Momentum and Impulse
A loaded freight train is hard to stop, and a thrown baseball stings the hand that catches it. Both facts come down to momentum, the physical quantity that measures how much motion an object carries. Closely linked is impulse, which describes how forces change that motion over time. Together they explain collisions, recoil, and a surprising amount of everyday life.
What momentum is
Momentum is the product of an object’s mass and its velocity:
It is a vector, meaning it has both size and direction. A heavy object moving slowly can have the same momentum as a light object moving quickly. Momentum is measured in kilogram-metres per second (kg·m/s). The greater an object’s momentum, the harder it is to stop or turn, which is exactly why the train is so unstoppable while the baseball is manageable.
Impulse: changing momentum
To change an object’s momentum you must apply a force for some length of time. The product of force and the time it acts is called impulse, and it equals the change in momentum:
This is really just Newton’s second law written in terms of time rather than acceleration. It reveals something practical: the same change in momentum can be achieved with a large force over a short time or a small force over a long time.
Airbags, crumple zones, and bending your knees on landing all work by extending the time over which momentum changes. A longer Δt means a smaller force for the same impulse, and a smaller force means less injury.
Conservation of momentum
The most powerful idea in this topic is that, in any system where no outside force acts, the total momentum stays constant. When two objects interact, they push on each other with equal and opposite forces (Newton’s third law), so whatever momentum one gains, the other loses. The total never changes:
This conservation law holds even in messy collisions where energy is lost to heat and sound. That makes it an extraordinarily reliable tool for predicting outcomes that would be hopeless to calculate force by force.
Elastic and inelastic collisions
Collisions come in two broad types, and momentum is conserved in both.
- Elastic collisions: Both momentum and kinetic energy are conserved. Billiard balls and gas molecules come close to this ideal.
- Inelastic collisions: Momentum is conserved, but some kinetic energy is converted to heat, sound, or deformation. A car crash is highly inelastic.
- Perfectly inelastic: The objects stick together and move as one, losing the maximum possible kinetic energy while still conserving momentum.
Recoil and rockets
Conservation of momentum explains recoil. When a gun fires, the bullet shoots forward with some momentum, so the gun must move backward with equal and opposite momentum to keep the total at zero. Because the gun is much heavier, it moves much more slowly than the bullet.
A rocket works the same way. It hurls hot exhaust gas downward at high speed, and the equal and opposite momentum drives the rocket upward. This is why rockets work in the vacuum of space, where there is nothing to push against; they push against their own expelled fuel.
Why follow-through matters in sport
Coaches insist on follow-through for good reason. Continuing to push a ball, racket, or bat through the swing extends the contact time Δt. A longer contact time means a larger impulse, and therefore a larger change in the ball’s momentum, sending it off faster. The same physics that protects you in a car crash helps you hit a longer drive.
Frequently asked questions
How is momentum different from kinetic energy?
Momentum is mass times velocity and is a vector that is always conserved in collisions. Kinetic energy is half mass times velocity squared, a scalar, and is conserved only in elastic collisions. They measure different aspects of motion.
Why do airbags reduce injury?
They increase the time over which your body’s momentum drops to zero. Since impulse equals force times time, stretching the time means the force on you is much smaller, even though the change in momentum is the same.
Is momentum always conserved?
Total momentum is conserved whenever no net external force acts on the system. Internal forces between colliding objects cancel out, but an outside force, such as friction or gravity acting over time, can change the system’s total momentum.
