Any force applied to a body creates a torque around some reference point, but if we ignore all other forces (gravity etc.) the body will rotate if and only if the torque is not zero relative to the centre of mass? How can we prove that? Why is it the centre of mass and not some other point?
If the torque around the CoM is zero, I will still be able to find infinitely many other points such that torque around all of them is not zero, but the body won't rotate at all.
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