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I've encountered problems like this: A bullet with velocity v strikes a stick (intially at rest) at a distance d from the center of mass, then the bullet sticks to it, and the bullet-stick system rotates about the center of mass. But they ask me to find weird things like thespeed of center of mass(v in the equation below), which requires me to apply conservation of LINEAR momentum.

Question: Isn't the center of mass MOTIONLESS if the bullet-rod system is rotating? Although it IS possible to calculate the linear velocity of the center of mass after the collision, why is it even relevant in the case of a rotating system?

If the bullet had striked the rod AT the rod's center of mass, then sure, this question makes sense, as the bullet-stick moves forward with that linear velocity, and conservation of linear momentum is relevant. But if the bullet strike anywhere AWAY from the stick's center of mass, the system will rotate and the center of mass will NOT move.So, WHAT DOES THIS NON-ZERO VALUE I GOT FOR THE LINEAR VELOCITY OF CENTER OF MASS REPRESENT IN THE CASE OF A ROTATING SYSTEM?

Thanks in advance,

Lilly

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# Homework Help: Conservation of linear momentum applied to rotating systems? (with picture)

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