Chapter 12, Problem 33A

A sizable quantity of soil is washed down the Mississippi River and deposited in the Gulf of Mexico each year. What effect does this tend to have on the length of a day? (Hint: Relate this to a spinning skater who extends her arms outward.)

To determine

The effect on the length of a day when sizeable quantity of soil is washed down in Mississippi river.

Answer to Problem 33A

The length of a day will be extended by a small amount.

Explanation of Solution

Introduction:

Angular momentum can be expressed as: $L=I\omega$

Here, $\omega$ is the angular velocity while $I$ is the moment of inertia.

Description:

A spinning skater extends her arms to slow down the spinning, hence decreasing the angular velocity using such movement. Due to this, moment of inertia increases and thereby decreasing the angular velocity. This is due to law of conservation of angular momentum.

According to the given statement, the washed down soil gets collected at a larger distance just as the case of spinning skater discussed above. Instead of arms, here is the case of Earth, it extends the length of the day to slow down its rotational motion. Here, the amount of slowing down is lowkeeping the angular momentum conserved.

Conclusion:

Thus, the length of the day extends to slow down the rotational motion of Earth.