# Dimensions of Angular Momentum

## Dimensional Formula of Angular Momentum

The dimensional formula of angular momentum is given by,

M1 LT-1

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Angular Momentum = Angular Velocity × Moment of Inertia . . . . (1)

Since, Angular Velocity = Angular displacement × [Time]-1 = [M0L0T0] [T]-1

∴ The dimensional formula of Angular Velocity = MLT-1 . . . . . . (2)

And, Moment of Inertia, M.O.I = Mass × (Radius of Gyration)2

∴ The dimensional formula of M.O.I = M1 LT0 . . . . . (3)

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

Angular Momentum = Angular Velocity × Moment of Inertia

Or, M = [MLT-1] × [M1 LT0]-1 = M1 LT -1.

Therefore, the angular momentum is dimensionally represented as M1 LT -1.

### ⇒ Check Other Dimensional Formulas:

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#### 1 Comment

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