Everybody in his/her childhood had played with “HIT-ME” at least once. Remember the toy, which no matter how much you punch it, never goes down! A truck however slow it may be, can cause casuality to any person to which it collides while a bicycle cannot cause much of a problem though it speed was quite high! Why does a rubber ball, a plastic ball, a super ball, all retract to different heights even though thrown from same height initially?

The Answer to all such queries lies in this chapter which opens new insight.

CENTER OF MASS:

It is the point in a system which behaves as though the entire mass of system is concentrated there and its motion is same if the resultant of all forces acting on the system were applied directly to it.

Mathematically:

Co-ordinates of Center of mass:

Where is total mass

Position Vector of Center of Mass:

Where are position vector of i^th particle.

Dumb Question:

1)      Why does the Center of Mass divide internally the line joining two particles in inverse ratio of their masses?

Ans:

Consider two particles at O and P. Suppose Center of Mass is at C, Now fix origin at O. Then,

So,

This implies that the Center of Mass is nearer to the heavier particle (obviously) and so the distance is inversely related to mass!

For a continuous body, the formulae for Center of Mass becomes

A) Center of Mass of a uniform straight rod:

Derivation: