In this article, you will learn to calculate the dimensional formula of linear momentum and angular momentum.

## Dimensional Formula of Linear Momentum

The dimensional formula of Linear Momentum is

**[ M**^{1}** L**^{1}** T**^{-1}** ]**

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

From the above formula, the **dimensions of momentum are (1, 1, -1)**.

We can derive this formula using the definition of linear momentum.

## Derivation of Dimensional Formula of Linear Momentum

In physics, we can define momentum as the quantity of motion contained in a moving body. Mathematically, it is given as the product of mass and velocity.

```
Momentum (P) = mass * velocity
```

We know that, **velocity = distance / time**. Substituting the value of **velocity** in the above equation, we get

```
Momentum (P) = mass * (distance / time)
P = mass * distance * time
```^{-1}

Dimensionally, we use

**[M]**to represent mass**[L]**for distance**[T]**to represent time

Now the formula becomes

```
Linear Momentum = [M
```^{1}] * [L^{1}] * [T^{-1}]

Hence, the **dimensional equation of momentum is P = [ M ^{1} L^{1} T^{-1} ]**.

## Dimensional Formula of Angular Momentum

Similarly, the dimensional formula of angular momentum is

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

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

From the above formula, the **dimensions of angular momentum are (1, 2, -1)**.

We can derive this formula using the formula of angular momentum.

## Derivation of Dimensional Formula of Angular Momentum

In Physics, we can define angular momentum as a physical quantity possessed by a body moving around a point. Mathematically, it is given as the product of mass, velocity, and radius.

```
Angular Momentum (J) = mass * velocity * radius
```

Angular Momentum (J) = mass * velocity * radius

We know that, **velocity = distance / time**. Substituting the value of **velocity** in the above equation, we get

```
Angular Momentum = mass * (distance / time) * radius
= (mass * distance * radius) / time
= mass * distance * radius * time
```^{-1}

Dimensionally, we use

**[M]**to represent mass**[L]**for both distance and radius**[T]**to represent time

Hence, the formula becomes

```
Angular Momentum = [M
```^{1}] * [L^{1}] * [L^{1}] * [T^{-1}]
= [M^{1}] * [L^{2}] * [T^{-1}]

Hence, the **dimensional equation of angular momentum is J = [ M ^{1} L^{2} T^{-1} ]**.

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