A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown.As the string is slowly pulled through a small hole in the table:
A)the angular momentum of M remains constant
B)the angular momentum of M decreases
C)the kinetic energy of M remains constant
D)the kinetic energy of M decreases
E)none of the above

Question

A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown.As the string is slowly pulled through a small hole in the table: 
A)the angular momentum of M remains constant 
B)the angular momentum of M decreases 
C)the kinetic energy of M remains constant 
D)the kinetic energy of M decreases 
E)none of the above

Quizplus · Accepted Answer

When the string is pulled through the hole, the radius of the circular motion of the block decreases. Since the block is still moving at the same speed, its linear momentum remains constant. Therefore, its angular momentum (which depends on both its linear momentum and the distance from the axis of rotation) must also remain constant according to the conservation of angular momentum. The kinetic energy, however, decreases because the work done by the tension in the string goes into changing the potential energy of the block-Earth system.

A Block with Mass M, on the End of a String