Question

Two particles, each of mass m and speed u travel in opposite directions along the 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.

Answer 1

Hey mate,

● Proof-
[Refer to the figure]

Consider, Two particles be at points P and Q at any instant.

Angular momentum of the system about point P:
Lp = mv × 0 + mv × d
LR = mvd …(1)

Angular momentum of the system about point Q:
LQ = mv × d + mv × 0
LR = mvd ….(2)

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 about point R:
LR = mv × (d – y) + mv × y
LR = mvd ….(3)

Comparing equations (1), (2), and (3), we get:
LP = LQ = LR

Thus, we can say that the angular momentum of a system is same wherever taken.

Hope that helps you...