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.

Solution

## Let at a certain instant two particles be at points P and Q, as shown in the following figure. Angular 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) 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=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.   PhysicsNCERT TextbookStandard XI

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