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
[M1L2T−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=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]=[M0L0T−1]
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]×[T−1]=[M1L2T−1]
Unit of Angular Momentum is Kg−m2/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
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