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 . 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)

Answer 1

I = 97.2 10³⁶ kg m²

Step-by-step 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