Answer
No, the conservation of momentum does not directly follow from Newton's third law.
Newton's third law states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. While this law is related to the conservation of momentum, it is not the same thing.
The conservation of momentum is a fundamental principle of physics that states that the total momentum of a closed system remains constant if there are no external forces acting on the system. This means that if two objects collide and interact with each other, their total momentum before the collision must be equal to their total momentum after the collision, regardless of the forces they exert on each other.
While Newton's third law is related to the conservation of momentum, it does not necessarily imply it. For example, in the case of an isolated system with no external forces, Newton's third law would still hold true (every action has an equal and opposite reaction), but it would not necessarily lead to the conservation of momentum. The conservation of momentum requires additional assumptions beyond the third law, such as the absence of external forces on the system.
Work Step by Step
The conservation of momentum
$p_{i} = p_{f} $
Newton's 3rd Law
$ \vec{F_{12}} = \vec{-F_{21}}$
