Question

Earth has a mass of 5.97×1024 kg and a radius of 6,370 km. What is its moment of

inertia if it is assumed to be a solid sphere of uniform density?

Answer 1

The moment of inertia of a uniform solid sphere is:

$$I = \dfrac25mr^2$$

where $m = 5.97\times 10^{24}kg$ is its mass, and $r = 6.37\times 10^6m$ is its radius. Thus, obtain:

$$I = \dfrac25\cdot 5.97\times 10^{24}\cdot (6.37\times 10^6)^2 \approx 9.7\times10^{36} kg\cdot m^2$$

Answer. $9.7\times10^{36} kg\cdot m^2$.