Linear Momentum Calculator

Linear momentum: Q = m·v

Linear momentum (also called quantity of motion) is the vector quantity Q = m·v, measured in kg·m/s. The law of conservation states that in an isolated system the total momentum before equals the total after: Σ Q_before = Σ Q_after. Elastic collisions conserve both kinetic energy and momentum; inelastic collisions conserve only momentum. The impulse equals the change in momentum: J = F·Δt = ΔQ. Example: an 80 kg player at 5 m/s tackles a stationary 80 kg goalkeeper in a perfectly inelastic collision — both move together at 2.5 m/s afterward.

Applications

Airbags increase Δt to reduce the force on passengers (J = F·Δt). Recoil from a firearm and rocket propulsion (Tsiolkovsky equation) both follow conservation of momentum — action and reaction. Billiards, American football tackles, and crash safety design all use the same principle. In relativity, momentum generalizes to p = γmv.

FAQ

Is momentum a vector? Yes — direction matters. Two equal masses moving in opposite directions can have zero total momentum even though both are moving.

Momentum vs kinetic energy? Both depend on mass and velocity, but Ec = (1/2)mv² is scalar and quadratic in v, while Q = mv is vectorial and linear. They conserve under different conditions.

Why does an airbag reduce injury? By extending the deceleration time Δt, the average force F = ΔQ/Δt drops sharply, even though the change in momentum is the same.