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)`

Step-by-step 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=(2)/(5)MR^(2)` (1)

Where:

`M=5.97(10)^(24)kg`

`R=6.38(10)^(6)m`

`I=(2)/(5)(5.97(10)^(24)kg)(6.38(10)^(6)m)^(2)` (2)

Finally:

`I=9.72(10)^(37)kg.m^(2)`