What Is Momentum?

Momentum tells us how much “oomph” an object has while it’s moving. It’s calculated by multiplying an object’s mass by its velocity:

𝑝 = 𝑚𝑣

For example, a heavy truck moving at 60 km/h has much more momentum than a small car moving at the same speed, because the truck has more mass.

Momentum is a vector, meaning it has direction as well as size. If two cars are moving in opposite directions, their momentum also points in opposite directions.

The Conservation of Momentum

Momentum is conserved. This means that the total momentum in a system stays the same, as long as no external force is acting on it. This idea comes from Newton’s Third Law of Motion: for every action, there is an equal and opposite reaction. When two objects interact, they push or pull on each other with equal forces in opposite directions. As a result, the momentum lost by one object is exactly gained by the other.

Momentum and Force

Newton’s Second Law of Motion also connects to momentum. It tells us that force changes momentum over time:

𝐹 = 𝑑𝑝 / 𝑑𝑡

This means that force is the rate at which momentum changes. A bigger force, or a longer time applying it, creates a larger change in momentum. This leads to the concept of impulse, which is the change in momentum caused by a force acting over time:

𝐽 = Δ𝑝 = 𝐹 ⋅ Δ𝑡

A small force applied for a long time can have the same impact as a large force applied briefly. This is why airbags save lives. They increase the time it takes for your body to stop in a crash, which spreads out the force and reduces the risk of injury.

Internal vs. External Forces

There’s an important distinction between internal and external forces. Internal forces are forces between objects within the system. These forces can cause individual objects to gain or lose momentum, but they do not change the total momentum of the system. External forces, on the other hand, come from outside the system and can change the total momentum.

For example, if you push a skateboard from the ground, you are applying an external force that gives it momentum. But if you and a friend are both standing on the skateboard and push against each other, your individual momenta change, but the total momentum of you and the skateboard remains the same.

Momentum and Newton’s First Law

Newton’s First Law can also be described in terms of momentum. If no external force is acting, an object’s momentum stays constant. A moving object will continue moving at the same speed and in the same direction unless something from outside the system pushes or pulls on it. 

Frame of Reference

Momentum depends on your frame of reference. If you’re in an inertial frame of reference (one that is not accelerating), momentum behaves just as Newton’s laws describe. But in a non-inertial frame (one that is accelerating or rotating), things get weird. It can feel like a force is acting on an object, even when it’s not. What you’re actually feeling is the result of the frame’s motion.

For example, if you’re in a car that suddenly turns, it might feel like you’re being pushed to the side. But to someone watching from outside the car, it’s clear that you’re just trying to keep moving in a straight line while the car turns beneath you.