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.

Explanation

As is clear from Fig. vector angular momentum of the two particle system about any pt. `A` on `X_(1)Y_(1)`
`overset rarr(L_(A)) = m overset rarr(v) xx 0 + m overset rarr(v) xx d = m overset rarr(v)d`
Similarly, vector angular momentum of the two particle system about any pt. `B` on `X_(2)Y_(2)`
`overset rarr(L_(B)) = m overset rarr(v) xx d + m overset rarr(v) xx 0 = m overset rarr(v)d`
Let us consider any point `C` on `AB`, where `AC = x`
`:.` Vector angular momentum of the two particle system about `C` is
`overset rarr(L_(C)) = m overset rarr(v) (x) + m overset rarr(v) (d - x) = m overset rarr(v)d`
Clearly, `overset rarr(L_(A)) = overset rarr(L_(B)) = overset rarr(L_(C))`, which was to be proved.