System of particles and Rotational motion NCERT Solutions Class 11 Physics - Solved Exercise Question 7.7

Question 7.7:
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 X 0 + mv x d  =  mvd   ...(i)
Angular momentum of the system about point Q:
LQ = mv X d + mv X 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 X (d - y) + mv X 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.

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