A "real" force has an actor, something that exerts the force. Centrifugal force is not a real force as there is no actor creating a force; it's just an artifact of describing things from a non-inertial (rotating) frame of reference. (Often it is extremely useful to describe things from within a non-inertial frame.)nuby said:I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?
I'm curious as to what you consider to a criteria for existence? It may seem odd but this question goes to the heart of the matter when it comes to things such as the inertial force, of which centrifugal force is one of them.nuby said:I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?
Also, do centrifugal and centripetal effects/forces exist in outer space, i.e. on space shuttle.
Thanks
There is a similar comment in Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.
Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]
Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.
From the standpoint of an observer in the accelerating frame, the inertial force is actually present. If one took steps to keep an object "at rest" in S', by tying it down with springs, these springs would be observed to elongate or contract in such a way as to provide a counteracting force to balance the inertial force. To describe such force as "fictitious" is therefore somewhat misleading. One would like to have some convenient label that distinguishes inertial forces from forces that arise from true physical interactions, and the term "psuedo-force" is often used. Even this, however, does not do justice to such forces experienced by someone who is actually in the accelerating frame of reference. Probably the original, strictly technical name, "inertial force," which is free of any questionable overtones, remains the best description.
The presence of a centrifugal force does not require the existence of a reaction force. Centrifugal forces are the inertial force on a particle which is only measured by observers in rotating frames of reference and is directed in the outward direction from the center of rotation.Jeff Reid said:Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.
No.dst said:So in other words, a "fictitious force" in a particular reference frame is one which has no 3rd law pair for that reference frame?
I'd say yes. (In Newtonian physics, at least.)dst said:So in other words, a "fictitious force" in a particular reference frame is one which has no 3rd law pair for that reference frame?
(emphasis added by DaleSpam)Jeff Reid said:Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.
Exactly.DaleSpam said:NO! The centrifugal force is not a reaction force. It is a ficticious force and as such it does not obey Newton's 3rd law.
You are probably aware that there are many descriptions that you can use to accurately describe the same thing, each description capturing a different aspect of the thing.nuby said:However, I was thinking more along the line that either Centrifugal and Centripetal is actually an affect of gravity, and possibly a form of counter gravity. And inertia is a kinetic (stored) energy, which isn't directly related to the inward pulling and outward pulling on an object due to centripetal or centrifugal force.
For example, isn't the centripetal force that keeps an object in orbit, in space (planets, satellite) due to gravity? Why would centripetal force be any different on earth?
With the string and ball analogy. Why does a mass rotating around an axis, rise up against gravity the faster it spins. Could a gravitational force be coming from within the string?
Jeff Reid said:Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.
DaleSpam said:(emphasis added by DaleSpam)
NO! The centrifugal force is not a reaction force. It is a ficticious force and as such it does not obey Newton's 3rd law.
No "rules" are being changed. To accelerate something in a circular path requires a centripetal force; that force, like any other, will be paired with a "reaction" force per Newton's 3rd law. But that "reaction force" is not the centrifugal force. The reaction to a centripetal force is an equal and opposite force on whatever is creating the centripetal force. See my examples in post #3.rcgldr said:I don't understand, it clearly seems to be just like any other reaction force. Any acceleration on an object, regardless of direction, creates a reactionary force. Why change the rules for the one case where the force just happens to be perpendicular to the objects direction of travel? Why should the direction of the force matter at all?
NO! How can you possibly say it seems to be just like any other reaction force? An action-reaction pair act on two different bodies. The centripetal and centrifugal force act on the same body. They cannot possibly form an action-reaction pair.rcgldr said:I don't understand, it clearly seems to be just like any other reaction force. Any acceleration on an object, regardless of direction, creates a reactionary force.
Doc Al said:Exactly.
Einstein was motivated by this idea, i.e. that what Newtonians called "fictitious" forces were really, in Einstein's opinion anyway, "real" forces because they behaved like the "real" force of gravity. However others have interpreted this to mean that since inertial forces are identical in nature to "fictitous" forces that it meant that gravity was also to be considered a "fictitous force." This was never Einstein's view though, although it appears to be the view of some physicists today.nuby said:Thanks everyone for your replies and references.
Einstein's idea that gravity and inertia could be identical is similar to what I was assuming. However, I was thinking more along the line that either Centrifugal and Centripetal is actually an affect of gravity, and possibly a form of counter gravity.
Inertia and kinetic energy are very different things. First off it is incorrect to think of kinetic energy as being stored anywhere and second it is incorrect to think that because kinetic energy and inertial mass are related that they are the same thing. That would be like saying that velocity and kinetic energy are the same thing and that's obviously wrong.And inertia is a kinetic (stored) energy, ..
Give an example of a 3rd law pair with centrifugal force.pmb_phy said:I disagree. The centrifugal force does obey Newton's third law.
"I disagree" is insufficient. I just gave a concrete example showing that it did not obey Newton's 3rd law. Please point out the error in my analysis and provide a counter-example.pmb_phy said:I disagree. The centrifugal force does obey Newton's third law.
Pete, are you objecting to the word "ficticious"? If so then I am glad to use the term "inertial force" instead of "ficticious force", it is just a label.pmb_phy said:Einstein was motivated by this idea, i.e. that what Newtonians called "fictitious" forces were really, in Einstein's opinion anyway, "real" forces because they behaved like the "real" force of gravity. However others have interpreted this to mean that since inertial forces are identical in nature to "fictitous" forces that it meant that gravity was also to be considered a "fictitous force." This was never Einstein's view though, although it appears to be the view of some physicists today.
I consider all of these to be 3rd law pairs:Doc Al said:Give an example of a 3rd law pair with centrifugal force.
Let's take a look.rcgldr said:I consider all of these to be 3rd law pairs:
3rd law pair? Yes! No centrifugal force here. (Though I don't like the term "inertia reaction"--seems meaningless to me. You push on something; it pushes back. It's that simple.)While turning, due to slip angle, a car's tires exert an outwards force on the pavement, and the pavement in turn exerts an inwards force onto the tires, which through the tires, wheels and suspension, exert an inwards force on the rest of the car, and the rest of the car's inertia reaction ultimately results in an outwards force on the tires.
Again: 3rd law pair? Yes! No centrifugal force here.A moving object has a force applied to it to cause it to turn. At the point of applicaton of force, the applied force accelerates the object inwards, and the object's inertia reaction results with an equal and opposite outwards reaction force (at the point of application).
Again: No centrifugal force here.A cyclotron generated field results in an inwards force on a moving electron. The electron's inertia reaction results in an outwards force on the cyclotron.
The 3rd law pair here is the gravitational force that each exerts on the other. No other forces operate.Two objects orbit in a circular path in space. The gravitational force results in an inwards forces on both objects, and the two objects' inertia reactions result in an equal and opposite outwards reaction forces.
Doc Al said:No centrifugal force here. (Though I don't like the term "inertia reaction"--seems meaningless to me. You push on something; it pushes back. It's that simple.)
That's not how the term centrifugal force is used in physics today. That "pushing back" is a real force, nothing to do with inertial forces.rcgldr said:"inertia reaction"--seems meaningless to me. You push on something; it pushes back.If there's a net acceleration an object, some or all of that "pushing back" is what some of us call an inertia reaction force, and in when this force is perpendicular to the direction of travel, some of us call that reaction force centrifugal force. Rather than define centrifugal force as having no meaning, some of us would prefer to define centrifugal force as the inertial reaction force resulting for the real force component perpedicular to an objects direction of travel.
When you exert a contact force (which is a real electromagnetic force) on something, it exerts a contact force back on you (which is also a real electromagnetic force). Both forces are quite real.Except for field based forces, at the point of application, when a object is pulled or pushed, there's an net tension or compression at the point of application, and this requires equal and opposite forces. In some cases, one of these is a "real" force and the other a "reaction" force due to inertial resistance to acceleration.
Apparently. There's a somewhat archaic usage of "centrifugal force" to mean the reaction force to the centripetal force. I guess that's what you mean. But that's totally different from the standard usage of the term centrifugal force. It even acts on a different body! (And if that's all you mean, there's not much to argue about!)So this seems like an argument about terminology.
The outward-directed friction force on the pavement does indeed form an action-reaction pair with the inward-directed friction force on the tires. However, it is a real force which exists in inertial reference frames, so it is not the centrifugal force.rcgldr said:I consider all of these to be 3rd law pairs:
While turning, due to slip angle, a car's tires exert an outwards force on the pavement, and the pavement in turn exerts an inwards force onto the tires, which through the tires, wheels and suspension, exert an inwards force on the rest of the car, and the rest of the car's inertia reaction ultimately results in an outwards force on the tires.
There is only a single object considered here, so you cannot possibly have an action-reaction pair since they always act on different objects.rcgldr said:A moving object has a force applied to it to cause it to turn. At the point of applicaton of force, the applied force accelerates the object inwards, and the object's inertia reaction results with an equal and opposite outwards reaction force (at the point of application).
No, the electron's electromagnetic field results in an outwards force on the cyclotron.rcgldr said:A cyclotron generated field results in an inwards force on a moving electron. The electron's inertia reaction results in an outwards force on the cyclotron.
This is actually quite clever. For the sake of argument we will assume a Newtonian approach where gravity is a real force. We will consider the reference frame rotating about the barycenter such that both objects are at rest. The gravity forces do indeed form an action-reaction pair, so they are equal and opposite. Since each body is at rest in the rotating frame the centrifugal force acting on each body must be of equal magnitude and opposite direction to the gravity force acting on that body. Therefore the centrifugal forces are equal and opposite to each other. Thus they do appear to form a 3rd law action-reaction pair: they act on different bodies, they are the same "kind" of force, and they are equal in magnitude and opposite in direction.rcgldr said:Two objects orbit in a circular path in space. The gravitational force results in an inwards forces on both objects, and the two objects' inertia reactions result in an equal and opposite outwards reaction forces.
Okay. You wroteDaleSpam said:"I disagree" is insufficient. I just gave a concrete example showing that it did not obey Newton's 3rd law. Please point out the error in my analysis and provide a counter-example.
It is meaningless to refer to a particular force as either an action force or a reaction force in general (friction is the only counter example I can recall at the moment).How can you possibly say it seems to be just like any other reaction force? An action-reaction pair act on two different bodies. The centripetal and centrifugal force act on the same body. They cannot possibly form an action-reaction pair.
Okay. This is for both of you - Let us consider the electric force as an example; A styrofoam ball as an excess of charge on it and is initially at rest in an inertial frame of reference. Now let there be an electrical field applied. The charged ball will then start to accelerate. There is only an action force and no reaction force acting on the ball. But the force is quite real. Newton's 3rd law does not apply to this case since it applies to situations when there are a pair of forces acting on a body. Now let us suppose that the charged ball is in contact with a wall whose unit normal is parallel to the electric field and the direction of the electric force is towards the wall. When the ball comes in contact with the wall we can then apply Newton's 3rd law. The force exerted by the ball on the wall is equal and opposite to the force the wall exerts on the ball. This is the action-reaction pair. Similarly if there is an uncharged ball but now the force of gravity is acting on a ball on a table. The table exerts and equal and opposite force on the ball. This too is an action-reaction pair. If the ball is in free-fall then there is no reaction force and Newton's 3rd law does not apply. Now let us consider a (non-charged) ball in free-fall as observed in the rotating frame. Since the object is not in contact with anything and there is no counter force acting then there is no reaction force. Now let us suspend the ball by a spring in the rotating frame. Now there is an action-reaction force. The centrifugal force acts outwards while the centripetal force exerted by the spring in the oppsite (i.e. inward) direction.Doc Al said:Give an example of a 3rd law pair with centrifugal force.
I was attempting to answer nuby's original question, i.e.DaleSpam said:Pete, are you objecting to the word "ficticious"?
nuby said:I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?
A shuttle is in free-fall and as such is in a locally inertial frame, not an inertial frame. Therefore there are no forces acting on the shuttle other than the tidal forces exerted by the Earth. However the term "locally inerital frame" refers to the notion that the tidal forces are as such that they can be neglected for the purposes of the problem under consideration. Such a frame of reference could be a hundred feet wide or they could be smaller that the nucleus of an atom. It also depends on the time required to execute the experiment.Also, do centrifugal and centripetal effects/forces exist in outer space, i.e. on space shuttle.
Bold face added by me.Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.
Forgive me for intruding and allow me to point out that I have not followed the discussion in it's entirety. However in the quoted example, surely the centrifugal force arises purely as a consequence of the rotating reference frame. In other words, both the centrifugal and centripetal forces are not observable in the same reference frame and hence one cannot consider them an action-reaction pair. Perhaps I have misinterpreted your example and I apologise if that is the case.pmb_phy said:Now let us suspend the ball by a spring in the rotating frame. Now there is an action-reaction force. The centrifugal force acts outwards while the centripetal force exerted by the spring in the oppsite (i.e. inward) direction.
Newton's 3rd law (in its simplest version) applies whenever two bodies interact. The "pair" of 3rd law forces acts on different bodies. The "reaction" force in this case will be an electrostatic force on whatever is producing the field.pmb_phy said:Okay. This is for both of you - Let us consider the electric force as an example; A styrofoam ball as an excess of charge on it and is initially at rest in an inertial frame of reference. Now let there be an electrical field applied. The charged ball will then start to accelerate. There is only an action force and no reaction force acting on the ball. But the force is quite real. Newton's 3rd law does not apply to this case since it applies to situations when there are a pair of forces acting on a body.
That's true. Now there are two forces identified as acting on the ball and those forces are not 3rd law pairs.Now let us suppose that the charged ball is in contact with a wall whose unit normal is parallel to the electric field and the direction of the electric force is towards the wall. When the ball comes in contact with the wall we can then apply Newton's 3rd law. The force exerted by the ball on the wall is equal and opposite to the force the wall exerts on the ball. This is the action-reaction pair.
The force of gravity and the normal force from the table are not 3rd law pairs.Similarly if there is an uncharged ball but now the force of gravity is acting on a ball on a table. The table exerts and equal and opposite force on the ball. This too is an action-reaction pair.
Sure there is and sure it does. (Using the non-GR view of gravity for the moment.)If the ball is in free-fall then there is no reaction force and Newton's 3rd law does not apply.
The "centrifugal force" acts outward on the ball and is an artifact of viewing things from a rotating frame. It is obviously not the 3rd law "reaction" to centripetal force for two reasons: (1) Both centripetal and "centrifugal" forces act on the same body!; (2) "Centrifugal" force is not a "real" force--there is no actor!Now let us consider a (non-charged) ball in free-fall as observed in the rotating frame. Since the object is not in contact with anything and there is no counter force acting then there is no reaction force. Now let us suspend the ball by a spring in the rotating frame. Now there is an action-reaction force. The centrifugal force acts outwards while the centripetal force exerted by the spring in the oppsite (i.e. inward) direction.
Cryptonic said:If a circular space station is rotating, deep in some intergalactic void with no visible stars or galaxies, how do you know it is rotating? Wouldn't it seem as if something "outside" is pulling you towards the floor (ie outer hull of stationary space station)?
I guess what I'm asking is, how can we say convincingly that the space station is rotating, and not the rest of the universe rotating around the stationary space station?
Isn't all motion relative?...or something?
No, Newton's 3rd law does not apply here because it applies to situations where there are two bodies interacting. You can have as many forces as you wish acting on a single body, you don't invoke the 3rd law until you are considering another object interacting with the first.pmb_phy said:Okay. This is for both of you - Let us consider the electric force as an example; A styrofoam ball as an excess of charge on it and is initially at rest in an inertial frame of reference. Now let there be an electrical field applied. The charged ball will then start to accelerate. There is only an action force and no reaction force acting on the ball. But the force is quite real. Newton's 3rd law does not apply to this case since it applies to situations when there are a pair of forces acting on a body.
Yes, and neither is centrifugal.pmb_phy said:Now let us suppose that the charged ball is in contact with a wall whose unit normal is parallel to the electric field and the direction of the electric force is towards the wall. When the ball comes in contact with the wall we can then apply Newton's 3rd law. The force exerted by the ball on the wall is equal and opposite to the force the wall exerts on the ball. This is the action-reaction pair.
If you are considering only the ball then you are right. But there is an equal-and-opposite (Newtonian) gravity reaction force on the Earth if you are considering the Earth too.pmb_phy said:Similarly if there is an uncharged ball but now the force of gravity is acting on a ball on a table. The table exerts and equal and opposite force on the ball. This too is an action-reaction pair. If the ball is in free-fall then there is no reaction force and Newton's 3rd law does not apply.
Yes, there is no reaction force, but there is a centrifugal force. The centrifugal force is therefore not a reaction force.pmb_phy said:Now let us consider a (non-charged) ball in free-fall as observed in the rotating frame. Since the object is not in contact with anything and there is no counter force acting then there is no reaction force.
Sure, but the action-reaction pair is the compression force of the spring on the ball and the compression force of the ball on the spring. The centrifugal force is not part of any action-reaction pair.pmb_phy said:Now let us suspend the ball by a spring in the rotating frame. Now there is an action-reaction force. The centrifugal force acts outwards while the centripetal force exerted by the spring in the oppsite (i.e. inward) direction.
Yes, I would like you to discuss them.pmb_phy said:Would you like me to discuss the four properties that you mentioned or can you obtain what I meant from the explanation I gave in this post?
This is a valid and interesting piont. I will have to modify or remove my property number 1. To be honest, I was not considering boosts, particularly not relativistic boosts. I was considering linearly accelerating and rotating reference frames. I need to think about that a bit.pmb_phy said:You spoke of distinguishing characteristics of force. No two forces of a different nature are identical for the sole fact that they are different. E.g. the magnetic force may exist in one frame but may not exist in another frame. In such cases the magnetic force becomes the electric force.
Yes there is! Strap an accelerometer on it.pmb_phy said:But when you're making an observation in a single frame then there is nothing about the motion that will tell you whether the force is inertial or not.
That's all I mean. I prefer the archaic usage of centrifugal force because it had a meaning. The "standard" usage of the term defines it to be non-existing. As posted previously, I am not alone in preferring the archaic usage of centrifugal force:Doc Al said:There's a somewhat archaic usage of "centrifugal force" to mean the reaction force to the centripetal force. I guess that's what you mean. But that's totally different from the standard usage of the term centrifugal force.
It even acts on a different body! (And if that's all you mean, there's not much to argue about!)
rcgldr said:http://www.encyclopedia.com/doc/1E1-centripe.html
See section on "reactive force":
http://peswiki.com/index.php/PowerPedia:Centrifugal_force
Examples of action-reaction pairs
The centrifugal force (modern meaning) does exist in the rotating frame. I think you are just getting hung up on the word "ficticious". It doesn't mean that it doesn't exist.rcgldr said:I prefer the archaic usage of centrifugal force because it had a meaning. The "standard" usage of the term defines it to be non-existing.
That is always a completely arbitrary distinction. Together they are an action-reaction pair, beyond that it does not matter.rcgldr said:The tough call here is which forces are the action forces and which are the reaction forces.
I'm not sure that the OP was concerned about modern versus classis usage.DaleSpam said:Your archaic usage does nothing but add a lot of confusion to this thread, which has been dealing with the modern usage.
Centrifugal force, in the modern sense, most certainly has a precise meaning and an existence.rcgldr said:That's all I mean. I prefer the archaic usage of centrifugal force because it had a meaning. The "standard" usage of the term defines it to be non-existing.
As Dale already pointed out, the distinction between "action" and "reaction" is arbitrary. Better to call them "3rd law pairs".The tough call here is which forces are the action forces and which are the reaction forces.
Hmmm .. you're right. I now see that I had something else in mind. In any case, in reality there actually is a reaction force present. The charged particle exerts a force on the source of the field. I now see that this was a poor example.DaleSpam said:No, Newton's 3rd law does not apply here because it applies to situations where there are two bodies interacting. You can have as many forces as you wish acting on a single body, you don't invoke the 3rd law until you are considering another object interacting with the first.
Yes there is! Strap an accelerometer on it.
[/qoute]
So what? An accelerometer in free-fall in a gravitational field will read zero, contrary to what you are attempting to imply. We are discussing Newtonian physics here right??
Pete
"Action-reaction" pairs do not act on the same object!pmb_phy said:Consider this - An observer is at rest in a uniformly rotating frame of reference. In that frame there is a ball suspended by a spring. The centrifugal force exerts a force on the ball and the ball exerts a force on the spring. The force exerted on the ball is the centrifugal force. The force the string exerts on the ball is the centripetal force. This is an action-reaction pair.
Don't forget that the EM fields carry momentum. In fact, in this case each particle interacts directly with the local field, rather than the other particle. Taking that into account momentum is conserved and therefore Newton's 3rd law is satisfied at all times.pmb_phy said:Consider instead two charged particles moving along two straight lines which intersect at a right angle. Each particle has a force exerted on it which is caused by the other particle. However, at least in this case, Newton's 3rd law does not apply. Contrary to your claim that "real" forces must obey Newton's 3rd law the forces acting here, i.e. the Lorentz forces, are quite real.
I already mentioned exactly this point in post 24. I also have not introduced an example using gravity and when someone else has I made it clear if I thought they were using the Newtonian approach. I like this way of classifying inertial forces, and I am perfectly content to consider gravity an inertial force. I have no qualms about using ficticious/inertial forces.pmb_phy said:An accelerometer in free-fall in a gravitational field will read zero, contrary to what you are attempting to imply. We are discussing Newtonian physics here right??
I agree with you 100% on this point. It is one of my personal "pet peeves". In poetry it is great for words to have multiple meanings and all sorts of ambiguity. In physics it only causes problems.rcgldr said:Then again, if some group decides to change the meaning of a "classic" term, why not create a new term instead of changing the meaning of the old one? This is how to prevent confusion.
dipstik said:dale: i think coriolis forces are the result of the conservation of angular momentum in rotating frames, but i could be wrong.
Conservation of momentum states that when the total force acting on a system is zero then the momentum of that system is conserved. If a centrifugal force is acting on a particle then there is no reason to assume the momentum should be conserved. In GR this is well defined because the source of the centrifugal field (which Einstein viewed as a gravitational field) is the mass of the universe, i.e. the "fixed stars." This isn't all that hard to demonstrate since you merely have to consider a rotating spherical shell. The spacetime inside the shell is flat but the rotating shell causes the spacetime to rotate.DaleSpam said:Hi Pete,
One quick thought. Newton's 3rd law essentially defines the conservation of momentum in terms of forces. One way to see that the centrifugal force does not follow the 3rd law is simply to consider the momentum of an isolated system in a rotating reference frame. In the rotating reference frame the isolated system will accelerate, so momentum is not conserved in the rotating frame. Therefore the 3rd law is violated.
