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If I attach a weight to a string, and spin it, I notice that the faster I spin it, the more it pulls away from me. So, I imagine what would happen if I arranged a very large machine, designed so that it would spin a big weight in a circle, accelerating it so that it moves fast when the weight is pointing north, and slow when it is pointing south. Since the weight is pulling on the center more strongly when it points north, doesn't that mean that the machine as a whole should move in that direction?

This sounds like it would produce movement without the need for any thrust, i.e. the machine would go forward, but nothing would be sent backwards in reaction.

Since I'm pretty sure I'd have heard of it if newton's third law was somehow disproved, I imagine I'm missing something - would this machine not work? If it does work, where is the equal and opposite force?

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  • $\begingroup$ Could you please add a sketch of this situation? I have a hard time imagining it. How is the object spun, and what do you mean with "it pulls away from me"? What does "weight is pointing north, and [...] south" mean and how does weight pull differently when it is in different positions? $\endgroup$ – Steeven Jul 4 '16 at 8:10
  • $\begingroup$ In practice we calculate things the other way around, by using the third law to describe such scenarios. the spinning weight will transfer as much momentum to your rig as the rig transfers to the spinning weight, hence there is no movement of the center of mass. Now you can ask why the third law has to be correct? It doesn't have to be. We even known when it's not. The necessary condition is given by Noether's theorem: en.wikipedia.org/wiki/Noether%27s_theorem, which proves that momentum conservation is a consequence of the homogeneity of space. $\endgroup$ – CuriousOne Jul 4 '16 at 8:21
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It is true that the weight will pull the machine to the north when it points north because the machine is pulling the weight to the south; by Newton's Third Law, that means the weight is pulling the machine northward. However, you have to think about what happens during the rest of the rotation. To have a faster velocity while the weight points north, the weight must be accelerated while it us moving north, that is, while it is pointed west (if the rotation is clockwise). During this time, the machine pushes the weight northward, so the weight pushes the machine southward. Similarly, to have the weight move slowly when it points south, the machine must decelerate the weight as it moves south (when it points east). Here, the machine pushes the weight northward, so the weight pushes the machine southward.

These two southward pushes when the weight points east or west counteract the northward pushes when the weight points north or south. The change in velocity after a whole rotation is zero.

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