# How to calculate the energy required to rotate a planet?

How to calculate the energy required to rotate a planet from non-rotating state? Say the planet is Venus with equally distributed mass of $4.8676 \times 10^{24}$ kg, and desired rate of 1 rotation per 24 hours.

## 1 Answer

The rotational energy of a body is given by:

$$E = \tfrac{1}{2}I\omega^2$$

where $I$ is the moment of inertia and $\omega$ is the angular velocity. For a uniform sphere the moment of inertia is related to the mass of the sphere, $m$, and the radius of the sphere, $r$, by:

$$I = \frac{2}{5}mr^2$$

You already have the mass, and you can Google for the radius of Venus. That will give you everything you need to answer the question.