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Two particles, each of mass mand speed v...

Two particles, each of mass mand speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Text Solution

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Angular momentum of the system about any point P on `X_1 Y_1` is :
`vecL_p = mvecv xx0 + mvecvxxd`
`vecL_p = mvecvd`
Similarly angular momentum of the system about a point Q on `X_2 Y_2` is

`vecL_Q = mvecvd + mvecv xx 0 = mvecvd `
Angular momentum about R,
`vecL_R = mvecv(x) + mvecv(d-x) = mvecvd`
Clearly `vecL_p = vecL_Q = vecL_R`
Hence, the vector angular momentum of the given system is same irrespective of the point about which it is taken.
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