I know that internal forces won't accelerate the centre of mass of system, but assuming there are three objects in a system and two of them move due to the internal force exerted by one and the reaction force exerted by the other, will the position of the centre of mass of the system still be the same even though the third object didn't move?
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1$\begingroup$ I do not understand your question, can you clarify it better? You claim to know internal forces won't accelerate CMS, but then you seem to ask whether internal forces do accelerate the CMS if the third object does not move. Why, if the principle holds in the general case, would it stop hold in this particular one? $\endgroup$– UmaxoCommented Jun 9, 2021 at 9:35
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$\begingroup$ Why does the third object not move? Either it has no net internal forces acting on it, or there are some internal forces balanced by an external force. If there is no external force the COM will not move. If there is an external force, it will move. $\endgroup$– alephzeroCommented Jun 9, 2021 at 11:21
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2 Answers
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If the combination of all three objects is defined as the system and there are no external forces (forces other than those between the objects) acting on the combination, then the center of mass (COM) of the system will be at rest or move in a straight line at constant speed per Newton's third law.
Let's say your third object is not initially part of the system. We can do this since we are free to define the system however we wish. Then the center of mass (COM) of the system is that of the two interacting objects. Since there are no external forces on the two objects, its COM is either at rest, or moves in a straight line at constant speed with respect to the selected point of reference.
We now introduce the third object into the system. This introduction changes the location of the center of mass of the system. If the COM of the original two object system was at rest, the new COM with the introduction of the third object will also be at rest. If the original COM was moving in a straight line at constant speed, the new system will move in a straight line but at a different constant speed because the third object is at rest, still satisfying Newton's third law.
Hope this helps.
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The way to think about problems like this is to consider the three masses as a "system". Then ask yourself whether any forces are being exerted on any part of the system by anything that is not in the system. If the answer is no, then the momentum of the system is conserved, which means that the center of mass of the system moves at a constant velocity. In particular, if it was at rest to begin with, it will not move.
From your description it sounds like your system consists of A, B, and C; and then A & B exert forces on each other while C doesn't do anything. There are no forces on A, B, or C by anything other than A, B, or C, and so the center of mass of the system remains at rest.
answered Jun 9, 2021 at 11:49