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

As the block moves in a circle, its angular momentum is given by L = mvr, where m is the mass of the block, v is its velocity, and r is the radius of the circular path. As the string is pulled through the hole, the radius of the circular path decreases, but the velocity of the block increases to maintain angular momentum conservation. Therefore, the angular momentum of the block remains constant. Since there are no external forces acting on the block, the kinetic energy of the block also remains constant, so the best choice is A.

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