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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 the two particle system the same whatever be the point about which the angular momentum is taken.
Asked by Abhay Last Modified
Answer 
Let at a certain instant two particles be at points P and Q, as shown in the following figure.
Lp = mv × 0 + mv × d = mvd …(i)
Angular momentum of the system about point Q:
LQ = mv × d + mv × 0 = mvd ….(ii)
Consider a point R, which is at a distance yfrom point Q, i.e.,
QR = y
∴ PR = d – y
Angular momentum of the system about point R:
LR = mv × (d – y) + mv × y
mvd – mvy + mvy
= mvd ….(iii)
Comparing equations (i), (ii), and (iii), we get:
LP = LQ = LR …(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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