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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

[M1L2T1]

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=Iω
Where L -> Angular Momentum
I -> Moment of Inertia

ω-> Angular velocity

Now of Angular velocity is defined as

ω=dθdt=change in angular displacementtime

Now Angular displacement is Dimension less and Dimension of time is [T1]

So, Dimension of Angular velocity ω is =[M0L0T0[T1]=[M0L0T1]

Now Moment of inertia is defined as

I=mr2

Dimension of Mass =[M1]

Dimension of distance(r) = [L1]

So,Dimension of Moment of inertia =[M1]×[L1]×[L1]=[M1L2]

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

dimension of Angular momentum=dimension of moment of inertia×dimension of Angular velocity

=[M1L2]×[T1]=[M1L2T1]

Unit of Angular Momentum  is Kgm2/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
  • 2
  • 3
  • 4
  • 5
1. The dimension of angular velocity is

Question 1 of 5

2. Which of the following has the dimensions of pressure?

Question 2 of 5

3. The dimensions of universal gravitational constant are

Question 3 of 5

4. The dimension of torque is

Question 4 of 5

5. A unitless quantity

Question 5 of 5


 


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