# Rotational Kinetic Energy Formula

RotationalÂ kineticÂ energyÂ isÂ theÂ energyÂ whichÂ the bodyÂ absorbsÂ byÂ virtueÂ ofÂ itsÂ rotation. ThroughÂ theÂ work-energy theory, the term for linear and rotational kinetic energy can be developed in a parallel way. Consider the contrast that occursÂ betweenÂ aÂ constantÂ torqueÂ exertedÂ onÂ aÂ flywheelÂ withÂ aÂ 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,Â 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,Â theÂ rotationalÂ kineticÂ energyÂ providedÂ toÂ theÂ flywheelÂ isÂ equalÂ toÂ the work done by the torque. (Rotational work = Ï„Î¸Â  andÂ angular acceleration= Î± 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 Ï‰

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

### Rotational Kinetic EnergyÂ Solved Example

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

Known:

(Angular velocity)Â Ï‰Â = 7.29Â Ã—Â 10-5Â rad s-1,
(Moment of inertia) I = 8.04Â Ã—Â 1037Â kgm2

The rotational kinetic energy isÂ

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