**Law of Conservation of Momentum**

The law of conservation of momentum is a fundamental principle in physics that states that the total momentum of a system remains constant if no external forces act on it. This law is based on the principle of inertia and is a consequence of Newton's third law of motion. The law of conservation of momentum can be mathematically expressed as:

**Total initial momentum = Total final momentum**

This law holds true for any isolated system, where an isolated system refers to a system that doesn't interact with its surroundings or experiences negligible external forces.

**Explanation**

The conservation of momentum can be explained by considering the interactions between objects or particles within a system. When two objects interact, they exert equal and opposite forces on each other according to Newton's third law. These forces cause changes in the objects' momentum, but the total momentum of the system remains constant.

1. **Momentum**:
- Momentum is a vector quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity.
- Mathematically, momentum (p) is given by the equation: p = m * v, where m is the mass of the object and v is its velocity.
- Momentum has both magnitude and direction, and it is conserved in an isolated system.

2. **Newton's Third Law of Motion**:
- Newton's third law states that for every action, there is an equal and opposite reaction.
- When two objects interact, the forces they exert on each other are always equal in magnitude and opposite in direction.

3. **Impulse**:
- Impulse is defined as the change in momentum of an object. It occurs when a force is applied to an object over a certain period of time.
- Mathematically, impulse (J) is given by the equation: J = F * Δt, where F is the force applied and Δt is the time interval over which the force acts.

4. **Conservation of Momentum**:
- According to Newton's third law, the forces exerted by two objects on each other are equal and opposite. This means that the impulse experienced by each object is equal and opposite as well.
- As a result, the change in momentum of each object is equal and opposite.
- Since momentum is a vector quantity, the vector sum of the individual momenta before the interaction is equal to the vector sum of the individual momenta after the interaction.
- Therefore, the total momentum of the system remains constant, as long as no external forces act on it.

The law of conservation of momentum is a powerful tool in understanding and predicting the behavior of objects and systems in various physical phenomena, such as collisions, explosions, and other interactions. It helps in analyzing the before and after scenarios of interactions and provides insights into the conservation principles of nature.

law of conservation of momentum States that the the total momentum of two objects before collision and after collision are equal .