# Rotational Kinetic Energy Calculator

By Bogna Szyk
Last updated: Oct 05, 2021

This rotational kinetic energy calculator is a tool that lets you determine the energy of a rotating object, such as a spindle or a wheel or a carousel. In this article, we will provide you with all information you will need to make your calculations, including a rotational kinetic energy formula. We will also show you how to calculate rotational kinetic energy, illustrating the guidelines with a step-by-step example.

## What is the rotational kinetic energy?

Rotational energy is a form of kinetic energy. It describes the energy of an object in motion. While regular kinetic energy was related to objects moving along a straight line, the rotational energy is linked with objects that are rotating. This is why, instead of a regular speed, we have to use angular velocity in our calculations.

Remember that if an object is both in translation (moving along a straight line) and rotation (turning around its axis), it has both regular and rotational kinetic energy. Therefore, to find out its total energy, you need to calculate both values and add them.

## Rotational kinetic energy formula

Just as any other form of energy (including potential energy, the rotational kinetic energy can be expressed with a straightforward formula. In this case,

`RE = 0.5 * I * ω²`

where:

• RE is the rotational kinetic energy, expressed in Joules.
• I is the moment of inertia of the object, expressed in kg*m².
• ω is the angular velocity of the body, expressed in radians per second or in Hertz/RPM (revolutions per minute) after the appropriate units conversion. If you're not sure how to calculate this value for a body in rotary motion, head straight to our centrifugal force calculator to find out.

## How to calculate the rotational kinetic energy?

Let's analyze the following example together: a wheel of radius `R = 0.5 m` and mass `M = 1 kg` is rolling along a track, making 30 revolutions per minute. What is its rotational energy?

1. First, we need to determine what is the angular velocity of the wheel. We know that it is equal to 30 RPM, what is equivalent to about 3.1416 rad/s.
2. Then, we need to calculate the moment of inertia of the wheel. We already know its radius. As the wheel has the shape of a circle, its moment of inertia can be expressed with the equation

`I = M * R²`

`I = 1 * 0.5² = 0.25 kg m²`

1. Once we know both the angular velocity and the moment of inertia, all we have to do is plug them into the rotational kinetic energy formula:

`RE = 0.5 * I * ω²`

`RE = 0.5 * 0.25 * 3.1416²`

`RE ≈ 1.2337 J`

1. We have found that the rotational kinetic energy of the rolling wheel is equal to about 1.2337 J.

And if you'd like to learn about three-dimensional rotations, make sure to check Omni's quaternion calculator.

Bogna Szyk
Angular velocity
Moment of inertia
lb*ft²
Rotational kinetic energy
J
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