A ball of mass M moves in a circular path on a horizontal, frictionless surface. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase. Complete the following sentence: This occurs because
A)the linear momentum of the ball is conserved.
B)it is required by Newton's first law of motion.
C)the angular momentum of the ball is conserved.
D)the angular momentum of the ball must increase.
E)the total mechanical energy of the ball must remain constant.

Question

A ball of mass M moves in a circular path on a horizontal, frictionless surface. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase. Complete the following sentence: This occurs because 
A)the linear momentum of the ball is conserved. 
B)it is required by Newton's first law of motion. 
C)the angular momentum of the ball is conserved. 
D)the angular momentum of the ball must increase. 
E)the total mechanical energy of the ball must remain constant.

Quizplus · Accepted Answer

As the radius of the circular motion decreases, the linear velocity of the ball must increase in order to maintain constant angular velocity. This means that the angular momentum of the ball (L = Iw) must remain constant, as the moment of inertia of the ball does not change. Therefore, the correct choice is C, the angular momentum of the ball is conserved.

A Ball of Mass M Moves in a Circular Path