Question

A sphere is rolled on a rough horizontal surface. If gradually slows down and stops. The force of friction tries to
(a) decrease the linear velocity
(b) increase the angular velocity
(c) increase the linear momentum
(d) decrease the angular velocity.

Answer 1

The force of friction tries to decrease the linear velocity and increase the angular velocity

Explanation:

• If a sphere on a rough horizontal surface is rolled, the friction force will attempt to counteract linear motion and favor angular motion.
• Ff (Friction force) acts in the opposite direction of linear motion. It forms the torque in the direction of the clock, which helps to increase the rotation or angular velocity w.
• The specific question is what the friction force tends to do? Obviously, the linear velocity of the sphere vv will be reduced, but it tends to increase its angular velocity  w.
• The body slides along the surface without any rotation for zero frictional force. So we'd have zero angular speed. The angular velocity is only increased due to the frictional force.              

Hence, option (a) and (b) is the right answer.