Question

on melting of ice on a North Pole of earth its moment of inertia will be

Answer 1

Melting ice from polar regions is one of numerous processes that affect the speed of Earth’s rotation. It also affects the tilt of the axis of rotation, by about one degree per million years. This could also affect sunset times, as the length of Earth's day depends on the speed at which the planet rotates on its axis. Prior research found the rate at which Earth spins has changed over time.

Melting polar ice enters the oceans as water and one effect of this process is to move mass around on Earth’s surface. The shifting weight also causes material to move around inside the planet, thereby changing its shape. The combined effect of these motions is to make Earth less round and more squished from pole to pole, compared to the Equator. This net mass shift slows the Earth’s spin rate, just as a spinning ice skater pushes out her arms to slow down. That has the effect of lengthening the day. Again, when polar ice caps melt, they remove weight off underlying rock, which then rebounds upward. This makes the poles less flat and the planet more round overall. This should in turn cause Earth to tilt a bit and spin more quickly. Recent calculations indicate that loss of mass in Greenland and the Antarctic makes the day about 0.6 milliseconds longer per century.

At the same time, however, Earth is still changing shape in response to the massive melting from 23,000 to 10,000 years ago, coincidentally decreasing the day by about the same 0.6 milliseconds per century.

Note: The rotation of an object depends upon the moment of inertia of the object, which in turn depends upon the distribution of the mass. In case of all the ice on earth melting and flowing into the ocean, there will be a change in the distribution of the mass on earth. The concentrated mass of ice at the poles, far away from the center of the earth will be uniformly distributed across the earth in the form of water. This more than anything else will reduce the moment of inertia of the earth. In order to conserve its angular momentum, the rotational speed of the earth will increase to compensate for the decreased moment of inertia. This will shorten the length of day on earth. Experts estimate that in such a scenario, the length of day will be shortened by around 0.6 milliseconds per century.