Video narration
What happens when a sliding book catches an edge and starts turning? The block's center moves toward ridge O; the hit turns its sliding motion into rotation around O. About O, incoming angular momentum-the amount of turning motion-is Mv(a/2). During the brief hit, the impulse acts at O, so it cannot twist the block around O. That angular momentum is conserved. The moment of inertia, resistance to turning, is I = Ma2/6 + Ma2/2 = 2Ma2/3. So ω = (Mva/2)/(2Ma2/3) = 3v/(4a).