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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 is the same whatever be the point about which the angular momentum is taken.

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#### Let at a certain instant two particles be at points P and Q, as shown in the following figure.Consider a point R, which is at a distance y from point Q, i.e.,QR=y∴ PR=d−yAngular momentum of the system about point P:LP=mv×0+mv×d=mvd......(i)Angular momentum of the system about point Q:LQ=mv×d+mv×0=mvd....(ii)Angular momentum of the system about point R:LR=mv×(d−y)+mv×y=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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