Mathematically, the law of conservation of momentum can be expressed as:
Momentum before collision = Momentum after collision
or,
$$∑p_i = ∑p_f$$
where \(∑p_i\) represents the total momentum of the objects before the collision, and \(∑p_f\) represents the total momentum of the objects after the collision.
The total momentum of a system is defined as the vector sum of the momenta of all the objects in the system. Momentum is a vector quantity, which means that it has both magnitude and direction. The magnitude of momentum is equal to the mass of an object multiplied by its velocity. The direction of momentum is the same as the direction of the object's velocity.
In a collision, the momentum of an object can change if its mass or velocity changes. However, the total momentum of the system remains the same. This is because the momentum lost by one object is gained by another object in the collision.
The law of conservation of momentum is a fundamental principle of physics that has many applications in real life. For example, it is used to calculate the recoil of a gun, the motion of a rocket, and the impact of a car crash.
