# Dimensional Formula of Linear and Angular Momentum

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

[ M1  L1  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.

## How to calculate the 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 = [M1] * [L1] * [T-1]
``````

Hence, the dimensional equation of momentum is P = [ M1 L1 T-1 ].

## Dimensional Formula of Angular Momentum

Similarly, the dimensional formula of angular momentum is

[ M1  L2  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.

## How to calculate the 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  = [M1] * [L1] * [L1] * [T-1]

= [M1] * [L2] * [T-1]
``````

Hence, the dimensional equation of angular momentum is J = [ M1 L2 T-1 ].

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