In translator motion of a body; every particle experiences equal displacement with time; therefore the motion of the whole body may be represented by a particle. But when the body rotates or vibrates during translatory motion, then its motion can be represented by a point on the body that moves in the same way as that of a single particle subjected to the same external forces would move.
A point in the system at which whole mass of the body is supposed to be concentrated is called centre of mass of the body. Therefore if a system contains two or more particles, its translatory motion can be described by the motion of the centre of mass of the system.
