# Rotational Kinetic Energy Definition

In physics, **rotational kinetic energy** is defined as the **form of kinetic energy** that **causes an object to rotate about its axis of rotation**. It is directly proportional to the rotational inertia and the magnitude's square of an angular velocity. The SI unit to measure rotational kinetic energy is Joules (J), equivalent to the kg.m^{2}.s^{-2}. In mathematical form, Rotational kinetic energy is elaborated as the product of half of the moment of inertia rotating around its axis and the square of an object's angular velocity. The movement of hydropower plants, windmills, rollercoasters, and moving wheels are examples of rotational kinetic energy.

**Table of Contents**

## Formula Of Rotational Kinetic Energy

The formula used to derive average velocity is as follows:

\[{K_r}\; = \;\frac{1}{2}I{\omega ^2}\]

**Where,**

I = moment of inertia

ω = angular velocity of an object

**Note:**

If you want to calculate rotational kinetic energy, you can use our Rotational Kinetic Energy Calculator.

### Example

For a more clear understanding of concepts, let us have an example below:

Suppose a wheel has 1600 kg.m^{2} moment of inertia is rotating at 6 radians.s^{-1}. Find out the rotational kinetic energy of the wheel.

**Given data**

Moment of inertia= 1600 kg.m^{2}

Angular velocity = 6 radians.s^{-1}

**To Find**

The rotational kinetic energy of the wheel = ?

**Solution**

To find the energy in a rotating wheel, we can use the formula listed below:

\[{K_r}\; = \;\frac{1}{2}I{\omega ^2}\]

Putting values in the formula:

KR = (1600kg.m^{2}) (6radians.s^{−1})^{2}= (1600kg.m^{2})(36s^{−2})

Rotational kinetic energy = 28800 kg.m^{2}.s^{-2}= 28800 J