The conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant if no external forces are acting on it. Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) is given by the equation p = mv, where m represents the mass of an object and v represents its velocity.

To understand the concept of conservation of momentum, consider the following scenario: two billiard balls of equal mass are at rest on a frictionless table. When one ball is struck by a cue stick, it exerts a force on the other ball, causing it to move. As a result, the first ball loses momentum and the second ball gains an equal amount of momentum in the opposite direction. The total momentum of the system before and after the collision remains the same.

Another example that highlights the conservation of momentum is a rocket launching into space. According to Newton's third law, for every action, there is an equal and opposite reaction. As the rocket expels mass in the form of exhaust gases, it experiences a reaction force in the opposite direction, propelling it forward. This conservation of momentum enables the rocket to achieve lift-off and accelerate in space.