Question

A frog is sitting on the edge of an ice hockey puck. The puck is is spinning on an ice pond, ignore friction, If the frog moves to the center of the puck which statement is true.

The moment of inertia increases

the angular momentum increases

the angular velocity increases

the angular velocity decreases

the angular momentum decreases

Answer 1

Suppose, moment of inertia of the hockey puck = I

Initially the frog is at a distance r from the center of hockey puck.

So, total moment of inertia of the hockey puck with frog -

I1 = I + m*r^2

Suppose, initially w1 is the angular velocity and when the frog moves the center, then angular velocity becomes w2.

So, initial angular momentum = I1*w1 = (I + m*r^2)*w1

when the frog moves at the center, r = 0

So, total moment of inertia, I2 = I + m*0 = I

final angular momentum = I2*w2 = I*w2

Apply conservation of angular momentum -

initial angular momentum = final angular momentum

=> (I + m*r^2)*w1 = I*w2

=> w2 = w1 + (m*r^2) / I

=> w2 > w1

Therefore, third option 'angular velocity increases' is the correct answer.