# What is the Dimensional Formula of Moment of Inertia?

Posted in Dimensional Formulae | Email This Post |Moment of Inertia is defined as the product of mass and the square of the perpendicular distance to the specified axis of rotation.

Mathematically,

Moment of Inertia is defined as the product of mass and the square of radius of gyration

**Moment of Inertia = Mass X (Radius of Gyration) ^{2} **

Now we know

Dimensional Formula of Mass= (M^{1}L^{0}T^{0})

Dimensional Formula of Radius of Gyration= (M^{0}L^{1}T^{0})

(Radius of Gyration)^{2}=M^{0} L^{2} T^{0}

Putting these values in above equation we get

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

SI unit

**of Moment of Inertia is**

**kg m**

^{2}
Use of dimension

Thanks for your help