Rotational Kinetic Energy can be defined as the kinetic energy associated with rotational motion of an object. kinetic energy = 1/2 (mv2) we all know that every particle in an object has same angular speed ω, and tangential speed depends on the distance r from the axis of rotation. Total kinetic Energy of rotating object is the sum of kinetic energy of all individual particles of an object.
so Rotational kinetic energy (KR) = ∑ 1/2 (mv2) = 1/2 ∑ (m r2 ω2) = 1/2 (∑ m r2) ω2.
We can also write it as KR = 1/2 Iω2.——- (Moment of Inertia (I)= ∑ m r2 ).
Rotational kinetic energy (KR) = 1/2 Iω2
Rotational kinetic energy (KR) = 1/2 (Moment of Inertia x (Angular velocity)2)
Now we know,
Dimensional Formula of Moment of Inertia= M1L2T0
Dimensional Formula of Angular Velocity = M0L0T-1
Putting these values in above equation we get
So Dimensional Formula of Rotational kinetic energy = M1L2T-2
SI unit of Rotational kinetic energy is Joule (J).