Ncert Exercises & Solutions

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

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:

{\vec{L}}_{P} = mv \times 0 + mv \times d

= mvd . . . . . . . . . . (i)

Angular momentum of the system about point Q:

{\vec{L}}_{Q} = mv \times d + mv \times 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:

{\vec{L}}_{R} = mv \times (d - y) + mv \times y

= mvd - mvy + mvy

= mvd . . . . . . . . . . . (iii)

Comparing equations (i), (ii), and (iii), we get:

{\vec{L}}_{P} = {\vec{L}}_{Q} = {\vec{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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