__Question 7.7__:*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:

L

_{p}= mv X 0 + mv x d = mvd ...(i)

Angular momentum of the system about point Q:

L

_{Q}= 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:

L

_{R}= mv X (d - y) + mv X y

mvd - mvy + mvy

= mvd ....(iii)

Comparing equations (

*i*), (

*ii*), and (

*iii*), we get:

L

_{P}= L

_{Q}= L

_{R}...(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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