# Dimensions of Rotational Kinetic Energy

## Dimensional Formula of Rotational Kinetic Energy

The dimensional formula of Rotational Kinetic Energy is given by,

M1 L2 T-2

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Rotational Kinetic Energy (R.Ke) = 2-1 × [Moment of Inertia] × [Angular velocity].  . . . (1)

Since, the moment of inertia (MOI) = Mass × (Radius of Gyration)2

∴ The dimensions of MOI = M1 LT0 . . . . . (2)

And, angular velocity = Δθ × t-1

∴ the dimensional formula of angular velocity = [MLT-1] . . . .(3)

On substituting equation (2) and (3) in equation (1) we get,

Rotational Kinetic Energy = 2-1 × [Moment of Inertia] × [Angular velocity]2

Or, R.Ke = [M1 LT0] × MLT-1]= [M1 L2 T-2].

Therefore, rotational kinetic energy is dimensionally represented as [M1 L2 T-2].