Two particles each of mass $m$ and speed $v$ , travel in opposite directions along parallel lines separated by a distance $d$ , Show that the vector angular momentum of this system of particles is the same about any point taken as origin,

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Solution

$L e t t h e p o i n t a b o u t w h i c h a n g u l a r m o m e n t u m i s t a k e n i s (x, y) \to J =_{1} \times m_{1} +_{2} \times m_{2} =_{1} = x_{1}^i + y^j,_{1} = v^i_{1} = x_{2}^i + (y + d)^j,_{2} = - v^i P u t t i n g t h e v a l u e s \to J = - (m y v - m (y + d) v)^k = m d v^k, w h i c h i s i n d e p e n d e n t o f (x, y)$

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