Home / Topics / Momentum & Collisions
Conservation of momentum
Beginner
In an isolated system total momentum is constant.
m₁u₁+m₂u₂ = m₁v₁+m₂v₂When no net external force acts, total momentum before equals after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. It holds even when kinetic energy is lost.
A 1 kg ball at 4 m/s hits a stationary 3 kg ball and sticks: v = 1 m/s.
Check the system is isolated at the moment of interest.
In more detail
The total momentum of an isolated system stays constant, whatever forces act between its parts. This is one of the most powerful conservation laws in physics.
Real-world uses
- Engineers use momentum conservation to predict the motion of spacecraft after separation.
- Collision reconstruction experts use it to estimate speeds in car accidents.
- Billiard players use momentum conservation to predict how two balls will move after a collision on the table.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
When is momentum conserved?
When no net external force acts on the system.
Does conservation apply to gravity and friction?
Momentum is conserved for internal forces, but external forces like friction from the ground change it.
Does momentum conservation need the collision to be elastic?
No. Momentum is conserved in every collision with no external forces, whether or not kinetic energy is conserved.
Related topics in Momentum & Collisions
Impulse · Impulse–momentum theorem · Why airbags work · Isolated system · Recoil of a gun · Elastic collision