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.

Answer 1

Answer: $9.72(10)^{37} kgm^{2}$

Explanation:

Assuming that the Earth is a solid sphere, of mass $M$ and radius $R$ around an axis that passes through its center, with uniform density (that is: its center of mass coincides with the center of the sphere), its moment of inertia $I$ is given by the following formula:

$I=\frac{2}{5}MR^{2}$   (1)

Where:

$M=5.97(10)^{24}kg$

$R=6.38(10)^{6}m$

$I=\frac{2}{5}(5.97(10)^{24}kg)(6.38(10)^{6}m)^{2}$   (2)

Finally:

$I=9.72(10)^{37}kg.m^{2}$