Chapter 12, Problem 14A

If a skater who is spinning pulls her arms in so as to reduce her rotational inertia to half, by how much will her angular momentum increase?

To determine

The way in which the angular momentum of the skater will increase if her rotational inertia reduced to half.

Answer to Problem 14A

No change

Explanation of Solution

Introduction:

The angular momentum is given by,

  $L=I\omega$

Where,

  $I=$ rotational inertia

  $\omega$ = rotational speed

But it is known that when no external torque acts on a system, then the angular momentum of the system remains conserved. And, since no external torque is exerted on the skater, thus her angular momentum remains conserved.

Conclusion:

Hence, the angular momentum of the skater remains unchanged since no external torque acts on her.