Chapter 11, Problem 1Q

If there were a great migration of people toward the Earth’s equator, would the length of the day (a) get longer because of conservation of angular momentum; (b) get shorter because of conservation of angular momentum; (c) get shorter because of conservation of energy; (d) get longer because of conservation of energy; or (e) remain unaffected?

To determine

The change that happens to the length of the day if there were a great migration of people toward the Earth’s equator.

Answer to Problem 1Q

Option (a)

Explanation of Solution

Moment of inertia is the sum of the products of the mass of each particle in a body with the square of its distance from the axis of rotation. The migration of more people towards the earth’s equator may result in the accumulation of more mass from the axis of rotation. As a result the moment of inertia of the Earth would increase.

The relation between the angular momentum and the moment of inertia is given by,

    $L=I\omega$

Here, $L$ is the angular momentum, $I$ is the moment of inertia, and $\omega$ is the angular velocity.

According to the conservation of angular momentum, the increase in moment of inertia will automatically decrease the Earths angular velocity. Thus the length of the day would increase.

Conclusion:

Since the angular momentum and the angular velocity are related option (a) is the correct answer.

Length of the day is increasing as a result of angular momentum so option (b) is the incorrect answer.

Since the length of the day is increasing option (c) is the correct answer.

Since the length of the day does not depends on the conservation of energy option (d) is incorrect.

The length of the day is increasing due to the angular momentum option (e) is incorrect.