Conservation of linear momentum is equivalent to Newton's third law of motion.

Newton's Third Law of Motion: Newton's third law states that for every action, there is an equal and opposite reaction. This means that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

Conservation of Linear Momentum: The principle of conservation of linear momentum states that the total linear momentum of a system of objects remains constant if no external forces act on the system. Linear momentum is the product of an object's mass and its velocity. Mathematically, it can be represented as:

Momentum (p) = mass (m) × velocity (v)

Explanation: The conservation of linear momentum is equivalent to Newton's third law of motion because both principles are based on the fact that forces occur in pairs. According to Newton's third law, when two objects interact, the force exerted by one object on the other is equal in magnitude and opposite in direction to the force exerted by the second object on the first.

When two objects interact, such as in a collision, the total momentum of the system remains constant if no external forces are involved. This is because the forces exerted by the objects on each other are equal and opposite, resulting in a cancellation of the changes in momentum. Therefore, the total momentum before the interaction is equal to the total momentum after the interaction.

In other words, the conservation of linear momentum is a consequence of Newton's third law of motion. The law implies that the forces acting on two interacting objects are equal and opposite, ensuring that the total momentum of the system is conserved. This principle is fundamental in understanding various physical phenomena, such as collisions, explosions, and the motion of objects in general.

In conclusion, the conservation of linear momentum is equivalent to Newton's third law of motion because both principles are based on the equal and opposite nature of forces. The conservation of momentum ensures that the total momentum of a system remains constant in the absence of external forces.