Law of Conservation of Momentum:

The total momentum of an isolated system of particles is conserved. The law follows from the second and third law of motion.

Explain with an example: An important example of the application of the law of conservation of momentum is the collision of two bodies. Consider two bodies A and B, with initial momenta pA and pB. The bodies collide; get apart, with final momenta p′A and p′B respectively. By the Second Law

(Where we have taken a common interval of time for both forces i.e. the time for which the two bodies are in contact.)
Since FAB = -FBA by the third law.

which shows that the total final momentum of the isolated system equals its initial momentum. Notice that this is true whether the collision is elastic or inelastic. In elastic collisions, there is a second condition that the total initial kinetic energy of the system equals the total final kinetic energy.

Linear Momentum:

It is defined as the quantity of motion contained in the body. Mathematically it is given by the product of mass and velocity. It is a vector quantity represented by p.

The principle of Conservation of Linear Momentum:

It states that in the absence of any external applied force total momentum of a system remains conserved.

Proof-

Physical Application

  1. The recoil of gun – when a bullet is fired in the forward direction gun recoils in the backward direction.
  2. When a person jumps on the boat from the shore of the river, boat along with the person on it moves in the forward direction.
  3. When a person on the boat jumps forward on the shore of river, boat starts moving in the backward direction.
  4. In rocket propulsion fuel is ejected out in the downward direction due to which rocket is propelled up in vertically upward direction.