Question

The polar ice caps contain about 1.8 · 1019 kg of ice. This contributes essentially nothing to the moment of inertia of the Earth because it is located at the poles, close to the axis of rotation.

(a.) Estimate the change in the length of the day to be expected if the polar ice caps melt, distributing the water uniformly over the surface of the Earth. The moment of inertia of a thin spherical shell of mass m and radius r is 2/3mr2, ME = 5.98 · 1024 kg and RE = 6.37 · 106 m. Assume the Earth itself is a uniform sphere.

(b.) In 300 years time, by how many hours would our clocks be off if we didn’t account for this change in the Earth’s period of rotation?

The answer for a is .433 sec, but I do not know how to do b.

Answer 1

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