## Kinetic Energy Introduction

Kinetic energy represents the energy possessed by the body by virtue of its motion. Whenever a body is in motion, it possesses kinetic energy. The kinetic energy of a body in linear motion is given by: where and are the mass and velocity of a body respectively.

In a similar way, the motion of a body in rotational motion also has kinetic energy. The kinetic energy in rotational motion is given by: where and are the moment of inertia and angular velocity of a body respectively.

## Formula of Kinetic energy in translational and rotational motion

The formula of kinetic energy in translational and rotational motion is shown in the below table.

Translational Motion | Rotational Motion |

= mass of a body = linear velocity of a body | = Moment of Inertia = angular velocity |

## Expression of Kinetic energy in rotational motion

Consider a rigid body in a rotational motion with constant angular velocity . Let’s say it is made up of ‘n’ number of particles of masses all have the same angular velocity as they are compactly arranged in a rigid body. But they have different linear velocities as .

Since, the kinetic energy of first particle is =

**The total kinetic energy in rotational motion of a rigid body can be calculated by adding the kinetic energy of all particles that form a rigid body.**

But So,

where is a moment of inertia of a rigid body.

This is the formula of Kinetic Energy in rotational motion.

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