A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a brief time interval t . Assuming that t is so small that the rod does not noticeably alter its direction while the force acts, calculate the angular speed of the rod about its centre of mass after the force ceases to act.

Step-by-step solution

The angular impulse about the centre of mass is given by the product of torque and time. Torque = F l 2 Angular impulse = F l t 2 Change in angular momentum L = I The moment of inertia of a uniform rod about an axis passing through its centre of mass and perpendicular to its length is I = m l^2 12 Equating the angular impulse to the change in angular momentum: m l^2 12 = F l t 2 = 12 F l t 2 m l^2 = 6 F t m l