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Question Number 22956 by Physics lover last updated on 24/Oct/17

Commented by Physics lover last updated on 24/Oct/17

$f i n d a n g u l a r v e l o c i t y a f t e r$ $c o l l i s i o n a n d l o s s i n k i n e t i c$ $e n e r g y ?$
Commented by ajfour last updated on 24/Oct/17

Commented by ajfour last updated on 24/Oct/17

$ω l / 2 = v_{1} - V . . . (i)$ $c o n s e r v i n g l i n e a r m o m e n t u m$ $(2 m) V + {m v}_{1} = m v$ $\Rightarrow 2 V + v_{1} = v . . . (i i)$ $c o n s e r v i n g a n g u l a r m o m e n t u m$ $a b o u t a p o i n t o n t a b l e j u s t b e l o w$ $t h e r i g h t e n d o f s t i c k (∙) .$ $(\frac{2 {m l}^{2}}{12}) ω - (2 m) V (\frac{l}{2}) = 0$ $\Rightarrow ω l = 6 V . . . (i i i)$ $u s i n g t h i s i n (i)$ $v_{1} - V = 3 V o r v_{1} = 4 V$ $u s i n g t h i s i n (i i)$ $6 V = v o r V = \frac{v}{6}$ $t h e n v_{1} = 4 V = \frac{2 v}{3}$ $ω l = 6 V = v$ $ω = v / l .$ $K_{i} = \frac{1}{2} {m v}^{2}$ $K_{f} = \frac{1}{2} (2 m) V^{2} + \frac{1}{2} (\frac{2 {m l}^{2}}{12}) ω^{2} +$ $+ \frac{1}{2} {m v}_{1}^{2}$ $= \frac{{m v}^{2}}{36} + \frac{{m v}^{2}}{12} + \frac{2 {m v}^{2}}{9}$ $= \frac{12 {m v}^{2}}{36} = \frac{{m v}^{2}}{3}$ $l o s s i n K = K_{i} - K_{f}$ $= \frac{{m v}^{2}}{2} - \frac{{m v}^{2}}{3} = \frac{{m v}^{2}}{6} .$
Commented by Physics lover last updated on 25/Oct/17

$t h a n k d y o u v e r y m u c h, M r A j f o u r .$
	Answered by ajfour last updated on 24/Oct/17

	$ω = \frac{v}{l}; l o s s i n K = \frac{{m v}^{2}}{6} .$
	Commented by Physics lover last updated on 24/Oct/17

	$y e s s i r!!$
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