Angular momentum of the system of particles changes when

A certain system of particles possesses a total momentum p and an angular momentum M relative to a point O. Find its angular momentum M^' relative to a point O^' whose position with respect to the point O is determined by the radius vector r_0 . Find out when the angular momentum of the system of particles does not depend on the choice of the point O.

The angular momentum of a system of particles is conserved:

The angular momentum of a system of particles is conserved

The angular momentum of a system of particles is conserved

The rate of change of angular momentum of a system of particles about the centre of mass is equal to the sum of external torque about the centre of mass when the centre of mass is :

The rate of change of angular momentum of a system of particles about the centre of mass is equal to the sum of external torque about the centre of mass when the centre of mass is :

Prove that the rate of change of total angular momentum of a system of particles is equal to the total torque acting on the system.