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3 years ago

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The Earth can be approximated as a sphere of uniform density, rotating on its axis once a day. The mass of the Earth is 5.97×102

4 kg , the radius of the Earth is 6.38×106 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. Express your answer in kilogram meters squared to three significant figures. View Available Hint(s)

1 answer:

svetlana [45]3 years ago

3 0

Answer:

I = 97.2 10³⁶ kg m²

Explanation:

The moment of inertia of a body the expression of inertia in the rotational movement and is described by the expression

I = ∫ r² dm

In this problem we are told to use the moment of inertia of a uniform sphere, the expression of this moment of inertia is

I = 2/5 M r²

where m is the mass of the earth and r is the radius of the earth.

Let's calculate

I = 2/5 5.97 10²⁴ (6.38 10⁶)²

I = 97.2 10³⁶ kg m²

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When the gravitational field strength is $g$ , the weight $(\text{weight})$ of an object of mass $m$ would be $m\, g$ .

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