3.12 Principle of Conservation of Momentum
The collection of objects is known as a system. If no external force acts on any object of the system, it is known as an isolated system.
Consider a system of two balls of masses m₁ and m₂. Suppose that the balls are moving with velocities v₁ and v₂ along a straight line in the same direction. If v₁ > v₂, the balls will collide. If their velocities become v₁' and v₂' respectively after collision, then:
Total momentum before collision = m₁v₁ + m₂v₂
Total momentum after collision = m₁v₁' + m₂v₂'
The principle of conservation of momentum states that:
lightbulbIf no external force acts on an isolated system, the final total momentum of the system is equal to the initial total momentum of the system.
This means that:
Total momentum before collision = Total momentum after collision
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
To explain this principle, let us consider the collision of two identical balls in which the second ball is at rest.
When there is a collision of two balls, there is a transfer of momentum from one ball to another. The ball at rest gains momentum and starts moving, whereas the striking ball slows down. If the balls are identical, we observe that there is a total transfer of momentum. The striking ball comes to rest and the other ball starts moving with the same speed. This suggests that the total momentum of the two balls after collision remains the same as the total momentum before collision.
The principle of conservation of momentum is applicable not only to macro-objects but also to micro-objects like atoms and molecules.