Question

A ball having velocity $v$ towards right and having angular velocity clockwise approaches the wall. It collides elastically with the wall and moves towards the left. Ground and wall are frictionless. Select the correct statement about angular velocity of the ball after collision.

(A) No change in angular velocity.
(B) It becomes zero.
(C) Angular speed decreases.
(D) It will be clockwise.

Answer 1

Hint The collision is the hitting of two bodies and it is of two types as elastic collision and the inelastic collision. In the elastic collision the kinetic energy of the two bodies remains the same, even after collision and in inelastic collision, there will be some loss of energy as heat etc.

Complete step by step solution
The ball is the elastic material, and the particles of the ball regain their original position up to a certain limit even after applying force. When the ball kicks to the ground, it comes back to the upward against the gravitational force. Hence when it is thrown to the right side to the wall, it again comes back by moving to the left. This collision of the ball and the wall and the ball and the ground are elastic collisions. This is because it is given that both wall and ground have no friction, so no tangential torque acts, only the normal forces and the $F = mg$ force acts along the center of the ball. Hence there is no change in the angular velocity.

Thus the option (A) is correct.

Note The above given case is peculiar, because the angular acceleration is zero but there is only the angular velocity. The ball has zero torque along its center, so $\tau = I\alpha = 0$ . Thus the acceleration $\alpha $ is also zero. The maintenance of the angular velocity is due to elastic collision.