Formulas & tables/Physics/Dynamics/Conservation of momentum

Conservation of momentum

p⃗before=p⃗after\vec{p}_{before}=\vec{p}_{after}

Result unit: kg·m/s (vector quantity)

What it describes

In an isolated system the total momentum before an interaction equals the momentum after it.

Symbols

p⃗\vec{p}
momentum of the system
[kg·m/s]

Where it comes from

In a system with no external forces acting on it, the total momentum (the vector sum) does not change — this is why in recoil the bodies fly apart in opposite directions.

When to use it

Collisions (elastic and inelastic), recoil, decay. Momentum is calculated as a vector — directions matter.

Example

A 2 kg cart (3 m/s) collides with a stationary 1 kg cart and they couple together. Find the velocity after the collision.
Substitutionpbefore=2⋅3=6p_{before}=2\cdot3=6 kg·m/s, combined mass 33 kg.
Resultv=63=2v=\dfrac{6}{3}=2 m/s.

Related formulas

Momentum Kinetic energy

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