# What is Dimensional Formula of Rotational Kinetic Energy?

Posted in Dimensional Formulae | Email This Post |Rotational Kinetic Energy can be defined as the kinetic energy associated with rotational motion of an object. kinetic energy = 1/2 (mv^{2}) 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 (mv^{2}) = 1/2 ∑ (m r^{2} **ω**^{2}) = 1/2 (∑ m r^{2}) **ω**^{2}.

We can also write it as K_{R} = 1/2 **I****ω**^{2}.——- (Moment of Inertia (**I**)= ∑ m r^{2} ).

Rotational kinetic energy (K_{R}) = 1/2 **I****ω**^{2}

Mathematically.

**Rotational kinetic energy (K _{R}) = 1/2 (Moment of Inertia x (Angular velocity)^{2})**

Now we know,

Dimensional Formula of Moment of Inertia= M^{1}L^{2}T^{0}

Dimensional Formula of Angular Velocity = M^{0}L^{0}T^{-1}

Putting these values in above equation we get

**So Dimensional Formula of Rotational kinetic energy = M ^{1}L^{2}T^{-2}**

**SI unit of Rotational kinetic energy is Joule (J).**