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# What is the dimension of angular momentum

## Dimensional Formula of Angular Momentum

with its Derivation

Dimensional formula for Angular Momentum is

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

Where
M -> Mass

L -> Length

T -> Time
We would now derive this dimensional formula.

### Derivation for expression of Dimension of Angular Momentum

Angular Momentum is defined

$L = I \omega$
Where L -> Angular Momentum
I -> Moment of Inertia

$\omega$-> Angular velocity

Now of Angular velocity is defined as

$\omega =\frac {d\theta }{dt} = \frac {\text {change in angular displacement}}{time}$

Now Angular displacement is Dimension less and Dimension of time is $[T^1]$

So, Dimension of Angular velocity $\omega$ is $= \frac {[M^0L^0T^0}{[T^1]} = [M^0L^0T^{-1}]$

Now Moment of inertia is defined as

$I= mr^2$

Dimension of Mass =$[M^1]$

Dimension of distance(r) = $[L^1]$

So,Dimension of Moment of inertia =$[M^1] \times [L^1] \times [L^1]= [M^1L^2]$

Now we know both the Moment of Inertia  and angular velocity dimension , we can calculate the dimension of Angular momentum  easily as

$\text {dimension of Angular momentum} = \text {dimension of moment of inertia} \times \text {dimension of Angular velocity}$

$= [M^1L^2] \times [T^{-1}] = [M^1L^2T^{-1}]$

Unit of Angular Momentum  is $Kg-m^2/sec$ and It is generally denoted by letter $L$

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

#### Quiz on Dimensional Analysis

1. The dimension of angular velocity is

Question 1 of 5

2. A unitless quantity

Question 2 of 5

3. Which of the following pair does not have similar dimensions

Question 3 of 5

4. Which of the following pair does not have the same dimensions

Question 4 of 5

5. The dimension of torque is

Question 5 of 5

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