As shown in the figure, a solid sphere is set into motion on a rough horizontal surface, possessing a forward linear speed v and an anticlockwise angular speed v/R . Determine the linear speed of the sphere at the instant it stops rotating.

Step-by-step solution

Let the mass of the solid sphere be m and its radius be R . The moment of inertia of the solid sphere about its center of mass is I = 2 5 mR^2 . Consider a fixed point on the horizontal surface along the line of motion. The net torque about this point is zero because the line of action of the frictional force passes through the surface, and the torques due to the normal reaction and gravitational force cancel each other out. Therefore, the angular momentum of the sphere about any fixed point on the ground is conser