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Conservation of momentum
Intermediate
Total momentum of an isolated system stays constant.
Σp_i = Σp_fIn an isolated system the total momentum is constant, because internal forces cancel in pairs. It applies to collisions, explosions and recoil, even when energy isn't conserved.
A 60 kg skater pushes a 40 kg skater: velocities are in ratio 2:3 opposite.
External forces such as friction must be negligible during the short collision.
In more detail
In an isolated system, total momentum is conserved. Collisions and explosions can change the momentum of each object, but the total stays the same.
Real-world uses
- Gun recoil is explained by conservation of momentum between the bullet and the gun.
- Collision investigators use momentum conservation to reconstruct the speeds of vehicles.
- In a gun recoil, the bullet and the gun start with zero momentum, so the gun moves backwards with momentum equal to the bullet's.
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Frequently asked questions
What makes a system isolated?
No net external force acts on it, so internal forces cannot change its total momentum.
Is momentum conserved in every collision?
Yes, if the system is isolated, even when kinetic energy is not conserved.
When is momentum conserved?
When no net external force acts on the system, such as in a collision between isolated bodies.
Related topics in Newton's Laws & Forces
Second law as rate of momentum change · Variable mass systems · Rocket propulsion · Circular motion dynamics · Banking of roads · Vehicle on flat circular turn