There are two motions for a rigid body i.e., rotatory motion and translatory motion. When a wheel moves on a horizontal plane, it rotates moves on a straight line path. If a particle on the rim of the wheel is considered, it will have a complicated path. But the particle at the axis of rotation is considered, then it has straight line motion. Suppose a ball is moved in spinning manner, then any particle on the surface having complicated path of motion. But the particle at the centre of the ball moves in a parabolic path.
From the above examples, we come to the conclusion that when a rigid body has both rotatory and translatory motions, the different particles on the body moves in different directions. But the particle at a specific point is moved along a particular direction and the body moves as if the whole external force is acting on it and represents the motion of the entire body.
The location of centre mass is determined as a fixed point of a system of particles or a rigid body within the boundaries of the system, where the entire mass of the system or body is supposed to be concentrated.
For a uniform rod, the centre of mass is the middle point of the rod. For a rectangular plate, the centre of mass is intersecting point of thediagonals of the rectangular plate. For a circular plate, the centre of mass is at the centre of the circular plate. For a ring, the centre of mass is not within the body, but within the boundaries of the system
So far we discussed about the motion of a rigid body, but in general, we have to deal with the system of bodies consisting of large number of particles which have mutual interactions such that they may change the positions with respect to each other in a complicated way during the motion. Such system is called Non-rigid body system. Planets moving around the sun and each planet having satellites moving around them is an example of Non-rigid system..
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