NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotational Motion Part 2

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Question 7.6:

Find the components along the axes of the angular momentum of a particle, whose position vector iswith components and momentum is with components. Show that if the particle moves only in the x-y plane the angular momentum have only a z-component.

Answer:

Linear momentum of the particle,

Position vector of the particle,

Angular momentum,

Comparing the coefficients of

The particle moves in the x-y plane. Hence, the z-component of the position vector and linear momentum vector becomes zero, i.e.,

Thus, equation reduces to:

Therefore, when the particle is confined to move in the x-y plane, the direction of angular momentum is along the z-direction.

Question 7.7:

Two particles, each of mass and speed , travel in opposite directions along parallel lines separated by a distance . 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.

Answer:

Let at a certain instant two particles be at points and , as shown in the following figure:

A certain instant two particles be at points P and Q, as sho …

Vector Angular Momentum of the Two Particle System

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Angular momentum of the system about point :

Angular momentum of the system about point

Consider a point, which is at a distance from point , i.e.,

Angular momentum of the system about point:

Comparing equations we get:

We infer from equation that the angular momentum of a system does not depend on the point about which it is taken.