Express angular momentum of a system of particles in term of M.I.

Angular momentum is :

Show that the total linear momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its centre of mass.

Two particles, each of mass m and speed v_3 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.

The angular momentum of a body is defined as the product of

Find the components along the xyz axes of the angular momentum I of a particle, whose position vector is r with components x_2 y_3 z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-componenTt.

Show the rate of change of angular momentum of a particle is equal to the torque acting on it.

Prove that angular momentum L = I omega .

Can momentum of a system be changed without changing its K.E.?

Find the following expression for the magnetic moment of an electron moving in a circular path mu_c = c/(2m_c) 1 Wherel is the angular momentum of the electron about the nucleus, e and m_c are its charge and mass.

Find the potential energy of a system of four particles each of mass m placed at the vertices of a square of side I .