A rod of mass `M` and length `L` is falling vertically with speed `v`. Suddenly its one end gets stuck in a friciitonless hook. Find the angular velocity of the rod just after its end gets struck.

Explanation

As all the impulse forces during the impact are applied by the hook thus they don't produce any torque about the hook. Thus angular momentum of the rod about the hook is conserved.
Initial angular momentum about hook `=M(L)/(2)v`
Final angular momentum about hook `=(M)/(3)L^(2)omega`
`implies(ML)/(2)v=(ML^(2))/(3)omegaimpliesomega=(3)/(2)(v)/(L)`