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Angular Analogue of Linear Momentum

Establish the...

Question

Establish the relation between moment of inertia and angular momentum. Define moment of inertia on the basis of this relation.

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Solution

$A n g u l a r m o m e n t u m = r a d i u s \times m o m e n t u m M o m e n t u m = m a s s \times v e l o c i t y A n g u l a r m o m e n t u m = m r v N o w d i v i d i n g a n d m u l i t i p l y i n g b y r^{2} w e g e t A n g u l a r m o m e n t u m = \frac{r^{2} m r v}{r^{2}} R e a r r a n g i n g t h e e q u a t i o n w e g e t A n g u l a r m o m e n t u m = I ω w h e r e I = m o m e n t o f i n e r t i a = r^{2} m a n d a n g u l a r v e l o c i t y ω = \frac{v}{r}$

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