A solid sphere rolling on a rough horizontal surface with a linear speed v elastically collides with a fixed, smooth, vertical wall. Determine the speed of the sphere after it commences pure rolling in the backward direction.

Step-by-step solution

Before the collision, the solid sphere is in pure rolling. Its linear velocity is v and its angular velocity is = v R . During the elastic collision with the smooth vertical wall, the linear velocity of the sphere reverses its direction, becoming v in the backward direction. Since the wall is smooth, it exerts no torque about the center of mass, meaning the angular velocity remains unchanged in magnitude and direction. Immediately after the collision, the sphere moves backward with speed v but continues to rotate i