Center of Mass frame

Does a body appear stationary in Center Of Mass frame? I am aware of the fact that a system is at rest in COM frame and its net momentum is zero, then is the net angular moment zero too and does the body appear in rotation in the COM frame or does it appear completely stationary. Let's say C is the centre of mass of a cylinder with radius $r$ and A is any arbitrary point and the body has a translational constant velocity $v_0$ and is also rotating about an axis perpendicular to the plane of motion and passing through COM . Now in the frame of COM its clear that $v_0$ needn't be considered but what about the rotational velocity. Let's say I want to find the acceleration of point A. Is it $v_0^2/R$ in the direction of C as centripetal acceleration or is it the same in the opposite direction as a pseudo acceleration?

The acceleration of your point $A$ in the COM frame is simply $r\omega^2$ as usual.
• @HarshSharma: suppose you choose a frame with the origin at the centre of mass and rotating at the same angular velocity as the cylinder. In that case the point $A$ will be stationary, but it will experience a fictional force directed away from the centre of mass. – John Rennie Sep 25 '16 at 12:24
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