1. The problem statement, all variables and given/known data 2. Relevant equations L = Iw v = wr 3. The attempt at a solution Friction acts on the ball while it is skidding, but goes away when the hoop starts to roll, because the velocity is 0 at a point on the ground. This is when v = wr. When skidding, friction decreases translational motion but the torque increases rotation. When the ball starts to roll without slipping, its angular momentum will be its rotational and translational angular momentum: L_f = Iw_f + mrv_f At this point, since w_f = v_f/R, and I for a hoop = MR^2 L_f = MR^2*v_f/R + MRv_f = 2MRv_f a. In the beginning, there is only rotational angular momentum. L_i = Iw_i Since w_i = v_i/2R and I = MR^2, L_i = MR^2*v_i/2R = MRv_i/2 Equating L_i = L_f MRv_i/2 = 2MRv_f v_f = v_i/4 b. Similarly, L_i = MR^2 *v_i/R = MRv_i Equating angular momentums, MRV_i = 2MRv_f v_f = v_i/2 c. Similarly, L_i = MR^2 *2v_i/R = 2MRv_i So 2MRv_i = 2MRv_f v_f = v_i So, my answer for a is correct, however for b and c, the final velocities are 0 and -v_i/2, respectively. Why?