Why a free rigid body at rest or going with constant velocity, when applied with an external force or after the application of an impulsive force, rotates only about its center of mass and the center of mass only goes in straight line with acceleration = F/m in case of net external force(F) applied on rigid body with mass m constantly or with constant velocity after the application of impulsive force? Why doesn't center of mass rotate about some other point on a rigid body or outside the rigid body?
The thing discussed in the linked questions which did not become clear to me is that if no external force is there on the body and we let the situation that the center of mass is rotating about some other point and we also know for sure that CoM and the whole body will translate with the same velocity, how does this picture become incorrect? There was an explanation that as no external force is there, so no rotation will happen except about CoM but what if I claim that the CoM will rotate with a constant angular velocity about that some other point as torque is zero, then angular velocity of CoM will be constant. Can't I claim this? Please help me prove myself wrong.
