Question

1) While standing on a stationary skateboard, Sunita catches a heavy ball thrown to her by a friend in the direction that the skateboard is pointing. What is the result of her catching the ball?

A. She begins rolling at the same speed the ball had before she caught it.

B. She begins rolling at a greater speed than the ball had before she caught it.

C. She begins rolling at a lower speed than the ball had before she caught it.

D. She remains stationary after catching the ball.

2)A figure skater performing a spin starts with his arms spread wide and then brings them in close to his body. What is the result?

A. His angular velocity increases, since his moment of inertia decreased.

B. His angular velocity increases, since his moment of inertia increased.

C. His angular velocity decreases, since his moment of inertia decreased.

D. His angular velocity decreases, since his moment of inertia increased.

Answer 1

1) Using conservation of momentum for Sunita and ball system

Pi = initial momentum of the system = m*v where m is mass of the ball and v is it's speed

(Sunita is at rest initially, hence her momentum is zero initially)

Pf = final momentum of the system = (m + M)V , M is Sunita's mass and V is Sunita's + ball speed after she cataches the ball

so Pf = Pi => (m+ M)V = m*v  

=> V = (m*v)/(m + M)    is Sunita's speed after she catches the ball.

The ratio (m)/(m + M) is less than one.

So, She begins rolling at a lower speed than the ball had before she caught it. Option C is correct.

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2) Using conservation of anugular momentum, when he brings his arms closer his moment of inertia decreases. Since the angular momnetum is constant so his angular velocity must increase.

Angular momentum = I*     if I decreases and momentum is constant then must increase.

So, his angular velocity increases, since his moment of inertia decreased. Option A is correct.