1277 ( From a Caltech freshman-physics problem book ) (a ) A uniform bowling ball of mass m and radius R is initially thrown such that when it hits the floor it begins sliding with velocity V and not rolling. Find the ball's CM velocity at the point where it begins rolling without slipping. Hint: This problem can be worked with Newton's Laws, assuming constant deceleration, or by the energy method, but it is quite a bit simpler to notice that there exists an axis about which angular momentum is conserved. State where this axis is, and why no torque acts about this axis. You will need the general expression for the angular momentum of a rigid body, considering translation of the CM and rotation around the CM. (b ) A spinning solid disk, rotating with angular velocity w , is put down on a level surface. It slides and rolls until it reaches an angular velocity w at which it rolls without sliding. Show that w = w /3