Physics Question

Question

A ball of mass M swings in a horizontal circle at the end of a string of radius R at an initial tangential speed (Vo) as it undergoes uniform centripetal motion. A student gradually pulls the string inward such that the radius of the circle decreases. Which of the following predictions is correct regarding the angular momentum and rotational inertia of the ball about the axis of revolution as the ball is pulled inward?

a) The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution decreases.

b) The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution stays the same.

c) The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution decreases.

d) The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution stays the same.

Answer 1

Angular momentum is conserved in this problem. As the ball is pulled inward, its distance from the rotation axis decreases, so its rotational inertia decreases. Answer (c) is correct.