Dimensions of Angular Momentum

Dimensional Formula of Angular Momentum

The dimensional formula of angular momentum is given by,

M¹ L² T^-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 = 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.

⇒ Check Other Dimensional Formulas:

• Dimensions of Strain
• Dimensions of Gas Constant
• Dimensions of Magnetic Flux
• Dimensions of Reynolds Number
• Dimensions of Gravitational Potential Energy