The law of conservation of linear momentum

let's learn what is the law of conservation of momentum ?

The law states that the initial momentum of a system is equal to the final momentum of the system when there is no external force is acting on the system.
Now, the question arises- "what is a system?"
System is the area or space where our work is concentrated. Suppose a ball '1' is colliding with another ball '2'. So, the system will be ball '1' and '2' together and we will be concentrating on their collision.
Now, let us consider that balls '1' and '2' are moving with initial velocities U₁ and U₂ respectively.
If U₁ > U₂, they will collide after travelling some distance. It means that if the ball '1' will be travelling with a greater velocity it will definitely collide with the ball '2' which is traveling with lesser velocity.
The bodies have collided and after collision they start moving with some different velocities suppose V₁ and V₂.

Initial momentum of the system ( balls 1 and 2 ) is  : M₁U₁ + M₂U₂
final momentum of the system is : M₁V₁ + M₂V₂
So, from the law of conservation of momentum.
Initial momentum = final momentum
M₁U₁ + M₂U₂ = M₁V₁ + M₂V₂

Some examples:

• Firing of bullet from a gun
• a man walking on a boat
• a boy getting off from a running bicycle
• a man jumping from a boat towards the shore

So, all these are some of the examples where momentum is being conserved during the process. In all these processes, there is a system. Like, bullet and the gun, man and the boat and boy and bicycle. All these come under a system. Now, as I said for the conservation of momentum, there should not be any external force acting on the system. The external force may be force which is being acted from outside of the system.

→ Let's see what is the main concept here. It's the internal forces.

Now, what are those internal forces acting on the system?
you see the first example i.e. firing of a bullet from gun, here the spring in the gun itself provides the force on the bullet and the gun itself feels the backward ( or recoil force ). So, this is an internal force of a system which is developed from within the system only. 

Now, let's move to another example, i.e. a man walking on a boat. What happens here ?
As the man walks here, he pushes the boat backwards from his leg. This force is the same force which a person applies on the ground and the ground pushes him back and enables him/her to walk. So, this force which acts on the boat makes the boat move in backward direction to the motion of the man. We observe here that these two forces are action and reaction pair which acts within the system.

In the next example, it is given that a boy is getting off from a running bicycle. Now, when the boy will get off he pushes himself away from the bicycle so that he lands safely on the ground and in the process he also pushes the bicycle with the same force in the direction of motion of the bicycle. Again these two form an action reaction pair which are the internal forces of the system.

The same concept as above is applied for a man jumping off a stationary boat towards the shore. As a Reaction Force, the man pushes the boat in the opposite direction. So, at all these places, we observe the conservation of momentum taking place.