Also let \(\omega\) be the rotational angular velocity of the ball about its center of mass, \(\Omega=d \theta / d t\) be the angular velocity of the ball's motion within the bowl, and \(v=(R-r) \Omeg...Also let \(\omega\) be the rotational angular velocity of the ball about its center of mass, \(\Omega=d \theta / d t\) be the angular velocity of the ball's motion within the bowl, and \(v=(R-r) \Omega\) the translational speed of the ball. If we take zero potential energy to be the point where the ball is at the bottom of the bowl, then the potential energy of the ball is
