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Two particles each of mass m and speed v...

Two particles each of mass `m` and speed `v`, travel in opposite direction 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.

Text Solution

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Let P, Q be the positions at time .t..
`bar(L)` of .P. about .O. is `bar(L_(P))=(x bar(i)+y bar(j))xx(-mv bar(i))`
`bar(L_(P))=mvy bar(k)`
`bar(L)` of .Q. about .O. is
`bar(L_(Q))=[x bar(i)+(y+d)bar(j)]xx mv bar(i)=mv(y+d)(-bar(k))`
`Sigma L =L_(P)+L_(Q)=mvd (-k)`. Hence proved.
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