Momentum & Impulse Calculator

Momentum and Impulse Guide

Momentum Fundamentals

Momentum (p) = mass (m) × velocity (v), measured in kg⋅m/s. It is a vector quantity — direction matters. A 1,000kg car at 20 m/s has the same momentum as a 2,000kg car at 10 m/s (20,000 kg⋅m/s each). Newton's second law in terms of momentum: F = dp/dt (force equals rate of change of momentum). This is more fundamental than F = ma, which assumes constant mass. Conservation of momentum: in any isolated system, total momentum before equals total momentum after a collision.

Impulse

Impulse (J) = Force × time = change in momentum. This is why airbags save lives — they increase the time of impact, reducing the force for the same change in momentum. A head hitting the steering wheel in 5ms vs the airbag in 50ms: same impulse, 10× longer time, so 10× less force. Same principle: catching a cricket ball by drawing your hands back, bending your knees when landing, crumple zones in cars, sports padding and helmets.

Conservation of Momentum

In elastic collisions, both momentum and kinetic energy are conserved (billiard balls, atomic collisions). In perfectly inelastic collisions, only momentum is conserved and objects stick together (clay, car crashes). Total momentum before = total momentum after, regardless of collision type. For a 70kg person at 5 m/s colliding with a stationary 50kg person in a perfectly inelastic collision: final velocity = (70×5 + 50×0)/(70+50) = 350/120 = 2.92 m/s.

Everyday Momentum

Sports: a cricket ball (0.16kg) at 90mph (40 m/s) has p = 6.4 kg⋅m/s. A rugby tackle: a 100kg player at 6 m/s has p = 600 kg⋅m/s — much more momentum despite lower speed. Rockets: Newton's third law means the momentum of exhaust gases equals the momentum gained by the rocket. Recoil: when a gun fires, the bullet and gun gain equal and opposite momenta. The gun's recoil velocity = (bullet mass × bullet velocity) / gun mass.