What is the dimension of angular momentum

Dimensional Formula of Angular Momentum

with its Derivation

In this article, we will find the dimension of Angular Momentum

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:-

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Quiz on Dimensional Analysis

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

work and torque

moment of inertia and moment of force

impulse and momentum

angular momentum and Planck's Constant

Question 1 of 5

2. The dimension of torque is

\([MLT^{-2}]\)

\([ML^2T^{-2}]\)

\([ML^3T^{-3}]\)

\([ML^{-1}T^{-1}]\)

Question 2 of 5

3. Choose the correct statement(s)

A dimensionally incorrect equation may be correct

A dimensionally incorrect equation may be incorrect

A dimensionally correct equation may be correct

A dimensionally correct equation may be incorrect

Question 3 of 5

4. A unitless quantity

does not exist

may have a nonzero dimension

never has nonzero dimensions

always has nonzero dimensions

Question 4 of 5

5. The dimensions of universal gravitational constant are

\([M^{-2}L^{3}T^{-2}]\)

\([M^{-1}L^{3}T^{-2}]\)

\([M^{-2}L^{2}T^{-1}]\)

\([ML^{2}T^{-1}]\)

Question 5 of 5

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