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#### Question

State and prove : Law of conservation of angular momentum.

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Find the components along the *x, y, z *axes of the angular momentum **l **of a particle, whose position vector is **r **with components *x*, *y*, *z *and momentum is **p **with components *p*_{x}, *p*_{y} and '*p_z`*. Show that if the particle moves only in the *x*-*y *plane the angular momentum has only a *z*-component.

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.

State the law of conservation of angular momentum and explain with a suitable example.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^{–1}. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of the angular momentum of the cylinder about its axis?