A uniform rod of mass m and length l has one end clamped. It rests on a smooth horizontal surface, rotating about the clamped end with a uniform angular velocity . The horizontal component of the force applied by the clamp on the rod is

Step-by-step solution

The center of mass of the uniform rod is at a distance r_ cm = l 2 from the clamped end. The rod is rotating with a uniform angular velocity on a smooth horizontal surface. The centripetal acceleration of the center of mass is a_ cm = ^2 r_ cm = ^2 ( l 2 ) . The net horizontal force on the rod is provided by the clamp. Using Newton's second law, the horizontal component of the force applied by the clamp is F = m a_ cm = m ^2 ( l 2 ) = 1 2 m ^2 l .