Conservation of angular momentum during rolling with slipping [closed]

Question

A block of mass m moves with a velocity $\mathbf{B}$ on a smooth horizontal surface. It then passes over a cylinder $R$ and mass $m$, capable of rotating about it's own axis through $O$. The block while passing over, slips on the cylinder. The slipping stops before it loses contact with the cylinder. The block then moves on a similar smooth horizontal surface with a velocity $\mathbf{U}$. Find velocity $\mathbf{U}$.

In this question why do we conserve the angular momentum of the system about the axis of the cylinder even though there is an external force acting on the block (gravity). Wouldn't torque provided by this external force taken into account?

Answer 1

Remember that the velocity of the block has no vertical component at all times as gravity is balanced by the normal force. Therefore this problem can be equivalently re-expressed as a block brushing past a fixed cylinder in free space.

The essence of this problem is that the block imparts angular momentum to the cylinder, and itself loses an equal amount of angular momentum because what really causes this transfer is the friction, which must be equal and opposite on the two objects by Newton's Third Law.