Dimensional Formula of Rotational Kinetic Energy
The dimensional formula of Rotational Kinetic Energy is given by,
M1 L2 T-2
- M = Mass
- L = Length
- T = Time
Rotational Kinetic Energy (R.Ke) = 2-1 × [Moment of Inertia] × [Angular velocity]2 . . . . (1)
Since, the moment of inertia (MOI) = Mass × (Radius of Gyration)2
∴ The dimensions of MOI = M1 L2 T0 . . . . . (2)
And, angular velocity = Δθ × t-1
∴ the dimensional formula of angular velocity = [M0 L0 T-1] . . . .(3)
On substituting equation (2) and (3) in equation (1) we get,
Rotational Kinetic Energy = 2-1 × [Moment of Inertia] × [Angular velocity]2
Or, R.Ke = [M1 L2 T0] × M0 L0 T-1]2 = [M1 L2 T-2].
Therefore, rotational kinetic energy is dimensionally represented as [M1 L2 T-2].