A ball is sliding on a rough horizontal surface such that its center of mass speed is greater than , where is the ball's radius and is its angular speed. Which statement describes the effect of the kinetic friction force on the ball?
- The friction force is in the forward direction, increasing and decreasing .
- The friction force is in the backward direction, decreasing and increasing . (correct answer)
- The friction force is in the backward direction, decreasing both and .
- The friction force is in the forward direction, increasing both and .
Explanation: Since the ball is sliding, the point of contact is moving forward relative to the surface. The kinetic friction force opposes this relative motion, so it acts in the backward direction. This backward force creates a net force that decreases the translational speed . This force also creates a torque about the center of mass that increases the angular speed . This continues until and the ball rolls without slipping.