Question

If global warming continues over the next one hundred years, it is likely that some polar ice will melt and the water will be distributed closer to the equator.

(a) How would that change the moment of inertia of the Earth?

(b) Would the duration of the day (one revolution) increase or decrease?

Short answer

• (a) The mass at the equator increases as the polar ice melts and water is dispersed to the equator. The mass moves away from the axis of rotation, the line of action distance increases, inertia increases, and angular speed falls.
• (b) The angular speed is inversely proportional to the time period. The period lengthens as the angular speed falls. As a result, the day's length will be lengthened.

Step-by-step solution

Definition of mass of inertia:

The total of the products of the mass of each particle in the body with the square of its distance from the axis of rotation is the moment of inertia, which is the property of the body that resists angular acceleration.

The expression for the moment of inertia is given by,

$I=\frac{2}{5}m{R}^2$

Here, the mass is , and the distance is R.

Moment of inertia of the earth increases or decreases:

• (a) The mass at the equator increases as the polar ice melts and water is dispersed to the equator. The mass moves away from the axis of rotation, the line of action distance increases, inertia increases, and angular speed falls.
• (b) The angular speed is inversely proportional to the time period. The period lengthens as the angular speed falls. As a result, the day's length will be