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Momentum Calculator

Calculate linear momentum with p = m v — enter mass and velocity, or solve for either. Momentum is measured in kilogram-metres per second (kg·m/s).

 

Formula

$$ p = m\,v \qquad m = \frac{p}{v} \qquad v = \frac{p}{m} $$

Worked example

A 1,000 kg car at 20 m/s has momentum \( p = (1000)(20) = 20{,}000\ \text{kg·m/s} \). Momentum is conserved in collisions, which is why this value determines the outcome when it hits another vehicle.

How it works

Linear momentum is the product of an object's mass and velocity: p = m v. It is a vector, pointing in the direction of motion, with units of kg·m/s.

Momentum matters because it is conserved: in the absence of external forces, the total momentum of a system stays constant. This is the principle behind collisions, recoil and rocket propulsion. A change in momentum equals the impulse, F·Δt.

Frequently asked questions

What is the formula for momentum?

Momentum is p = m v — mass times velocity. Mass is in kilograms and velocity in metres per second, giving kg·m/s.

How is momentum different from kinetic energy?

Momentum (mv) is a vector and is conserved in all collisions. Kinetic energy (½mv²) is a scalar and is only conserved in perfectly elastic collisions. Energy grows with velocity squared; momentum grows linearly.

Is momentum always conserved?

The total momentum of an isolated system (no net external force) is always conserved, even when kinetic energy is lost to heat or deformation in an inelastic collision.

What are the units of momentum?

Kilogram-metres per second (kg·m/s), which is equivalent to newton-seconds (N·s).

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