# Kinetic energy of rotation (Rotational kinetic energy)

We already have discussed the kinetic energy of an object and the related facts. A body can have two types of kinetic energies – Translational kinetic energy and Rotational kinetic energy. In this article, we are going to be more specific. Here, we are to explain the rotational kinetic energy i.e. the kinetic energy of an object due to its rotation only. The formula of rotational kinetic energy, its definition, unit and related facts are the things to highlight here.

1. What is rotational kinetic energy
2. Derive the formula of rotational kinetic energy
3. Unit of rotational kinetic energy
4. How to find rotational kinetic energy?
5. Examples of rotational kinetic energy in daily life

## Definition of rotational kinetic energy

Rotational kinetic energy of a body arises due to the rotation of the body. It is directly related to the moment of inertia and angular velocity of the object. The kinetic energy of a rotating object is defined as the half of the product between the moment of inertia and the angular velocity of the rotating object.

## Formula for rotational kinetic energy

There is an analogy in the formulae of the translational kinetic energy and rotational kinetic energy.

If an object of mass m is moving with a linear velocity v, then the expression for the linear kinetic energy is $\small {\color{Blue} E_{translational}= \frac{1}{2}mv^{2}}$.

In rotational motion, the moment of inertia (I) is the rotational mass of the object. Now, if the $\small \omega$ be the angular velocity of the rotating object then the equation of kinetic energy of rotating object is, $\small {\color{Blue} E_{rotational}= \frac{1}{2}I\omega ^{2}}$.

## Unit of rotational kinetic energy

The SI unit of moment of inertia is kg.m2 and the SI unit of the angular velocity is radian/s. Then the SI unit of the kinetic energy of rotation is kg.m2/s2 which is equal to Joule.

So, SI unit of rotational kinetic energy is Joule and the CGS unit is erg.

## How to find rotational kinetic energy of a rotating object?

To calculate rotational kinetic energy of an object, we need to know the moment of inertia of the object. So, we need to find the moment of inertia of the body first (Check the list of moment of inertia of different objects). Then find the angular velocity of the object i.e. the angle covered by the rotating object per second. The putting the values of moment of inertia and angular velocity in the equation of rotational kinetic energy, one can find the value of the kinetic energy of the rotating object easily.

## Examples of kinetic energy of rotation in daily life

Some of the examples of rotating systems having rotational kinetic energies are-

1. Rotation of Earth is an example of a system that have rotational kinetic energy. The rotational kinetic energy of the Earth is 2.138×1029 Joules.
2. If you roll a football on the ground, it will have rotational kinetic energy. You can find the value of the kinetic energy of rotation of the football by finding the moment of inertia and angular velocity of the football.
3. A spinning top also has the rotational kinetic energy.
4. The wheels of a running car or cycle also have the rotational kinetic energy when they are in motion.

## Numerical problems

1. Find the rotational kinetic energy of a disc of mass 50 grams and radius 10 cm moving at rpm of 100.
2. What is the rotational kinetic energy of moon due to its rotation around the Earth?

This is all from this article on the rotational kinetic energy of a rotating object. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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