First slide

Angular momentum

Question

A cubical block of side a is moving with a velocity v on a horizontal smooth plane as shown in the figure, it hits a bridge at O. The angular speed of the block after it hits the ridge at O, is

Difficult

A

$\frac{3 v}{4 a}$
B

$\frac{3 v}{2 a}$
C

$\sqrt{\frac{3}{2}} \frac{v}{a}$
D

zero

Solution

$f r o m c o n s e r v a t i o n o f a n g u l a r m o m e n t u m m v \frac{a}{2} = I ω m v \frac{a}{2} = \frac{2 m a^{2}}{3} ω (m o m e n t o f i n e r t i a a b o u t a c o r n e r o f a c u b e = \frac{2 m a^{2}}{3}) ω = \frac{3 v}{4 a}$

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