Rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy . Looking at rotational energy separately around an object's axis of rotation yields the following dependence on the object's moment of inertia:

where

The mechanical work applied during rotation is the torque (

The instantaneous power of an angularly accelerating body is the torque times the angular velocity:

Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:

In the rotating system, the moment of inertia takes the role of the mass and the angular velocity takes the role of the linear velocity.

As an example, let us calculate the rotational kinetic energy of the Earth (animated in Figure 1 ). As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10^{−5} rad/s. The Earth has a moment of inertia, I = 8.04×10^{37} kg·m2. Therefore, it has a rotational kinetic energy of 2.138×10^{29} J.

## The Rotating Earth

The earth's rotation is a prominent example of rotational kinetic energy.

This can be partially tapped using tidal power. Additional friction of the two global tidal waves creates energy in a physical manner, infinitesimally slowing down Earth's angular velocity. Due to conservation of angular momentum this process transfers angular momentum to the Moon's orbital motion, increasing its distance from Earth and its orbital period.