Physics - Rotation Question with Solution | TestHub

The moment of inertia of the earth, assumed to be a solid sphere, about its axis of rotation is $I=\frac{2}{5}M{R}^2$.

The angular velocity of the earth is $\omega =\frac{2\pi }{T}$.

The angular momentum $L$ is given by $L=I\omega$.

Substituting the values, we get:

$L=\left(\frac{2}{5}M{R}^2\right)\left(\frac{2\pi }{T}\right)=\frac{4\pi M{R}^2}{5T}$

Answer: $\frac{4\pi {\mathrm{MR}}^2}{5\mathrm{T}}$