Conservation of momentum
- Olympiad · NSEJS
The law of conservation of momentum says that when no outside force acts, the total momentum of a group of bodies stays the same.
Momentum is mass times velocity, p = mv. Its unit is kg m/s. It has a direction, so a body moving the other way has negative momentum.
When two bodies push on each other, the forces are equal and opposite. That is Newton's third law. So whatever momentum one body gains, the other loses. The total before an event equals the total after it. This holds for collisions, explosions and recoil.
A small example
A toy gun of mass 2 kg fires a 20 g ball at 100 m/s. Both start at rest. How fast does the gun move back?
- Total momentum before firing is 0, since nothing moves.
- The ball's momentum after is 0.02 kg × 100 m/s = 2 kg m/s.
- Let the gun's velocity be v. Total after: 2 × v + 2 = 0.
- So v = -1 m/s. The gun moves back at 1 m/s.
The minus sign means the opposite direction to the ball. This is recoil. The heavy gun moves slowly and the light ball moves fast, but their momenta are equal in size. To find how far the gun moves, you would use the equations of motion.
Where it fits
This goes beyond the Class 10 board syllabus. HBCSE's Junior Science syllabus lists it under force and Newton's laws. That syllabus is for NSEJS, which the Indian Association of Physics Teachers (IAPT) conducts.
Sources
Facts last checked against these sources on 30 September 2026.
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