I would like to calculate the change in linear position of a point on a bar whose center of mass is changing as the bar rotates. Assume an angular velocity of pi-rad/s, a negligible mass for the bar, and a mass of 1-kg for the weight (which is what is moving and causing the center of mass to change). The bar is 1-m long. I would also like to know whether the system would continue to rotate (with the CM shifting back and forth) if there are not other forces acting on the system. In other words: if the CM always ends up at the right after shifting the whole length of the bar while the bar rotates pi-rad, will the momentum carry the bar around and it will complete another cycle? If this is unclear, let me know.