Center of mass for symmetrical bodies
- CM of a square is at the point of intersection of its diagonals.
- CM of a sphere is at its centre.
- CM of a rigid bar is at the middle point.

Study of motion vis-a-vis CM

We have learnt that the centre of mass (CM) for symmetrical bodies is located at its geometric centre. Implicitly we understood all concepts of motion based on the motion of this particular point. We proceeded to understand complex twoâ€“dimensional motions, such as projectile motion and circular motion, by studying the motion of CM. We have always been restricting our examples to objects that were either pointâ€“like or symmetrical in shape, such as a ball or a coin, etc. This did not disturb our understanding of any of the fundamental concepts of motion.

Now let us go a notch higher into the real world. After all, an object in motion is not a point particle. It has dimensions. The first step for this level of knowledge
is to know what is CM of a body. CM of a body is defined
as the point at which the entire mass of a body can be assumed to be concentrated
for determining the motion of the body under the action of external forces.
CM of a body can be determined by its geometrical considerations. If
a body is symmetrical and of uniform composition, the CM will be located
at its geometrical centre.

If a body is irregularly shaped or if its density is unevenly distributed, its CM is not easy to locate, but still it can be done using many experimental
techniques.