# Dimensions of Moment of Inertia

## Dimensional Formula of Moment of Inertia

The dimensional formula of moment of inertia is given by,

M1 L2 T0

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Moment of Inertia (MOI) = Mass × [Radius of Gyration]. . . . (1)

Since, the dimensional formula of mass = ML0 T. . . . . . (2)

And, the dimensions of the radius of gyration = MLT. . . . . (3)

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

Moment of Inertia = Mass × [Radius of Gyration]2

Or, MOI = [ML0 T0] × [M0 LT0]2 = M1 L2 T0.

Therefore, the moment of inertia is dimensionally represented as M1 L2 T0.