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]² . . . . (1)

Since, the dimensional formula of mass = M¹ L⁰ T⁰ . . . . . . (2)

And, the dimensions of the radius of gyration = M⁰ L¹ T⁰ . . . . . (3)

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

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

Or, MOI = [M¹ L⁰ T⁰] × [M⁰ L¹ T⁰]² = M¹ L² T⁰.

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

⇒ Check Other Dimensional Formulas:

• Dimensions of Viscosity
• Dimensions of Pressure Gradient
• Dimensions of Surface Energy
• Dimensions of Displacement
• Dimensions of Gravitational Potential Energy