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Question
Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.
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Solution
At a specific moment, two particles are located at points P and Q, as depicted in the diagram provided.
Angular momentum of the system relative to point P:
`vecL_p = mv xx 0 + mv xx d`
= mvd ....(i)
Angular momentum of the system relative to point Q:
`vecL_Q = mv xx d + mv xx 0`
= mvd ....(ii)
Consider a point R, which is at a distance y from point Q, i.e.,
QR = y
∴PR = d – y
Angular momentum of the system relative to point R:
`vecL_R = mvxx(d-y) + mv xx y`
= mvd - mvy + mvy
=mvd ...(iii)
Comparing equation i, ii and iii we get
`vecL_p = vecL_Q = vecL_R` .... (iv)
We infer from equation (iv) that the angular momentum of a system does not depend on the point about which it is taken
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