Dimensional Formula of Angular Momentum
The dimensional formula of angular momentum is given by,
M1 L2 T-1
- M = Mass
- L = Length
- T = Time
Angular Momentum = Angular Velocity × Moment of Inertia . . . . (1)
Since, Angular Velocity = Angular displacement × [Time]-1 = [M0L0T0] [T]-1
∴ The dimensional formula of Angular Velocity = M0 L0 T-1 . . . . . . (2)
And, Moment of Inertia, M.O.I = Mass × (Radius of Gyration)2
∴ The dimensional formula of M.O.I = M1 L2 T0 . . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Angular Momentum = Angular Velocity × Moment of Inertia
Or, M = [M0 L0 T-1] × [M1 L2 T0]-1 = M1 L2 T -1.
Therefore, the angular momentum is dimensionally represented as M1 L2 T -1.