Question

A thin-walled, hollow sphere of mass M and radius R is free to rotate around a vertical shaft that passes through the center of the sphere. Initially, the sphere is at rest. A small ball of clay of the same mass M moving horizontally at speed v grazes the surface of the sphere at its equator. After grazing the surface, the ball of clay is moving at speed v/2. What is the angular momentum of the ball of clay about the shaft before it grazes the surface? After it grazes the surface?

Answer 1

Answer:

initial angular momentum is given as

$L_i = mv R$

final angular momentum is given as

$L_f = m(\frac{v}{2}) R$

Explanation:

Angular momentum of the ball about the axis of the thin walled sphere is given as

$L = m v R$

here we know that

before it grazes the surface the speed is "v" while after grazing the surface its speed is "v/2"

So we have

initial angular momentum is given as

$L_i = mv R$

final angular momentum is given as

$L_f = m(\frac{v}{2}) R$