What is Dimensional Formula of Rotational Kinetic Energy?

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 (K_R) = ∑ 1/2 (mv²) = 1/2 ∑ (m r² ω²) = 1/2 (∑ m r²) ω².

We can also write it as K_R = 1/2 Iω².——- (Moment of Inertia (I)= ∑ m r² ).

Rotational kinetic energy (K_R) = 1/2 Iω²

Mathematically.

Rotational kinetic energy (K_R) = 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).