The law of conservation of momentum states that the total momentum of a closed system of objects (which has no external forces acting on it) remains constant.



Newton's third law of motion states that for every action, there is an equal and opposite reaction.



When two objects interact, they exert forces on each other. According to Newton's third law of motion, these forces are equal in magnitude and opposite in direction. Let's consider two objects A and B.

- Object A exerts a force on object B (action).
- Object B exerts an equal and opposite force on object A (reaction).

Now, let's assume that the mass of object A is m1 and its velocity is v1, while the mass of object B is m2 and its velocity is v2.

From Newton's second law of motion, we know that force is equal to the rate of change of momentum. Therefore, the force exerted by object A on object B is given by:

- Force = (m1 * delta v1) / delta t

Similarly, the force exerted by object B on object A is given by:

- Force = (m2 * delta v2) / delta t

Since the forces are equal and opposite, we can equate them:

- (m1 * delta v1) / delta t = -(m2 * delta v2) / delta t

Multiplying both sides by delta t, we get:

- m1 * delta v1 = -m2 * delta v2

Rearranging the equation, we get:

- m1 * delta v1 + m2 * delta v2 = 0

This equation tells us that the total momentum of the system (m1 * v1 + m2 * v2) is conserved. In other words, the total momentum before the interaction is equal to the total momentum after the interaction.

Therefore, we can derive the law of conservation of momentum from Newton's third law of motion.