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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 - Physics

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Two particles, each of mass 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.

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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:

`vecL_p = mv xx 0 + mv xx d`

= mvd ....(i)

Angular momentum of the system about point Q:

`vecL_Q = mv xx d + mv xx 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:

`vecL_R = mvxx(d-y) + mv xx y` 

= mvd - mvy + mvy

=mvd ...(iii)

Comparing equation i, ii and iii we get

`vecL_p = vecL_Q = vecL_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

Concept: Torque and Angular Momentum
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NCERT Class 11 Physics
Chapter 7 System of Particles and Rotational Motion
Exercises | Q 7 | Page 178

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