What is Conservation of Momentum

The momentum of an isolated system is a constant. The vector sum of the momenta mv of all the objects of a system cannot be changed by interactions within the system. This puts a strong constraint on the types of motions which can occur in an isolated system. If one part of the system is given a momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same momentum in the opposite direction. As far as we can tell, conservation of momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.

So what that means is if a change in momentum is created an equal change is momentum is created on another object but in the opposite direction.

In the diagram if the cannon ball experiences a change in momentum, the gun powder goes off pushing the cannon ball out of the cannon. The velocity changes from 0 m/s to some other positive value

As a result the cannon also experiences a change in momentum, but the change in momentum the cannon experiences is equal to same amount as the cannon ball, but in the opposite direction.

Consider it this way, a 5 kg cannon ball is fired out of the cannon with a velocity of 150 m/s

So the change in momentum of the cannon ball is

Mass of the cannon ball x change in the velocity of the cannon ball

Mathematically it would look like this

Mass x (velocity final - velocity initial)

5 kg x ( 150 m/s - 0 m/s) or 750 kg m/s

The cannon must experience the same change in momentum just in the opposite direction so that we can say mathematically

Change in momentum of cannon ball + Change in momentum of the cannon = zero

or

750 kg m/s + Change in momentum of cannon =zero

which means that the change in momentum of the cannon is -750 kg m/s

But what this also means that regardless of the situation whether its collision or explosion the total momentum doesn't change. If you think of it this way, that you change the momentum of the cannon ball with the cannon, this act changes the momentum of the cannon ball changes the momentum of the cannon in the opposite direction.

so we can say that

Total initial momentum = Total final Momentum

And that this is always true