A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a short duration t . Assuming that t is so small that the rod does not appreciably change its direction while the force acts, find the angular momentum of the rod about its centre of mass after the force ceases to act.

Step-by-step solution

The angular impulse provided by the force about the centre of mass is equal to the change in angular momentum of the rod about its centre of mass. The torque acting on the rod about its centre of mass is = F l 2 . The angular impulse is given by J = t = F ( l 2 ) t = Flt 2 . Since the initial angular momentum is zero, the final angular momentum L is equal to the angular impulse. Thus, L = Flt 2 .