Chapter 12, Problem 15A

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

To determine

The way in which the rate of spin of the skater will increase if her rotational inertia is reduced to half.

Answer to Problem 15A

It will be doubled.

Explanation of Solution

Introduction:

When no external torque acts on a system, then the angular momentum of the system remains conserved.

The angular momentum is given by,

  $L=I\omega$

Where,

  $I=$ rotational inertia

  $\omega$ = rotational speed

Since no external torque is exerted on the skater, hence his or her angular momentum remains conserved.

Now, if the rotational inertia of the skater is reduced to half while spinning, then considering the above-mentioned formula, the rate of spin will become twice.

Conclusion:

Hence, for the given case, the rate of spin will be doubled.