent forces. This habit of mine "protected" me from the fallacy, but I had never spotted the nature of the mistake in sticking an arrow for a centrifugal force on the wrong object --Cleon Teunissen | Talk 12:08, 8 August 2005 (UTC)


 * Thank you.


 * Yes, the tension in the rope is just regular tension. And we know that tension in a rope or string is considered to "act" in either direction, depending on where we focus our attention.


 * Rather than an object in circular motion, consider exerting a force on a massive object at rest in space. We use our calibrated 1 N thought rocket hooked to a strong massless string to tow the object.  The force on the object will cause it to accelerate in inverse proportion to its mass.  The only force  on the object will be that applied by the string, so the acceleration vector will be toward the rocket.  The acceleration will continue as long as the force is applied.


 * All the while, the object will exert a third-law reaction force of 1 N back on the string. This is what we would call the centrifugal force, if the motion were circular.  It is this force that keeps the string under tension in both scenarios.


 * We know that a string that sustains a force on only one of its ends will not show any tension. It can't.  It will simply move limply in the direction of the force.  What is sometimes less clear is that all Newtonian force pairs behave like the tension in a string.  They either exist in both directions equally, or they don't exist.  A somewhat Zen-like rephrasing of the third law might be, "A force can be exerted only to the extent that it is resisted."


 * I illustrate this to my Physics students by having the strongest guy in the class (yes, I do get football players in Honors Physics) push on the wall as hard as hard as he can with his flat palm. If I like, I can measure the peak force with a gauge, but the apparent effort is enough to quantify it.  I ask him to remember what it felt like.  After he's demonstrated his strength, I tell him that, through my advanced mastery of the forces of the universe, I can prevent him him from pushing on my hand with even a small fraction of that force, and challenge him to do so.  I make a show of holding up my palm and bracing myself to resist.


 * When he pushes, of course, I don't resist, but move my hand back, gently yielding to all but a small amount of force. It is naturally impossible for him to push harder than I am willing to push back.  "Come on," I say, "that was weak. Can't you push harder than that?"  But, of course, there's nothing he can do to exert a larger force, and the class gets the point: Forces must exist in matched pairs.  You cannot touch without being touched, you cannot push (or pull) without being pushed (or pulled) in return. --Jeepien 15:05:30, 2005-08-08 (UTC)

So, recapitulating: A stone is being swung around on the end of a rope: the stone is exerting a force in centrifugal direction on the central pivot point.

Additional remarks: In the case of for example a hammer thrower in olympic hammer throwing. The only way for the hammer thrower to swing around the hammer is to make the hammer and his own body both circle around their common center of mass. Then there are two centripetal forces, pointing in opposite directions. (The two stars of a double star system both rotate around their common center of mass. That looks like a no-centrifugal-force scenario to me.)


 * Not at all, unless you're repealing the third law. It is a case of two centrifugal forces.  And this is not unique to hammer throwers and binary stars.  Every real-world case of two-body circular motion will have an element of this sort of motion, which will be less pronounced when the masses of the objects are very different.  Only a perfectly fixed center point could produce a perfectly circular path and such points do not exist.  Each of the forces between two stars, F1,2 and F2,1 is both a centripetal and a centrifugal force, depending on your point of view.  What matters is whether you consider the force to be exerted inward on a star (centripetal) or exerted outward by a star (centrifugal).  Of course each force is truly both, since each is exerted by one star upon its companion.--Jeepien 17:55:48, 2005-08-09 (UTC)

The assertion: 'the centrifugal force does not exist' refers to the fallacy of conceptually putting the point of action of centrifugal force in the wrong place. For example: what causes the weights of a centrifugal governor to swing out? Answer: an increase in angular velocity causes the weights to swing out. The weights of the centrifugal governor do exert a centrifugal force on the vertical axis. However, this centrifugal force is not involved in the weights swinging out.


 * Quite so, and the remedy, in my view, is not to repeat the false statement (that it does not exist), but rather to emphasize the true statement (that people tend to get confused about where it is exerted). In the case of the centrifugal governor, the centrifugal force is not exerted on the weights, and so can't be the cause of their increased radius.  It is exerted by the weights upon the central mechanism. The centrifugal force is what closes the steam valve. The weights swing out for the usual reason: their inertial tendency to move in straight lines, unless constrained by an increased centripetal force.  --Jeepien 17:55:48, 2005-08-09 (UTC)

We have that rotational dynamics is counterintuitive. So I feel that it is important to try an be helpful to people with little physics background. Sometimes the formally correct is at odds with the "common sense". I think then an effort must be made to reconcile the two; to explain to people what the tempting fallacy is. --Cleon Teunissen | Talk 17:33, 8 August 2005 (UTC)

Depending on your point of view
(The two stars of a double star system both rotate around their common center of mass. That looks like a no-centrifugal-force scenario to me.) --Cleon Teunissen | Talk 17:33, 8 August 2005 (UTC)


 * Each of the forces between two stars, F1,2 and F2,1 is both a centripetal and a centrifugal force, depending on your point of view. --Jeepien 17:55:48, 2005-08-09 (UTC)


 * Let me verify I understand you correctly:As seen from the point of view of star (1) the force that is exerted upon it is a centripetal force, and the force it exerts on star (2) is in a direction that is the centrifugal direction for star (1).Likewise, as seen from the point of view of star (2) the force that is exerted upon it is a centripetal force, etc.


 * The diagram representing forces being exerted in the double star system contains two arrows. --Cleon Teunissen | Talk 05:41, 10 August 2005 (UTC)


 * Yes. Each star is pulled upon by a centripetal force arising from its companion, and reacts, according to the third law, with a centrifugal force pulling back upon the companion star.  There are only two forces, but their names change depending upon which star you observe from.  When considering third-law force pairs, the question of which force is "really" the action force and which is the reaction force is rarely clear-cut, and often varies with the observer.


 * An outside observer might look at the force diagram and consider each of the arrows to be centripetal (=) until it reached the center of mass (X), and centrifugal (-) thereafter:

========>         X  <========


 * The same would be true if the stars were of different masses, shifting the center of mass:

===->    X  <---=============


 * This mass difference biases our thinking as to which force should "truly" be called centripetal. This is essentially the situation of our hammer-throw competitor, or me, with my rope and bucket.


 * And, of course, if you consider the center of mass itself, the vector sum of all forces toward and away from it is equal to zero, so the binary system as a whole would move with uniform (inertial) motion. --Jeepien 15:58:41, 2005-08-10 (UTC)


 * Well the verification was superfluous, the matter is clear to me, to my full satisfaction. Newton was sharp-eyed indeed in formulating his third law. It is, contrary to what I thought, possible to formulate one law (the third law) that covers both statics and dynamics, the key is to always recognize the reciprocal pairs. --Cleon Teunissen | Talk 17:21, 10 August 2005 (UTC)

The origin of the expression fictitious force
In the context of a rotating coordinate system the equation of motion contains a term for a centrifugal force (and a term for a coriolis force). In the context of the rotating coordinate system these fictitious forces perform the job that in the context of a non-rotating coordinate system is performed by F=ma.

Sometimes it is formulated as follows: "Centrifugal force is present only in a rotating coordinate system." That sounds very odd to me.

The confusion here is that a habit has grown to use the same label 'centrifugal force' for two quite different situations. Some people blindly assume that since in both situations the same name is used, it must actually be the same.

I try to spot that kind of confusion, and avoid it. When thinking about rotational dynamics, for example the dynamics of a gravitational slingshot I do all the thinking from/in the perspective of the non-rotating frame of reference. --Cleon Teunissen | Talk 17:28, 10 August 2005 (UTC)

Two Definitions
There are two completely different definitions of centrifugal force, that were mixed and matched in the entry. The author sounded confused. I kept some of their examples, and emphasised the distinction between the two definitions, and which one is more commonly used. I also removed some confusing extraneous material from the latter half of the entry. The entry could use some maths, perhaps deriving the centrifugal force from the chain rule and a time dependent coordinate change.


 * Can I define the terms "fictitious centrifugal force" and "reactive centrifugal force" and use them in this article, or would that count as original research? --Ihope127 17:49, 25 September 2005 (UTC)


 * Those terms seem very uncommon, if there is a better way to refer to a definition, try to find it. I'd suggest breaking the article into sections, one being titled "Fictitious force" and one being titled "Reaction force", or something like that.  &mdash; siro  &chi;  o  23:47, 26 September 2005 (UTC)

What does "plate spinning" use?
Can somebody help a Wikipedia-editor-wannabe (me) who barely got through high school physics? while checking up on some WikiLinks in other articles, I linked the article on Plate spinning to Centrifugal force. After reading through these comments, now I'm not so sure that was a good idea. Can one of you "physics" eggheads look at that article, figure out what's right, and either let me know or fix it yourself? Thanks. Joe 02:23, 3 October 2005 (UTC)

random_factor 10:23, 7 October 2005 (GMT) Centrifugal force is an illusion of angular momentum. The friction of an item against the spinning object that it is in or on causes it to accererate in a straight line, because forces act in straight lines. this causes the item to move along a chord of the circular path followed by any given point of the spinning object.this means that the friction force is now acting in a different direction, so the item is accelerated in that direction. This causes it to move along another chord, this one slightly further from the centre of spin and at a slight angle to the first one (because of how the item has moved). This process is repeated so that the item follows a spiral path outwards from the centre of the spinning object, until it reaches the edge. When it reaches the edge, it is able to do what it physics have been trying to make it do all along - fly off in a directon that is tangential to the circular direction of spin. If you are the item in the spinning object (say, one of those fairground rides where you get pressed against the wall and then the floor drops out and you stay stuck against the wall) then you feel as if there is a force flinging you outwards because you are being accelerated at a tangent to the circular path of the spinning fairground ride. Because the force is a straight line and the wall is not, an arrow used to show this force would intersect the wall. This means that there is a force pressing you against the wall, but that force is not some mystical power pushing outwards from the centre of the circle, but instead it is your own momentum pressing you sideways into the wall. You feel pushed back, not pushed sideways, because your inertia cancels out the feel of sideways motion. The simplest way to show that centrifugal force cannot exist is to note that there is no way for a force to push outwards from the centre without there being a solid object for it to push with (except magnetism, and humans aren't magnetic). The centrifugal force that everyone believes in is a fictitious kind of un-gravity, some force that is somehow created by spinning objects. If it did work like that, the people standing next to the fairground ride would be pushed back as well.


 * That's a great answer. But I'm not sure if it answered my question.  Simply put, is the link to Centrifugal force appropriately used in the article on Plate spinning?  Yes?  No?  If not, can somebody fix it or tell me what is more appropriate?  Joe 13:53, 12 October 2005 (UTC)


 * I changed it to "Plate spinning relies on the gyroscopic effect, like it also applies for a spinning top. This makes balancing easier." I think that is more relevant than centrifugal force.--Patrick 16:06, 12 October 2005 (UTC)

More on reaction to centrifugal force
The following unsigned text is from 220.233.107.29:


 * For every action there is an equal and opposite reaction. I am not the first wise person to say that. Who said it before me ? Ah, Newton did. Um, centrifigual force, reaction force to centripedal force.


 * Inertia is a force. F=MA. M is inertial, so therefor F is to !


 * The problem here is that there are too many sophomores who are repeating the answers that their 2nd year tutors expect based on the musings (not publifications) of a professor in astrophysics.


 * In the context of motion on earth, centrifigual force is quite real.

I have previously edited this article anonymously from IP addreses 85.81.19.235 and 192.38.79.130). I have mostly reverted the article edit by 220.233.107.29 which attempted to assert that centrifugal force is only the reaction force to the centripetal force, and that the fictitious force meaning is wrong. Nonwithstanding its factual merits (I think it reflects a grave misunderstanding of the physics), the style was decidely non-encyclopedic, containing internal commentary and gems such as "For this reason, teachers of science have gone bizzare and started to *emphasize* ..."

In general I have become less and less convinced that the "the real reaction force that complements the centripetal force" meaning is actually legitimate. I have been able to locate no authoritative sources that show this meaning actually being used in physics, whereas I think that every university-level textbook in mechanics will describe the fictitious force meaning. I'm considering to be bold and edit to present the reaction-force meaning as a common mistake rather than a legitimate meaning, unless somebody can point to respectiable source of the reaction-force usage. Henning Makholm 23:16, 22 December 2005 (UTC)


 * Be bold, give it a go, people will complain if they don't like it! William M. Connolley 15:52, 23 December 2005 (UTC).


 * So done. On further thought it does make sense to identify the reaction force with the centrifugal force in statics, so I have added an explanation of this in lieu of the "two definitions" concept. Henning Makholm 11:38, 26 December 2005 (UTC)


 * Good work. I have just one question. You write:
 * There is tension in the rope, pulling inwards on the ball (the centripetal force) and simultaneously pulling outwards on the pivot (the reaction force). The tension is real, so these two forces still exist if we move to a corotating frame. However, in the rotating frame there is also a centrifugal force that pulls outwards on the ball.
 * So we have three forces, the odd number arising because the centrifugal force is fictitious and has no third-law counterpart. So far so good. But then you write:
 * When solving statics problems in the rotating frame, [...] one often considers a force "the same" before and after it has been conveyed by a structural element, so according to this view the reaction force on the pivot is the centrifugal force.
 * This can't mean what it says. We have the centripetal reaction force, and the centrifugal force. They have identical directions and magnitudes, and because their objects are connected by a structural element, we consider them both as being applied to the pivot. But if we combine the two, the combined force on the pivot should be exactly double the centrifugal force, not equal to it. – Smyth\talk 14:51, 26 December 2005 (UTC)


 * We don't combine the two, we identify them. We could also measure the force thrice forces, because the outer half of the rope pulls the inner half of the rope with the same force, and so on.


 * How can I explain? The way I think myself is that force means a flow of momentum, by Newton's 2nd law. In a typical statics problem, gravity makes vertical momentum seep into the parts that make up a building, and we try to calculate how this momentum flows through beams and columns and ends up in the foundation; then we can check whether more momentum needs to flow through each element than it can carry (i.e. if the force on the element is larger than its strength). In the rotation problem, the centrifugal force magically makes momentum appear in the ball, and this momentum flows through the rope and into the pivot. We can then say that it is the same flow of momentum whether we look at it as it arises in the ball or as it arrives at the pivot. This is similar to the Thames carrying 65 cubic metres of water per second past London Bridge and 65 cubic metres of water per second past Greenwich. We do not add up the two numbers to find the water that arrives at the North Sea; the two measurements are of the same flow of water, and in a similar sense one can view the centrifugal force and the centripetal-force reaction as the same flow of momentum, i.e., the same force.


 * Of course, viewing force as momentum flux, while true, is not a suitable mode of explanation for an elementary encyclopedia article. I'm still trying to think of a way to explain this that does not create confusion more than it enlightens. Henning Makholm 00:55, 27 December 2005 (UTC)


 * I think you've done an excellent job – the article is definitely better now than it's ever been before. – Smyth\talk 21:20, 27 December 2005 (UTC)


 * Thanks :-) Henning Makholm 00:10, 28 December 2005 (UTC)

Pivot-ball example
Usually, when the pivot-ball example is utilized, the rope is not perpendicular to the pivot but oblique. Therefore the tension in the rope can be splitted into two component forces, one that is vertical and opposed to mg, and one that is horizontal, this last one being the centripetal force.

In a rotational reference frame, the horizontal component is in opposition with the centrifugal force. In an inertial reference frame, it is not, simply because there is no centrifugal force in that frame. --24.202.163.194 05:26, 5 January 2006 (UTC) --->new name: --Aïki 04:09, 7 January 2006 (UTC)

Component forces
In the inertial reference frame, as well as in the rotational reference frame, we must split the tension in the rope into two component forces to explain the behavior of the ball.

One component is horizontal and directed toward the pivot where the center of the plane of rotation is situated, and which component constitute the centripetal force acting on the ball.

The second component is vertical and directed upward, which component constitute the opposite force to the gravitational force (mg).

These two vertical forces explain why the ball doesn't move upward or downward i.e. stay at the same height.

Remark: As the two component forces replace the tension in the rope in the new scheme of forces acting on the ball, so we can say that these two forces are not real, at least as real as the rope, or the pivot and the ball, and thus are fictitious! The centripetal force, being the horizontal component, can therefore be called a fictitious force. --Aïki 05:27, 17 January 2006 (UTC)

View of the mind
To split the tension in the rope into two component forces, is like to replace this force, the tension in the rope, by two other different forces. To replace, means that the tension in the rope is no more there, and that in its place we have two forces. If the tension in the rope would still be there, we would have then three forces, which would not be a replacement but an addition.

As these two forces are not materialised by any body, on the contrary of the tension which is materialised by the rope, so we could attribute to these two forces the name 'fictitious'. The same thing can be said of a resultant force replacing two forces seen as components.

In using a system of forces, with its net force, and resultant, component, and equilibrant forces, to analyse and explain the behavior of an object, it is not necessary that each of these forces must represent a material thing.

To use a system of forces in the way exposed above, is simply to adopt a certain view of the mind on the situation under study. --Aïki 00:59, 21 January 2006 (UTC)

improve first paragraph?
Somewhere in the text it is written: "the reaction force on the pivot is the centrifugal force. This identification often leads to confusion about the "fictitious" nature of the centrifugal force, because the pull on the pivot is a perfectly real force". IMO that is the best description/explanation; but this is not apparent in the intro to the article, which even erroneously suggests that a centrifugal force isn't a contact force. My suggestion: rework the intro to include the clear and correct description from the body of the article, which explains that the centrifugal force is a reaction force to a ("real", in the sense of causal) contact force.

BTW, I'm a bit surprised by the apparently erroneous claim that this would be true only in the rotational frame. In my vocabulary, in a washing machine the centripetal force of the wall on the clothes is met by a centrifugal reaction force of the contents on the wall; this is true in the inertial frame. Harald88 18:20, 2 January 2006 (UTC)

The problem I think is that different people use the expression 'centrifugal force' in fundamentally different ways. I will present two examples of two totally different usages of the expression 'centrifugal force'.

Example 1: Take a pilot training centrifuge, and put a stack of three weighing scales in the pod of the pilot training centrifuge. Let the weighing scales be 1 kilogram of weight each. Start the pilot training centrifuge, and spin up until the pod is pulling 1 G of acceleration. The weighing scale at the bottom of the stack will read 2 kilograms of weight, for it is supporting two weighing scales, the middle weighing scale will read 1 kilogram of weight. The pattern of weight readings for the stack shows that the stack is transmitting accelerating force upwards. At every level of the stack the force and the reaction force are equal in strength. Of course, because the the pilot training centrifuge is attached to the Earth it is so much heavier that any motion due to the reaction force is negligable. (Then again, a badly loaded household centrifuge will wobble violently.)

Example 2: If you are inside a rotating space-station, co-rotating with the station, and you trow an object, then the trajectory of the object with respect to the rotating space-station will be curvilinear. (Of course, the actual motion of the object will be along a straigh line as inertially moving objects move along a straight line.) The curvilinear trajectory can be described by inferring a centrifugal acceleration factor.

Some people insist that the expression 'centrifugal force' should be used exclusively to express what is portrayed in example 2. It is my understanding that when people insist that centrifugal force is present exclusively 'in a rotating frame' they are referring to the context of example 2, not to the reaction force of example 1. --Cleonis | Talk 19:21, 2 January 2006 (UTC)


 * Cleon, thanks for the clarification; but the second interpretation is a contradiction in terms with "centrifugal", for the curvilinear motion does not generally correspond to a centrifugal force... Hmm, I think that Newton wrote about it; then it may help to cite him on this! Harald88 19:31, 2 January 2006 (UTC)


 * The transformed equation for motion with respect to a rotating coordinate system has a socalled 'centrifugal term' and a 'coriolis term'. It is my understanding that some people follow this line of thought: there is a centrifugal term present only in the equation of motion for a rotating coordinate system, hence there is only a centrifugal force 'in the rotating frame'.
 * The centrifugal term in the transformed equation for motion with respect to a rotating coordinate system does point in centrifugal direction.


 * Unfortunately, Newton did not express himself clearly when making statements about centrifugal force. Citing Newton is probably not helpful.
 * A somewhat baffling aspect of the pilot training centrifuge scenario is that there is a reaction force, but inertia itself is not a force. If you would categorize inertia as a force you would end up with self-contradiction. If you make a technical drawing of the pilot training centrifuge scenario, and you put in arrows to represent forces, then you do not put in an arrow for inertia. --Cleonis | Talk 20:37, 2 January 2006 (UTC)


 * I will look out for Newton's comments. In the training centrifuge scenario, the centriptal force is the causal force; according to you this is not due to inertia? According to me that force is due to the change of velocity of the chair in an inertial frame. Where is the self-contradiction? Harald88 23:08, 2 January 2006 (UTC)


 * As you state, in the pilot training centrifuge, the first in the causal chain is the centripetal force. The floor of the centrifuge pod exerts a centripetal force on any object resting on that floor, let's say a ball rests on the floor. The centripetal force causes acceleration towards the center (but there is also sideways velocity, so the distance to the center does not decrease.) Next in the causal chain is that inertia opposes the change of velocity, so the ball exerts a reaction force on the floor. I avoid equating inertia with the reaction force that the ball exerts on the floor. I prefer to define inertia as the property that a force is required to cause acceleration. Following that definition, inertia is not a force. --Cleonis | Talk 01:25, 3 January 2006 (UTC)

Harald, my contention is that the term "centrifugal force" is only used by serious physicists to refer to the fictitious force that appears in the rotating system. The reaction to the centripetal force is in itself perfectly respectable, but it is a different beast and not the thing physicists do actually call centrifugal force. If you disagree, feel free to cite respectable sources. Henning Makholm 00:30, 3 January 2006 (UTC)


 * Henning, your claim about "serious physicists"is tendentious (and I know it to be wrong). What are your respectable sources? Harald88 00:36, 3 January 2006 (UTC)


 * From what I have access to right at the moment: ScienceWorld, as cited in the article, and the Feynman Lectures on Physics, volume 1, section 12-5. The relevant paragraph from the latter reads, Another example of pseudo force is what is often called "centrifugal force". An observer in a rotating coordinate system, e.g., in a rotating box, will find mysterious forces, not accounted for by any known origin of force, throwing things outward toward the walls. These forces are due merely to the fact that the observer does not have Newton's coordinate system, which is the simplest coordinat system. Also the article centrifugalkraft in Den Store Danske Encyklopædi (which, however, is in Danish, and so may not be individually convincing). Henning Makholm 00:58, 3 January 2006 (UTC)


 * The centrifugal force that Feynman describes there corresponds quite well to my vocabulary: it appears as a mysterious force (a pseudo-causal force) in the rotating frame; and it's a perfectly physical reaction force in the inertial frame. Harald88 13:03, 3 January 2006 (UTC)


 * No it does not: Feynman clearly describes a force that appears to act on the object iself. That is the force that people in general call centrifugal force. The reaction force also appears in the rotating frame, but there is nothing mysterious about that in any frame. Henning Makholm 13:44, 3 January 2006 (UTC)


 * Hi Henning, I gather that you assert that the meaning of the expression 'centrifugal force' that you have in mind entails that it is most definitely not a force. I rather like to compare it to the expression 'retrograde motion of a planet'. The planet Mars does not actually change from prograde to retrograde motion, it only seems so as seen from the Earth. The true motion of Mars is its eccentric orbit around the Sun, the retrograde motion is apparent motion.
 * I think the name 'centrifugal force' is unfortunate, since what you have in mind is not a force at all. --Cleonis | Talk 02:24, 3 January 2006 (UTC)
 * Addendum. I should define here what I mean by force. I define force as a physcial interaction between two objects; if the objects can move freely, momentum is exchanged. Examples: electrostatic attraction (or repulsion) between two charged particles, and gravitational slingshot. --Cleonis | Talk 03:12, 3 January 2006 (UTC)


 * You are quite welcome to think that the centrifugal force should not be called a force, but in an encyclopedia it is our taske to describe things with the terminology that people out there actually use. Remember that truth per se is not our objective; an encyclopedic compilation of ideas that are already current independently of Wikipedia itself is. (Not because there is anything wrong with truth, but because Wikipedia is not an appropriate medium for conducting a discussion about what the truth is). Henning Makholm 13:44, 3 January 2006 (UTC)

Centrifugal force: 2 citations [] --24.202.163.194 06:23, 4 January 2006 (UTC) --Aïki 05:12, 10 January 2006 (UTC)

The concept of coordinate acceleration
In physics, it is customary to refer to acceleration with respect to the local inertial frame of reference as true acceleration. On the other hand, when motion/acceleration with respect to an accelerating coordinate system is considered, it is recognized that there is some apparent motion.

Example: the retrograde motion of Mars. The keplerian orbit of Mars around the Sun is its true trajectory. The motion of Mars as seen from the Earth is a linear combination of its true trajectory and the curvilinear motion of the Earth. In other words: a linear combination of Mars' true trajectory and a coordinate acceleration.

Formulated as generally as possible: if the motion/acceleration with respect to the local inertial frame is considered, then all the motion/acceleration can be accounted for as a consequence of action of one or more of the four fundamental forces of Nature: gravitational interaction, electromagnetic interaction, strong nuclear interaction, weak nuclear interaction. If motion with respect to a non-inertial coordinate system is considered, the motion is accounted for in terms of one or more forces, plus the coordinate acceleration that is involved. The coordinate acceleration is an artifact of having chosen a non-inertial coordinate system.

The only way to formulate laws of motion at all is to consider the motion with respect to the local inertial frame of reference. All laws of motion refer to the local inertial frame of reference. For example, the correction term for centrifugal coordinate acceleration: Let $$\omega_i$$ be the rotation rate with respect to the local inertial frame of reference.
 * $$ F_c = - m \omega_i \times  (\omega_i \times   r )$$

The correction term must use $$\omega_i$$, and $$\omega_i$$ refers to the local inertial frame of reference.

So of course it is possible to transform the equation of motion to a rotating coordinates system, but it should be recognized that the transformed equation of motion is still referring to the inertial frame of reference. Any law of motion that actually works is in one way or another referring to the inertial frame.

Using a rotating coordinate system instead of an inertial coordinate system introduces a coordinate acceleration, which must duly be taken into account. I regret that the expression 'centrifugal force' is used for the concept of coordinate acceleration. I think that using the expression 'centrifugal force' in that way is an open invitation to confusion. --Cleonis | Talk 11:28, 3 January 2006 (UTC)


 * I might even join you in that regret, but it is not our job here to change the terminology that people already use. We can explain the confusion as best we can, but we should not claim that words mean something else than the thing they are actually being used for, whether or not the actual use is desirable or not. Henning Makholm 13:47, 3 January 2006 (UTC)

That makes me unsuitable for editing wikipedia, for I have a severe dislike of misleading terminology.


 * You can edit all you want, as long as you do not try to use Wikipedia as a tool to change established terminology. That is not what an encyclopedia is for. Henning Makholm 14:55, 3 January 2006 (UTC)


 * I can be of help: against all odds I found Newton's definition of "centrifugal force". And guess what? His definiton is the same as that of Huygens, Jeepeen here above and myself. That should help to avoid changing established terminology! See below. Harald88 19:19, 3 January 2006 (UTC)

Currently, the article contains the statement: "Whenever a body is stationary in a rotating frame, there must be some force that cancels out the centrifugal force, or it would be seen to accelerate away from the center." That is a very misleading statement. Coordinate acceleration is an artifact of employing a non-inertial coordinate system. The suggestion that coordinate acceleration can either cancel a physical force, or be canceled by a physical force does not apply. Coordinate acceleration is frame-dependent, an exerted physical force is frame-independent. --Cleonis | Talk 14:18, 3 January 2006 (UTC)


 * In the rotating frame, the movement of the body is described by a modified second law:
 * m·a = fictitious forces + real forces
 * When the body is stationary in the rotating frame, the left-hand-side of this equation is zero; thus so must the right-hand side be. Two vectors that add to zero are said to cancel each other; this is a mathematical concept and is used irrespective of the physical interpretation (or lack of same) of the two vectors. We know the fictitious force, and so we deduce that a real force that is opposite to it somewhere in the system, and we call that force, whatever its origin is, the centripetal force. We could also have deduced the centripetal force by working in an inertial frame, but my point in this paragraph was to work within the rotating frame (because I'm building up to doing statics there, and in statics you don't want to be moving between frames) and show how the existence of the real centripetal force can be shown there, and how it happens to be minus the "fictitious force" term. Henning Makholm 14:55, 3 January 2006 (UTC)

The concept of 'being in a rotating frame'
In physics, only things that can be measured are considered to be things with physical meaning. For example, we can measure the physical effects of electromagnetism, therefore physicist deem it justified to postulate the existence of an electromagnetic field. Conversely, if some postulated field has no observable effects, then a physicist should not bother to postulate it, much like physicists do not bother anymore to postulate a luminiferous ether.

Clearly, there is no such thing as measuring whether you are 'in an inertial frame of reference' or 'in a rotating frame of reference'. There are no observable differences, any difference between the two is merely psychological, not physics

Let a tethered ball be circling a stationary pivot. The measurable quantities are the centripetal force, exerted by the pivot on the ball, and the reaction force, exerted by the ball on the pivot. The centripetal force and the reaction force are present both 'in the inertial frame' and 'in the rotating frame'. Any postulated centrifugal force that is supposed to be present only "in the rotating frame" is inherently unmeasurable.

Of course, the equation of motion for a rotating coordinate system is a good tool in the physicist's mathematical toolbox. But it should be recognized that their is no ground for ascribing physical meaning to the concept of 'being in a rotating frame of reference'.

Excellent time-saving calculational tools without physical meaning are not unusual in physics. For example, calculating the current in electronic oscillator components. To obtain a solution, second order differential equations must be solved, and a powerful mathematical tool to do that is to extend the problem to the number space of complex numbers. The complex number solutions show the way to real number solutions. That is an example of a powerful mathematical tool, without a physical counterpart to the actual mathematical operations. --Cleonis | Talk 15:25, 3 January 2006 (UTC)

Long time established terminology -- according to Newton
I found back some definitions by others. For example, The Columbia Electronic Encyclopedia   :

centripetal force and centrifugal force, action-reaction force pair associated with circular motion.

But also Newton, Principia : And by such propositions, Mr. Huygens, in his excellent book De Horologio Oscillatorio, has compared the force of gravity with the centrifugal forces of revolving bodies. The preceding Proposition may be likewise demonstrated after this manner. In any circle suppose a polygon to be inscribed of any number of sides. And if a body, moved with a given velocity along the sides of the polygon, is reflected from the circle at the several angular points, the force, with which at every reflection it strikes the circle, will be as its velocity: and therefore the sum of the forces, in a given time, will be as that velocity and the number of reflections conjunctly; that is (if the species of the polygon be given), as the length described in that given time, and increased and diminished in the ratio of the same length to the radius of the circle; that is, as the square of that length applied to the radius; and therefore the polygon, by having its sides diminished in infinitum, coincides with the circle, as the square of the arc described in a given time applied to the radius. This is the centrifugal force, with which the body impels the circle; and to which the contrary force, wherewith the circle continually repels the body towards the centre, is equal. (emphasis mine).

Assuming that the translation is not erroneous, I think this settles the issue about improving the article: just as centripetal, it has nothing to do with "frames". I suggest to stick to this straightforward and traditional definition in the introduction as well as in most of the article, and to put alternative "modern" interpretations in a separate paragraph (it would still be interesting to find out who kooked them up). Harald88 19:37, 3 January 2006 (UTC)

PS I already adapted the intro. Harald88 19:56, 3 January 2006 (UTC)

multiple meanings

 * Clearly there are multiple meanings of the expression 'centrifugal force' in circulation. Wikipedia neutral point of view policy calls for paying due attention to each of the meanings that is 'out there' in wide circulation. --Cleonis | Talk 20:22, 3 January 2006 (UTC)


 * Sure. I also left both meanings in the intro, just as it was before. Any idea where the alternative meaning originated? Harald88 21:03, 3 January 2006 (UTC)

In the Newton's example above, the two forces doesn't act on the same object: the centrifugal acts on the circle, and the centripetal acts on the object.

In a rotational reference frame, the two forces act on the same object.

This make a big difference and ... a lot of confusion if we don't see that difference! --24.202.163.194 04:40, 5 January 2006 (UTC)

Usage as "occasional"?
It is not beyond the bounds of possibility that the meaning of the term among scientists has become clarified or even modified in the last 300 years. I agree that both of the meanings described in the article are reasonable, but it is a fact that even the most obvious search shows that current scientific usage of the term is overwhelmingly limited to rotational reference frames. For the article to describe this usage as "occasional" is completely misleading. – Smyth\<sup style="color:gray;">talk 13:36, 7 January 2006 (UTC)


 * I agree, and there is no reason for such a word at all. Correct immediately. Harald88 15:22, 7 January 2006 (UTC)


 * Do you mean that the section 'Rotating frame of reference' of the article should be enlarged, or that the article suggest that it is use occasionally, or say it is so, or is it another meaning? If you could clarified a little bit more what you mean exactly, it would help. Thank you.   --Aïki 15:37, 7 January 2006 (UTC)

I mean that the article should be reverted to the version of 14:21, 3 January 2006. Scientists do not use the phrase "centrifugal force" to mean "any force oriented away from the center"; they use it to refer to one specific force, operating on one specific object, in a rotating reference frame. Just because such precision is not found in simplified explanations for non-scientists, or other encyclopedias, or even Principia Mathematica, does not mean that the other meanings have equal status. – Smyth\<sup style="color:gray;">talk 16:35, 7 January 2006 (UTC)

Alright, perhaps not completely reverted, because the statement "sloppy labeling can obscure which forces are acting upon which objects in a system" is an important one which escaped me for some time. But the statements about which forces are correctly referred to as "centrifugal" should be restored to what that version said. – Smyth\<sup style="color:gray;">talk 17:08, 7 January 2006 (UTC)


 * Thanks for putting our attention on the inaccurcy of that latest addition, I will correct that (but according to me, that whole part is superflous). But note that the version that you refer to was full of errors and started with a derived (and rather obscure) meaning of the term. In physics, we do not commonly regard rotating frames as valid physical reference frames. Harald88 17:54, 7 January 2006 (UTC)

"Derived and rather obscure"? That is the definition used by 9 out of the first 10 results of the above-referenced search. Even the 2 sites aimed at children correctly identify the centrifugal force as being suffered by the rotating object, not the fixed point. The one exception is from a meterology course, where of course all calculation is done from within a rotating reference frame, and a little oversimplification is forgivable.

Consider this an answer to your request above for sources about "serious physicists". This is the only meaning those physicists use, and the article should identify all other meanings as being simplifications or informal usage. – Smyth\<sup style="color:gray;">talk 18:31, 7 January 2006 (UTC)


 * Well, I have to disappoint you: I am a physical engineer, and I always used it in the Newtonian way. Jeepien above is a high school physics teacher and he obviously teaches the same. Thus your claims are outrageous. Harald88 03:33, 8 January 2006 (UTC)

The «meaning» and the «using»

 * I agree that the centrifugal force is mostly used in rotating reference frames.

But I think there is a distinction to be made between the «meaning» and the «using» of a word or expression. In problems to be solved using a rotating frame, the meaning of the centrifugal force is not usually express explicity by scientists, because for them, the meaning is evident. It is like the word «inertia», they don't give a definition of it each time they use it! The context is sufficient for them to know in what sense the word must be used. But here, we are in an encyclopedia open to every one. Therefore, we have to explain a little more, at least, what means the terms we use.

Regarding equal status or not, the official politics of wikipedia (NPOV) is to give a fair share to each one i.e. more space for the more important, and lesser space to the lesser important. --Aïki 18:51, 7 January 2006 (UTC)

In most of the pages I found, it is explicitly stated that "centrifugal force" only exists in an accelerating frame. In the others, the phrase is used in such a way as to imply the same thing.

There is no confusion here: it's clear which meaning scientists consider to be the "more important" one, and it's not the one currently asserted by the article. It was the one asserted by the version of several days ago. – Smyth\<sup style="color:gray;">talk 19:10, 7 January 2006 (UTC)


 * You show which opinion is apparently most talkative on internet. But the version of a few days ago made many categorical general claims that are factually erroneous in classical physics, and rotating frames are little used. In any case, there is a long paragraph about the derived meaning of centrifugal force in a rotating frame, so where is your problem? Harald88 03:33, 8 January 2006 (UTC)


 * I show which opinion is overwhelmingly expressed on .edu sites on the Internet. What "categorical general claims" do you mean? – Smyth\<sup style="color:gray;">talk 11:10, 8 January 2006 (UTC)

In my point of view, of the four texts that you have submited, #6 is the best one, and even the best one that I have seen up to now among all those vulgarisation texts.

Again, I agree with you that the centrifugal force is mostly used in rotating reference frames, the major raison being that from the standpoint of an inertial reference frame, it does not exist at all, meaning that we don't need it to explain the situation, while we absolutely need it in a rotating frame. But, this said, its utilisation in a rotating frame, and not in a inertial frame, does not change at all its meaning! Moreover, there is other utilisations of the concept of centrifugal force, one of them being in the Newton's Book 1.

Thus what is clearly more important is not the meaning, for the simple reason that there is only one, but its utilisation, which is with the rotating frame, (agreed again!), at least, as much as we can see from the outside of the physicists world. --Aïki 03:52, 8 January 2006 (UTC)

Proposition of agreement

 * Aiki, are you saying that the meaning of "centrifugal force" is "any force directed away from the center of rotation"? In that case, I think you are confusing meaning with derivation. Adrenaline is so called because it is produced by the adrenal glands. But this does not mean that every substance produced by the adrenal glands can properly be referred to as "adrenaline", even if scientists in the past may have done so. The defining characteristic of adrenaline is its molecular structure, not its place of origin, just as the defining characteristic of centrifugal force is its relationship to accelerating reference frames, not merely its orientation. At least, that is what the above search shows.


 * So let us reorganize the article again, distinguishing the two outward-directed forces as the "fictitious" and the "reactive" centrifugal forces. We will make no statement about which meaning is more "popular" or "important"; we will simply state the facts of usage. Do you agree? – Smyth\<sup style="color:gray;">talk 11:10, 8 January 2006 (UTC)


 * I agree, except for the logical sequence: it is evident which is the original meaning that is still in use, and which the secondary meaning, from improvising Newtonian physics for rotational frames. Putting that on its head is illogical and therefore confusing. Harald88 11:48, 8 January 2006 (UTC)

I agree to say that the words "fictitious" and "reactive" are the ones in usage. But if someone proves us the contrary, or give us serious informations to the contrary, we will have to reconsidered the situation. --Aïki 04:54, 10 January 2006 (UTC)

Centrifugal force without a rotating frame
A piece of rock coming from outer the solar system is now entering in it and is attracted by the sun. Depending on its initial direction, it will crash on the sun (or in!), or will turn around it and go away in the outer space. In the second case, his path will be a curved one called hyperbola.

In his coming approach, the object will go nearer and nearer of the sun, till a certain point where it will begin to go further and further away of the sun. At the approaching stage, the force acting on it is directed toward the sun; at the go away stage, the force acting on it is no more directed toward the sun but outward. Taking the sun as the center of the curve, we can then called the force toward the sun the centripetal force, because it is directed toward a center, and the force outward the sun the centrifugal force, because it is directed outward the center.

In this example, there is no need of a rotating frame to have a centrifugal force. The only thing that it is needed, it's to know the direction of the force. That's all!

What is the reason to call a force, any force, by the adjective centrifugal, it is not because that it is viewed from a rotational reference frame, or an inertial frame, or else, but because it is directed outward the center. Nothing else count! Note too, that in a rotating reference frame, the centripetal force is also in the same frame and it is not called centrifugal just because it is in that frame! --Aïki 19:41, 8 January 2006 (UTC)


 * You are obviously confused. In Newtonian physics, the force acting on the object is the gravitational force of the sun, and it's all the time directed towards the sun. And yes, it's a centripetal force. Harald88 20:59, 8 January 2006 (UTC)

Citation: 'And if the parabolic section of the cone (by changing the inclination of the cutting plane to the cone) degenerates into an hyperbola, the body will move in the perimeter of this hyperbola, having its centripetal force changed into a centrifugal force.' Newton. --Aïki 04:31, 9 January 2006 (UTC)

Newton's BOOK I. OF THE MOTION OF BODIES. SECTION II. Of the invention of Centripetal Forces.
1- First, thanks to our collaborator Harald88 for having bring to our attention this remarquable demonstration made by Newton.

2- In the two examples that are present in this text, the first one at the beginning, and the second, the Newton-Huygens one, in the SCHOLIUM of PROPOSITION IV. THEOREM IV., the body never goes along a circular path. It always goes in a straight line, and at a constant speed along this line i.e. in an uniform rectilinear motion, except at the points of deviation, of course. More than that, in the first one, there is not even a circle!

3- In the first one, the body receive impulses at equal amount of times, thus at same lenght of straight line and same areas of triangle. Each triangle have their summit at the same point S, the focal point. Each impulse comes from the outside of the triangles and is directed inward in the direction of the focal point S. This impulse is called here: the centripetal force, and is apply on the body.

4- In the Newton-Huygens one, it is the circle which, at first, receive an impulse when the body hurts this circle, coming from a straight line i.e. any side of the polygone. The force generated by this impulse is directed outward the circle and polygone, and it is called here: the centrifugal force, and it is not at all fictitious or fallacious or imaginary or other seemingly expression.

It's differ from the centripetal force of the first example, by its direction and its point of application: in the first example, the force is directed inward and applied on the body; in the Newton-Huygens one, the force is outward and applied on the circle. The name centripetal or centrifugal, depends only on the direction: if outward, it is centrifugal; if inward, it is centripetal. It does not depend at all on which body (we can see the circle as a wall i.e. a body) a force, whatever its nature could be, is applied. In both examples, each force is as real as the other one. ( to be continued) --24.202.163.194 20:20, 6 January 2006 (UTC)

New terminology -- according to whom?
Smyth writes here above: "the defining characteristic of centrifugal force is its relationship to accelerating reference frames". What is the source, and who started this alternative definition? &ndash Harald88 11:59, 8 January 2006 (UTC)


 * I have given a very large number of sources that show this to be a current definition, though I can't answer your historical question. – Smyth\<sup style="color:gray;">talk 17:46, 11 January 2006 (UTC)


 * Currently the article has no reference list. Perhaps you'd like to contribute by putting your selection WP:CITE of good sources there. Harald88 19:10, 11 January 2006 (UTC)

Note that apparently also in some modern texts the meaning of the word "force" differs from the standard meaning of "force"; apparentely some texts mean with "force" active force. &ndash Harald88 11:59, 8 January 2006 (UTC)


 * What do you mean by an "active force"? – Smyth\<sup style="color:gray;">talk 17:46, 11 January 2006 (UTC)


 * A force that deviates an object from inertial motion. Harald88 19:10, 11 January 2006 (UTC)

Some common misconceptions
--- ''I moved this Discussion item to here: no point should be discussed between editors in the article space. IMO such points should be discussed here until the discussion is over and consensus is reached about the opinions according to the two different meanings. Below is the current state of discussion, I number the points for ease.'' ---

Some commonly encountered misconceptions about centrifugal force include:

1 No matter how objects move, there is never any centrifugal force in an intertial frame of reference. No, that's overstating the case. Although an object's inertia should not be mistaken for a force acting upon itself, that doesn't stop it from acting upon other objects. If there is any force acting inward upon an object, then it exerts an equal and opposite force that may be acting outward at the point of contact -- upon a separate object.

2 Centrifugal forces always occur when objects are viewed in a rotating frame of reference, irrespective of whether the object follows the frame's rotation. No -- Inertia may be mistaken for a centrifugal force in a rotating frame, but that is not the only application of the term "centrifugal". In an inertial reference frame, an object forced inward will push back.

3 It is always wrong to speak about centrifugal force. No, This misconception is a very common over-reaction against the misunderstanding of inertia. The key here is not to eliminate "centrifugal" from our vocabulary but to detach it from what it is not and use it for what it fits. Since centrifugal force describes any force whose vector rotates with an object of interest to act continuously outwardly, it accurately describes forces like the passenger acting upon a car door during a turn.

4 Centrifugal force is not fictitious but real. That depends on what apparent force one labels "centrifugal". Used loosely to describe inertia within an rotating reference frame, the "force" is artificial (a product of an accelerating coordinate system). On the other hand (literally), if one spins around with a brick held at arm's length, while no real force pulls the brick outward, the brick does exert a very real centrifugal force upon one's hand.

5 Centrifugal force is just another word for inertia. In one application, but not all. Aside from the misunderstanding of inertia, there is also opposition to centripetal force -- but acting upon another object. Centrifugal is merely a descriptor indicating direction (like the "normal" force exerted by an inclined plane). "Centrifugal force" becomes a useful term when used to describe the force with which an object pushes back when forced into circular motion.

6 An outward reaction force against an object exerting centripetal force is a real centrifugal force. Correct.

Upto here was the discussion (without my comments). Harald88 08:08, 11 January 2006 (UTC)