Momentum depends on two things: an object’s mass and its velocity. The formula is simple: momentum equals mass times velocity (p = mv). A heavier object has more momentum, and a faster object has more momentum. Double either one, and you double the momentum.
Mass and Velocity: The Two Factors
Momentum is directly proportional to both mass and velocity. A 2,000-kilogram car traveling at 15 meters per second has twice the momentum of a 1,000-kilogram car moving at the same speed. Likewise, a car going 30 m/s has twice the momentum of the same car going 15 m/s. This straightforward relationship is what makes momentum useful for predicting what happens when objects collide, slow down, or speed up.
The standard unit of momentum in physics is the kilogram-meter per second (kg·m/s). If you know an object’s mass in kilograms and its speed in meters per second, multiplying them gives you its momentum in those units.
Direction Matters
Momentum is a vector quantity, meaning it has both a size and a direction. The direction of an object’s momentum is always the same as the direction of its velocity. A ball rolling east has eastward momentum; if it bounces off a wall and heads west, its momentum has reversed direction even if its speed stays the same.
This matters when you’re dealing with more than one object. Two cars of equal mass moving toward each other at the same speed have equal and opposite momenta, so their total momentum is zero. When adding momenta together, you have to account for direction, treating one direction as positive and the opposite as negative.
How Momentum Changes: Force and Time
Since momentum depends on mass and velocity, anything that changes an object’s velocity changes its momentum. The amount of change depends on how much force is applied and for how long. This relationship is captured by the impulse-momentum theorem: the force multiplied by the time it acts equals the change in momentum (F × t = m × Δv).
This is why airbags work. In a car crash, your momentum has to drop to zero regardless of whether you hit a hard dashboard or a soft airbag. The change in momentum is the same either way. But the airbag stretches the impact over a longer time, which means the force on your body is proportionally smaller. A tenfold increase in impact time produces a tenfold decrease in force.
How Momentum Differs From Kinetic Energy
People often confuse momentum with kinetic energy because both depend on mass and speed. The key difference is how much velocity matters in each formula. Momentum equals mass times velocity (p = mv), while kinetic energy equals one-half times mass times velocity squared (KE = ½mv²). That squared term means kinetic energy grows much faster as speed increases. An object moving twice as fast has twice the momentum but four times the kinetic energy.
There’s another important distinction: momentum is a vector (it has direction), while kinetic energy is a scalar (it’s just a number). Two identical balls flying toward each other can have a total momentum of zero, but their total kinetic energy is decidedly not zero.
Conservation of Momentum in Collisions
One reason momentum is so central to physics is that it’s conserved in isolated systems. As long as no net external force acts on a group of objects, their total momentum before any interaction equals their total momentum afterward. This holds whether the collision is elastic (objects bounce apart with no energy lost), inelastic (some kinetic energy converts to heat or sound), or perfectly inelastic (objects stick together).
Consider two billiard balls colliding. The total momentum of both balls before the collision equals the total momentum after. Individual balls may speed up or slow down, but the system’s combined momentum stays constant. In a perfectly inelastic collision where two objects stick together, the combined mass moves at whatever velocity preserves the original total momentum. A heavy object hitting a light stationary one will barely slow down, while the light object will fly off quickly.
Conservation of momentum applies only when external forces are negligible. During projectile motion, for instance, momentum is conserved horizontally (no horizontal forces, ignoring air resistance) but not vertically, because gravity acts as an external force pulling the object downward.
Angular Momentum: The Rotational Version
For spinning or orbiting objects, momentum depends on different variables. Angular momentum replaces mass with “moment of inertia,” which accounts for both the object’s mass and how that mass is distributed relative to the axis of rotation. A figure skater spinning with arms extended has a large moment of inertia. Pull the arms in and the moment of inertia drops, but angular momentum is conserved, so the skater spins faster. Halving the radius of rotation reduces the moment of inertia by a factor of four, which means the spin rate quadruples.
Momentum at Extreme Speeds
The simple formula p = mv works perfectly for everyday speeds, but it breaks down as objects approach the speed of light. At very high speeds, momentum also depends on a correction factor from Einstein’s special relativity. This factor, called the Lorentz factor, grows larger as speed increases and approaches infinity as an object nears light speed. The result is that momentum climbs far more steeply than you’d expect from mass times velocity alone, which is one reason no object with mass can actually reach the speed of light. At ordinary speeds (cars, planes, even spacecraft), the correction is so tiny it can be ignored entirely.