What is the relationship between momentum and law of conservation of momentum?

Momentum is the product of the mass and velocity of a body. As momentum has a direction, it is a vector quantity:

p = m ⋅ v

Law of conservation of momentum: In a collision between two objects in an isolated system, the total momentum of the two objects before the collision and after the collision is equal. This means that the momentum loss of object 1 is equal to the momentum gain of object 2.

During the interaction of the two bodies, Newton's third law states:
   - F12 = F21
We replace F = m × a (NEWTON's second law of motion):
    - m1 × a1 = m2 × a
We assume the acceleration to be constant:
     - m1 × Δv1 / Δt  =  m2 × Δv2 / Δt
Δt is reduced and we use Δv = v - v':
   - m1 × (v1' - v1)   = m2 × (v2' - v2)
   - m1 v1'  +  m1 v1   = m2 v2'  -  m2v2
   m1 v1 + m2 v2  = mv1'   +  m2v2'
   p1 + p2 = p1' + p2'






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