 # Rotational Kinetic Energy Formula

Rotational kinetic energy is the energy which the body absorbs by virtue of its rotation. Through the work-energy theory, the term for linear and rotational kinetic energy can be developed in a parallel way. Consider the contrast that occurs between a constant torque exerted on a flywheel with a moment of inertia I and a constant force exerted on a mass m, both starting from rest.

Starting from the rest, in the case of linear motion, according to Newton’s second law, acceleration is equal to the ratio of the final velocity and time. The average velocity is half of the final velocity which represents the work done on the object gives it a kinetic energy equivalent to the work done on the object.

Starting from the rest, in case of rotation motion, according to Newton’s second law, the angular acceleration ratio of the final angular velocity with time. The average angular velocity is equivalent to the half of the final angular velocity.

Accordingly, the rotational kinetic energy provided to the flywheel is equal to the work done by the torque. (Rotational work = τθ  and angular acceleration= α provided to the flywheel)

## Rotational Kinetic Energy Formula

The rotational kinetic energy is expressed as

$$\begin{array}{l}E_{k}=\frac{1}{2}Iw^{2}\end{array}$$

Where,

• Moment of inertia is I
• Angular velocity of the rotating body is ω

The rotational kinetic energy formula is made use of to calculate the rotational kinetic energy of the body in rotational motion. It is expressed in Joules (J).

### Rotational Kinetic Energy Solved Example

Problem 1: Calculate the rotational kinetic energy if angular velocity is 7.29 × 10-5 rad s-1 and the moment of inertia is 8.04 × 1037 kgm2.

Known:

(Angular velocity) ω = 7.29 × 10-5 rad s-1,
(Moment of inertia) I = 8.04 × 1037 kgm2

The rotational kinetic energy is

$$\begin{array}{l}E_{k}=\frac{1}{2}Iw^{2}\end{array}$$