CBSE (Science) Class 11CBSE
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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 - CBSE (Science) Class 11 - Physics

ConceptTorque and Angular Momentum

Question

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.

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:

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

Is there an error in this question or solution?

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NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 7: System of Particles and Rotational Motion
Q: 7 | Page no. 178

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Solution 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 Concept: Torque and Angular Momentum.
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