Statement

2.7.32^∗. On a smooth horizontal plane, two identical thin rotating rings move towards each other. Their velocities $v_1$ and $v_2$ are directed along a staright line connecting the centers of rings. Angular velocities of the rings $w_1$ and $w_2$. Determine the angular velocities of the rings after impact, if their slippage relative to each other disappears at the last moment of impact?