Final answer:
Conservation of momentum states that the total momentum in an isolated system remains constant before and after an event, which in integral form is expressed as the sum of initial momenta equaling the sum of final momenta.
Step-by-step explanation:
The concept of conservation of momentum is foundational in physics, particularly when analyzing interactions such as collisions and explosions within a closed system. By definition, momentum is a vector quantity, represented by components in the x, y, and possible z-axis. According to the law of conservation of momentum, the total momentum of an isolated system remains unchanged before and after an event. In mathematical terms, this can be represented in integral form as follows:
∑ P₁ + ∑ P₂ = ∑ P'1 + ∑ P'2
Where ∑ indicates the sum of the initial and final momenta of two objects in a system, assuming no external net force acts on the system (Fnet = 0). In problems involving one-dimensional elastic collisions, the conservation of momentum equation simplifies to m₁V₁ + m₂V₂ = m₁v'1 + m₂v'2.
It's crucial to note that the conservation of momentum principle is valid in both classical and relativistic physics, with modifications to account for relativistic effects when particles are moving at velocities comparable to the speed of light.