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Question Number 22487 by ajfour last updated on 19/Oct/17

Commented by ajfour last updated on 19/Oct/17

$Q . 22473 (s o l u t i o n)$
	Answered by ajfour last updated on 19/Oct/17

	$\int_{0}^{△ t} f d t = m (u \sin α - v \cos α)$ $= 0.1 (20 \times \frac{1}{2} - 10 \times \frac{\sqrt{3}}{2})$ $= (1 - \frac{\sqrt{3}}{2}) N s$ $\int_{0}^{△ t} N d t = m (u \cos α + v \sin α)$ $= 0.1 (20 \times \frac{\sqrt{3}}{2} + 10 \times \frac{1}{2})$ $= \sqrt{3} + \frac{1}{2}$ $I △ ω = - R \int_{0}^{△ t} f d t$ $\frac{1}{2} (ω - 2) = - \frac{1}{2} (1 - \frac{\sqrt{3}}{2})$ $\Rightarrow ω = 2 - 1 + \frac{\sqrt{3}}{2} > 0$ $\Rightarrow I m m e d i a t e l y a f t e r c o l l i s i o n$ ${r i n g}^{'} s a n g u l a r v e l o c i t y i s i n t h e$ $s a m e d i r e c t i o n .$ $F o r T r a n s l a t o r y m o t i o n : l e t V b e$ $f i n a l t r a n s l a t i o n a l v e l o c i t y o f$ $r i n g, t h e n$ $M (V - v_{0}) = - \int_{0}^{△ t} (f \sin α + N \cos α) d t$ $2 (V - 1) = - (\frac{1}{2} - \frac{\sqrt{3}}{4} + \frac{3}{2} + \frac{\sqrt{3}}{4})$ $\Rightarrow 2 V - 2 = - 2 o r V = 0$ $R i n g s t o p s .$ $S o i m m e d i a t e l y a f t e r c o l l i s i o n r i n g r o t a t e s$ $a b o u t s t a t i o n a r y c e n t r e o f m a s s$ $i n t h e s a m e s e n s e a s b e f o r e o n l y$ $l i t t l e s l o w e r, f r i c t i o n a c t s l e f t .$ $L a t e r i t s h o u l d b r i n g r i n g i n t o$ $p u r e r o l l i n g c o n d i t i o n .$
	Commented by Sahib singh last updated on 19/Oct/17

	$T h a n k y o u v e r y m u c h$ $s i r .$
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