Ball Rolling on Hemisphere

This lecture discusses the motion of a ball of mass m on the surface of a hemisphere of radius R. The ball is considered a point particle and is attached to one end of an elastic with zero rest length, negligible mass, and spring constant k. The ball is fixed at the other end to the top of the hemisphere and follows the sphere's shape. Various forces acting on the ball are analyzed, and the equations of motion on the hemisphere are derived. The conditions for the ball to reach the base of the hemisphere without detaching are determined.