Chapter 12, Problem 34A

If all of Earth’s inhabitants moved to the equator, how would this affect Earth’s rotational inertia? How would it affect the length of a day?

To determine

To explain: The effect on Earth’s rotational inertia and length of days if all of the Earth’s inhabitants moved to the Equator.

Answer to Problem 34A

Rotational Inertia would increase that results in longer days.

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 population of the Earth is shifted towards the equator. This results in an increase in rotational inertia, which decreases the Earth’s rotation rate to keep the angular momentum constant. Now, if the Earth starts rotating slower than the actual rotation rate will result in longer days.

Conclusion:

Thus, if the world’s populations move to the Equator then due to an increase in rotational inertia, the angular velocity of the Earth would decrease, and consecutively the length of a day would increase.