# What exactly is the reactive centrifugal force (split)

by A.T.
Tags: centrifugal, force, reactive, split
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 Quote by DaleSpam However, this is not simply a difference of equally-valid opinions. You wish to state Newton's 3rd law in terms of changes in momentum instead of forces.
What Newton meant by "Newton's third law" is perfectly clear. First he defines
 Quote by Principia Definition IV An impressed force is an action exerted upon a body...
In other words, "actions" are "forces".
 Quote by Principia Law III For every action there is always opposed an equal reaction: ...
The examples following the definition are clearly about forces, not momentum. For the example of a horse drawing a stone tied to a rope, he is talking about the equal and opposite forces the rope exerts on the horse and the stone. By any reasonable interpretation of that scenario, the changes of momentum of the horse and the stone are not equal and opposite, in general.

The explanation of law III continues
 If a body impinge upon another, and by its force changes the momentum of the other, the change in momentum of that body will be equal and opposite; that is to say, if the (movement of the) bodies are not hindered by any other impediments.
(My bold).

To summarize, action and reaction forces are always equal and opposite in pairs, but they don't necessarily cause equal and opposite changes of momentum if the motion of the two bodies is constrained in some other way.

That explains why the changes in momentum of the horse and the stone are not equal and opposite, of course.

Reformulating classical mechanics in terms of "Mason's laws of motion" is fine by me, but don't mis-attribute Mason's laws to Newton where they are different.
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 Quote by AlephZero What Newton meant by "Newton's third law" is perfectly clear. ..... In other words, "actions" are "forces".
If it was "perfectly clear" there would be no discussion of how confusing it is, as in this quote that I referred to earlier from a physicist , Mark Hammond:
"Newton’s explanation starts out talking about forces and pressures, speaks of obstructing and advancing “progress,” and finally ends up talking about what appears to be momentum. I’ll say right here that I am unimpressed with the clarity of Newton’s explanation. I go back and forth between thinking action/reaction should be read as the change in motion as opposed to being read as the thing that changes the motion. But rather than pick nits (and criticize an author who can’t defend himself), let’s zero in on what Newton seems most intent upon telling us in this, his third law of motion: there is a specific relationship between the changes in the motions of two interacting objects. Hence, this is a law of motion."

 To summarize, action and reaction forces are always equal and opposite in pairs, but they don't necessarily cause equal and opposite changes of momentum if the motion of the two bodies is constrained in some other way.
They do cause equal and opposite changes of momentum if you look at the motions of the body and the rest of the inertial system the body is interacting with. You can always do that.
 That explains why the changes in momentum of the horse and the stone are not equal and opposite, of course. Reformulating classical mechanics in terms of "Mason's laws of motion" is fine by me, but don't mis-attribute Mason's laws to Newton where they are different.
It is not that the principle of reciprocity of forces between contact points is wrong (it is correct in most cases). But this reciprocity is demonstrated by the changes in momentum that the forces create as measured by the changes in motion of the centres of mass of the two interacting parts of an inertial system. If you want to explain it in terms of the reciprocity of forces, it is explained by the forces as measured by the accelerations of the centres of mass of the interacting parts of an inertial system. It is neither illuminating nor practical to apply Newton's third law in terms of the reciprocity of forces between the contact points. So I have difficulty believing that is what Newton fundamentally intended to convey in the third law.

In the simple situation of an astronaut pushing off from a space ship with his legs, the third law is demonstrated by the equal and opposite changes of momentum that result to the two parts of this inertial system (ie. astronaut and space ship). If you just apply the reciprocity of forces between the astronaut's feet and the surface of the space station, this does not explain the physics. You have to take into account what the feet and space station surface are connected to. You then have to take into account the masses of those bodies and the motions of the centres of mass of those bodies. Those are legitimate third law action/reaction pairs. They do not lose that quality simply because the centres of mass are not touching. There are a myriad of other forces (between different parts/atoms etc.) that we simply ignore because they are not important.

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 Quote by Andrew Mason It is neither illuminating nor practical to apply Newton's third law in terms of the reciprocity of forces between the contact points. So I have difficulty believing that is what Newton fundamentally intended to convey in the third law.
Then find a good reference that supports your interpretation. Otherwise you are simply engaging in personal speculation.

In context, Newton's Principia does not support your approach, and I have yet to see any other scientific reference that does either.

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