The earth can be approximated as a sphere of uniform density, rotating on its axis once a day. the mass of the earth is 5.971024 kg, the radius of the earth is 6.38106 m, and the period of rotation for the earth is 24.0 hrs. part a what is the moment of inertia of the earth? use the uniform-sphere approximation described in the introduction.

Question

Giana Sosa

Geography

11 November, 15:22

The earth can be approximated as a sphere of uniform density, rotating on its axis once a day. the mass of the earth is 5.971024 kg, the radius of the earth is 6.38106 m, and the period of rotation for the earth is 24.0 hrs. part a what is the moment of inertia of the earth? use the uniform-sphere approximation described in the introduction.

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Eliana Jarvis · Answer 1

In the problem, we were asked to solve for the moment of inertia of the earth. It is already given that the moment of inertia (I) of a "uniform" sphere of radius R is 2/5 M R^2 and the coefficient of a uniform sphere is 2/5, or 0.40.

M refers to the mass of the uniform sphere in question

R refers to the Radius of the uniform sphere (squared).

The following is the process in finding the moment of inertia.

I = (0.40) (5.97 x 10^24 kg) (6.38 x 10^6 m)

I = 9.72 x 10^37 kg * m^2

Thus, the answer is 9.72 x 10^37 kg * m^2.