Chapter 12, Problem 35A

If the world’s populations move to the North and South Poles, would the length of a day increase, decrease, or stay the same?

To determine

To identify: Whether the length of a day increase, decrease, or stay the same.

Answer to Problem 35A

The length of a day would decrease.

Explanation of Solution

Introduction:

An increase in rotational inertia of an object would decrease its rotation rate. Angular momentum $L$ is always conserved.

  $L=I\omega$

Where $I$ is Rotational Inertia and $\omega$ is angular velocity.

If all of the Earth’s inhabitants are shifted towards the North and the South Pole. This results in a decrease in rotational inertia, which increases the Earth’s rotation rate to keep the angular momentum constant. Now, if the Earth starts rotating faster than the actual rotation rate will result in a shorter day span.

Conclusion:

Thus, due to an increase in rotational inertia, the angular velocity of Earth would decrease. If all of the world’s inhabitants move towards the North and South Poles, the length of a day would decrease.