First slide

Law of conservation of angular momentum

Question

An impulse I is applied at the end of a uniform rod if mass m. then :

Moderate

A

KE of translation of the rod is $\frac{l^{2}}{2 m}$
B

KE of rotation of the rod is $\frac{3 l^{2}}{2 m}$
C

KE of the rod is $\frac{2 l^{2}}{m}$
D

all of these

Solution

$f r o m c o n x e r v a t i o n o f l i n e a r m o m e n t u m t h e r o d a l s o h a s t h e s a m e l i n e a r m o m e n t u m I a n d k i n e t i c o f t r a n s t i o n i s \frac{l^{2}}{2 m} f r o m \cos e r v a t i o n o f a n g u l a r m o m e n t u m L = I l = \frac{m l^{2}}{3} ω ω = \frac{3 I}{m l}; r o t a t i o n a l k i n e t i c e n e r g y \frac{1}{2} L ω = \frac{1}{2} I l \frac{3 I}{m l} = \frac{3 I^{2}}{2 m}$

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