Dimensional Formula of Moment of Inertia
The dimensional formula of moment of inertia is given by,
M1 L2 T0
- M = Mass
- L = Length
- T = Time
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.