Chapter 12, Problem 32A

You sit in the middle of a large, freely rotating turntable at an amusement park. If you crawled toward the outer rim, would your rotational speed increase, decrease, or remain unchanged? What law of physics supports your answer?

To determine

Whether the rotational speed increase, decrease, or remain unchanged when the person crawled toward the outer rim.

Answer to Problem 32A

Decrease

Explanation of Solution

Introduction:

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

And, the more the distance of the mass’s concentration from the axis of rotation, the more is the rotational inertia of the object.

The angular momentum is given by,

  $L=I\omega$

Where,

  $I=$ rotational inertia

  $\omega$ = rotational speed

Since no external torque is exerted on the turntable, hence its angular momentum remains conserved.

Now, when the person is crawled towards the outer rim, then the rotational inertia will increase. Then, since the angular momentum is conserved, its rotational speed will decrease.

Conclusion:

Hence, for the given case, the rotational speed will decrease.