Chapter 12, Problem 16A

Why are your answers different to the previous two questions?

To determine

To explain: The difference in the results obtained for angular momentum and spin rate.

Answer to Problem 16A

Since angular momentum tends to remain conserved, spin rate changes as the rotational inertia changes.

Explanation of Solution

Introduction: Angular momentum is the product of rotational inertia and spin rate.

  $\text{L = I}\omega$

Angular momentum of an object tends to remain conserved. If a skater pulls her arms in while spinning to reduce her rotational inertia to half, the spin rate similarly, increases by the same proportion to keep the angular momentum conserved. Thus, the spin rate will increase twice.

Conclusion: Thus, to keep the angular momentum conserved, if rotational inertia decreases then the spin rate increases by the same proportion.