The Earth can be approximated as a sphere of uniform density, rotating on its ax

Question

The Earth can be approximated as a sphere of uniform density, rotating on its axis once a day. The mass of the Earth is 5.97×1024 kg , the radius of the Earth is 6.38×106 m , and the period of rotation for the Earth is 24.0 hrs .

A.What is the moment of inertia of the Earth? Use the uniform-sphere approximation described in the introduction.

I=?

B.Consider the following statements, all of which are actually true, and select the one that best explains why the moment of inertia of the Earth is actually smaller than the moment of inertia you calculated.

C.Where did the rotational kinetic energy of the Earth come from?

a-The Earth is an oblate spheroid rather than a perfect sphere. For an oblate spheroid, the distance from the center to the equator is a little larger than the distance from the center to the poles. This is a similar shape to a beach ball resting on the ground, being pushed on from above.
b-The Earth does not have uniform density. As the planet formed, the densest materials sank to the center of the Earth. This created a dense iron core. Meanwhile, the lighter elements floated to the surface. The crust of the Earth is considerably less dense than the core.
c-While the Earth currently has a period of 24 hours, it is in fact slowing down. Once it was rotating much faster, giving days that were closer to 20 hours than 24 hours. In the future, it is expected that days will become longer.

Explanation / Answer

A. for solid sphere,

I = 2 m R^2 / 5

= (2 x 5.97 x 10^24 x (6.38 x 10^6)^2) / 5

= 9.72 x 10^37 kg m^2

B. Ans(b)

C. Ans(A)

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