The dimensional formula of Moment of Inertia is

**[ M**^{1}** L**^{2}** T**^{0}** ]**

where **[M]**, **[L],** and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

From the above formula, we can derive the **dimensions of the moment of inertia as (1, 2, 0)**.

## Derivation of Dimensional Formula of Moment of Inertia

We can derive this formula using the definition of the moment of inertia.

In physics, we can define the moment of inertia as the force required to stop a rotating body. Suppose a body is rotating along an axis; mathematically, the moment of inertia is the sum of the product of masses and squared radius of different particles of the body.

```
Moment of Inertia (I) = m
```_{1}r_{1}^{2} + m_{2}r_{2}^{2} + m_{3}r_{3}^{2} + …

This is equivalent to,

```
I = mass * radius
```^{2}

Dimensionally, we use

**[M]**for mass**[L]**for radius

Now the formula becomes

```
Moment of Inertia (I) = [M
```^{1}] * [L^{2}]

Since the formula doesn’t include the fundamental quantity **Time**, we can use **[T ^{0}]**, which is equal to

**1**.

```
Moment of Inertia (I) = [M
```^{1}] * [L^{2}] * [T^{0}]

Hence, the **dimensional equation of moment of inertia is I = [ M ^{1} L^{2} T^{0} ]**.

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