Momentum & Impulse Calculator
Compute linear momentum p = m × v and impulse J = F × Δt.
p = m × v. SI units: kilograms and m/s give kg·m/s.
Linear momentum is p = m × v: mass times velocity. An object of 2 kg moving at 3 m/s has momentum p = 2 × 3 = 6 kg·m/s. Impulse J = F × Δt equals the change in momentum, so a force applied over time is what speeds an object up or slows it down.
What momentum and impulse are
Momentum measures how hard it is to stop a moving object: p = m × v. A heavy, fast object carries more momentum than a light or slow one. Impulse is the action that changes momentum — a force F applied for a time Δt delivers an impulse J = F × Δt, and that impulse equals the resulting change in momentum, Δp. This link is the impulse–momentum theorem, the time-integrated form of Newton’s second law.
p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s); F = force (N), Δt = time (s)
Worked example
A 2 kg object moves at 3 m/s. What is its momentum?
- 1 Write the momentum formula. p = m × v, with mass in kilograms and velocity in m/s.
- 2 Substitute the known values. p = 2 kg × 3 m/s.
- 3 Compute the momentum. p = 6 kg·m/s, directed along the object’s velocity.
Momentum, impulse, and their units
Impulse and momentum share the same dimensions: 1 N·s = 1 kg·m/s.
| Quantity | Formula | SI unit |
|---|---|---|
| Momentum | p = m × v | kg·m/s |
| Impulse | J = F × Δt | N·s |
| Impulse–momentum theorem | J = Δp = m × Δv | kg·m/s |
| Average force | F = Δp ÷ Δt | newton (N) |
Direction, conservation, and softening impacts
Momentum is a vector. It points along the velocity, so direction matters. When you add momenta — for two objects, or before and after a collision — combine them as vectors, keeping signs for opposite directions.
Momentum is conserved. With no external force, the total momentum of a system stays constant. In a collision the objects can exchange momentum, but the sum before equals the sum after — the principle behind rocket thrust, recoil, and crash analysis.
Impulse explains safety gear. Since J = F × Δt = Δp, the same change in momentum can be achieved with a small force over a long time or a large force over a short time. Airbags, crumple zones, and bending your knees on landing stretch Δt to shrink the peak force.