Consider the meter stick.
It is an extended object. In other words we can’t simply treat it as a particle.
For example if we twirl it, each piece moves in a different radius circle with
different speeds!
Imagine that this meter stick is moving as well as spinning.
Now the motion of each piece of the meter stick is even more complicated!
However, there is one point on the meter stick that moves just like a simple particle!
This point is also special because it is the point on which the meter stick would
balance.
In fact, if we threw the meter stick through the air, this point would act just like a
projectile, it would follow a parabolic path.
Hence, this point acts as if all of the mass of the object is concentrated at that point.
Center of Mass – the point in an object or system of particles which acts as a
simple particle
– the point at which all of the mass of an object or system of
particles can be thought to be concentrated
– the point that moves as if all of the external forces were
applied at that point
– the balancing point
Rotating Projectile
The center of mass need not lie within an object.
Line of Symmetry
Let’s see how this applies to explosions and collisions between two carts.
Momentum of the
Center of Mass
For this system of two carts there could be two types of forces.
1. Forces between the carts.
2. External forces on the carts from outside the system.
However, by Newton’s Third Law, any force between the two carts would always have an
equal and opposite pair and would therefore sum to 0!

Fexternalt  p

p  0
As you saw in the demos, if there are no external forces, then the momentum of the
center of mass point does not change!