1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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.

Open in App
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.

Suggest Corrections
4
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program