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 vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.
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Answer 1

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According to the Question the answer is like the following :

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.

Answer 2

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Refer the attachment.