p = m × v
Last reviewed: May 2026
Momentum is one of the most conserved quantities in the universe. Newton's second law can be restated as F = dp/dt (force equals the rate of change of momentum).[1] This makes momentum central to understanding collisions, propulsion, and nearly every mechanical interaction. The conservation of momentum explains why rockets work in space, why recoil happens when firing a gun, and why pool balls scatter predictably. See also: Kinetic Energy Calculator.
| Object | Mass | Speed | Momentum (kg·m/s) |
|---|---|---|---|
| Baseball (pitch) | 0.145 kg | 42 m/s (94 mph) | 6.1 |
| Running person | 75 kg | 5 m/s (11 mph) | 375 |
| Bicycle + rider | 85 kg | 8 m/s (18 mph) | 680 |
| Car (highway) | 1,500 kg | 27 m/s (60 mph) | 40,500 |
| Semi truck | 36,000 kg | 27 m/s (60 mph) | 972,000 |
Linear momentum is calculated as p = mv, where m is mass in kilograms and v is velocity in meters per second. The SI unit of momentum is kg·m/s (kilogram-meters per second), which has no special name. Unlike kinetic energy, momentum is a vector quantity — it has both magnitude and direction. A 1,000 kg car traveling east at 20 m/s has momentum of 20,000 kg·m/s eastward. The same car traveling west at the same speed has the same magnitude but opposite direction. This directional nature is why head-on collisions are far more destructive than rear-end collisions at the same speed — the momenta are in opposing directions, requiring a much larger change in momentum for each vehicle.
| Object | Mass | Speed | Momentum (kg·m/s) |
|---|---|---|---|
| Baseball pitch | 0.145 kg | 42 m/s (94 mph) | 6.1 |
| Running human | 75 kg | 5 m/s (11 mph) | 375 |
| Bicycle + rider | 85 kg | 8 m/s (18 mph) | 680 |
| Car (city speed) | 1,500 kg | 13 m/s (30 mph) | 19,500 |
| Car (highway) | 1,500 kg | 30 m/s (67 mph) | 45,000 |
| Semi truck | 36,000 kg | 27 m/s (60 mph) | 972,000 |
| Freight train | 4,000,000 kg | 22 m/s (50 mph) | 88,000,000 |
In any closed system where no external forces act, total momentum is always conserved — the total momentum before an event equals the total momentum after. This principle is one of the most fundamental laws in all of physics. In a collision between two cars, the combined momentum of both vehicles before impact equals their combined momentum after impact, regardless of whether the collision is elastic (objects bounce apart), inelastic (objects deform but separate), or perfectly inelastic (objects stick together). For a 2,000 kg car traveling at 20 m/s hitting a stationary 1,000 kg car, the combined post-collision velocity (if they stick together) is v = (2,000 × 20) / (2,000 + 1,000) = 13.3 m/s. This calculation is used by accident reconstruction specialists to determine pre-crash vehicle speeds from post-crash evidence.
Impulse (J) equals the change in momentum: J = Δp = F × Δt. This means a given change in momentum can be achieved with a large force applied briefly or a smaller force applied longer. This principle explains virtually every safety device in existence: airbags extend the deceleration time from 5–10 milliseconds (hitting the steering wheel) to 100–200 milliseconds, reducing peak force on the occupant by 10–20×. Crumple zones extend the collision time for the vehicle structure itself. Bungee cords decelerate a jumper over several seconds. Catching a ball with "soft hands" (pulling the glove back during the catch) increases the stopping time and reduces the force on your hand — the impulse is the same either way.
Rockets work by conservation of momentum — expelling mass (exhaust gases) in one direction creates an equal and opposite momentum change in the rocket. The rocket equation Δv = v_exhaust × ln(m_initial / m_final) shows that the velocity change depends on the exhaust speed and the ratio of initial to final mass. This is why rockets are mostly fuel — a typical rocket at launch is 85–90% propellant by mass. The Saturn V moon rocket weighed 6.5 million pounds at launch but only 100,000 pounds reached lunar orbit. Every gram of unnecessary structure reduces payload capacity, which is why aerospace engineering pursues extreme weight optimization in materials and design.
→ Momentum is proportional to velocity, not velocity squared. Unlike kinetic energy (½mv²), momentum (mv) scales linearly. Doubling speed doubles momentum but quadruples kinetic energy.
→ Direction matters. Objects moving in opposite directions have opposite momentum. In a head-on collision, their momenta partially cancel — the combined wreck moves in the direction of the larger initial momentum.
→ Use impulse for safety analysis. To reduce force, increase the time over which momentum changes. Every safety device — airbags, helmets, padding — works by extending the deceleration time.
See also: Kinetic Energy · Projectile Motion · Speed Calculator · Gravitational Force
Angular momentum (L = Iω) is the rotational equivalent of linear momentum. A spinning figure skater pulls their arms in to reduce moment of inertia, which increases angular velocity to conserve angular momentum — this is why they spin faster with arms tucked. Angular momentum conservation also governs planetary orbits, gyroscope stability, helicopter rotor dynamics, and the formation of spiral galaxies. In quantum mechanics, angular momentum is quantized — particles like electrons can only have specific discrete values of angular momentum, a principle that determines atomic orbital shapes and chemical bonding properties. The conservation of angular momentum is as fundamental as the conservation of linear momentum — both derive from symmetry principles identified by Emmy Noether in 1915.
In sports, angular momentum explains why a diver can perform multiple flips by tucking tight (low I, high ω) and slowing rotation by extending their body before entry (high I, low ω). Gymnasts, divers, and trampolinists intuitively manipulate angular momentum conservation every time they perform aerial maneuvers — adjusting body position to control rotation speed without any external torque.
Understanding momentum — both linear and angular — provides insight into nearly every physical interaction from subatomic particle collisions to galaxy formation. The conservation laws governing momentum are among the most tested and confirmed principles in all of physics, holding true at every scale from quantum mechanics to cosmology. For related physics calculations, see our Gravitational Force Calculator and Projectile Motion Calculator.
Whether analyzing car crashes, designing spacecraft, or simply understanding why a bowling ball is harder to stop than a tennis ball at the same speed, momentum is the quantity that makes the physics of motion intuitive and predictable across every scale of the physical world.
From Newton's cradle desk toys to interplanetary spacecraft trajectories, momentum conservation governs every collision, explosion, and propulsion event in the physical world — making it one of the most practically useful and theoretically profound concepts in all of science and engineering.
→ Momentum is always conserved. In every collision and interaction, total momentum remains constant.[1]
→ Heavier and faster = more momentum. But velocity and mass contribute linearly (unlike KE where velocity is squared).
→ Use for collision analysis. Enter both objects to model elastic and inelastic collisions.[2]
→ Pair with energy calculations. The Kinetic Energy Calculator shows energy transfer in collisions.
See also: Kinetic Energy · Speed · Gravity · Newton’s Laws