# 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 centre of mass frame is the inertial frame in which the total linear momentum is zero, however the total angular momentum can be non-zero. Your rotating cylinder is a good example of this.

It is possible to pick a rotating frame in which both the momentum and angular momentum are zero, however this will be a non-inertial frame and as such wouldn't normally be described as the centre of mass frame.

The acceleration of your point $A$ in the COM frame is simply $r\omega^2$ as usual.

• Which means a body can be in rotational motion in COM frame.
– user118752
Sep 25, 2016 at 11:23
• @HarshSharma: yes. Sep 25, 2016 at 11:23
• If the COM would have been non-inertial, would the point A still appear to be in rotational motion because it is now acted by a pseudo force and I believe that the path must be distorted from the usual circular path. Is it true?
– user118752
Sep 25, 2016 at 11:27
• @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. Sep 25, 2016 at 12:24