Head-to-head
Momentum vs Impulse
Momentum describes what a moving body has: mass times velocity. Impulse describes what is done to it: a force applied over a period of time. The two are linked by the impulse-momentum theorem, which says the impulse applied to a body equals the change in its momentum.
That relationship is the reason the pair matters. If you want to stop a car, the momentum tells you how much has to be removed, and the impulse tells you how. The same change can be delivered by a small force over a long time or a large force over a short one, and the impulse is identical in both cases.
The difference in feel between those two options is enormous, which is the whole of vehicle crash safety. A brick wall and a set of crash barriers remove the same momentum from the same car. The barriers do it over a longer time, so the force — and therefore the acceleration the occupants experience — is far lower.
Momentum is also a conserved quantity, which impulse is not. In a closed system with no external force, total momentum before a collision equals total momentum after it. Impulse is not conserved at all; it is a transfer, and the momentum one body loses is exactly the momentum another gains or the ground absorbs.
Momentum
How To Calculate Momentum
Momentum is mass multiplied by velocity, and it is the quantity that decides how hard something is to stop. It is a vector, so direction matters, and unlike kinetic energy it grows in a straight line with speed.
Impulse
How To Calculate Impulse
Impulse explains why a long soft stop hurts less than a short hard one: the same change in momentum, delivered over more time, needs far less force.
How They Differ
| Attribute | Momentum | Impulse |
|---|---|---|
| What it describes | A state — the motion a body has | An event — a force applied over time |
| Formula | p = m × v | J = F × Δt |
| Units | kg·m/s | N·s, which is the same dimension |
| Conserved? | Yes, in a closed system | No — it is a transfer |
| Depends on duration? | No — it is instant-by-instant | Yes — time is in the definition |
| Direction | The same as the velocity | The same as the applied force |
| Where it is used in this library | Working out what a moving body carries | Working out what a force does over time |
The Same Numbers, Both Ways
A 1,500 kg car travelling at 20 m/s, brought to a stop by braking.
- Mass
- 1,500 kg
- Speed
- 20 m/s
- Braking force
- 6,000 N
| Line | Momentum | Impulse |
|---|---|---|
| Momentum carried | 30,000 kg·m/s | Not applicable — impulse is an event |
| Impulse needed to stop it | 30,000 kg·m/s to remove | 30,000 N·s in the other direction |
| Braking at 6,000 N | 30,000 kg·m/s | 30,000 N·s over 5 s |
| Braking at 15,000 N | 30,000 kg·m/s | 30,000 N·s over 2 s |
| Average acceleration | None while cruising | 4 m/s² softly, 10 m/s² hard |
| Stopping distance | Not part of momentum | 50 m softly, 20 m hard |
A 1,500 kg car at 20 m/s carries 30,000 kg·m/s of momentum, and stopping it takes an equal and opposite 30,000 N·s of impulse. That can be 6,000 N for 5 s or 15,000 N for 2 s — the momentum removed is identical, the impulse is identical, and only the acceleration differs: 4 m/s² against 10 m/s².
When To Use Each
Momentum
- You are working out what a moving object carries, before and after a collision.
- You are checking whether momentum is conserved in a two-body interaction.
- You know mass and velocity and want a single quantity of motion.
Impulse
- You are working out what a force achieves over a known duration.
- You are designing for a force limit, as in crash structure or packaging.
- You want to know how changing the duration changes the peak force.
Common Questions
Are momentum and impulse the same unit?
Yes. A newton-second is a kilogram-metre per second, since a newton is a kg·m/s². That dimensional match is exactly why the impulse-momentum theorem works: the impulse applied equals the momentum change, with no conversion factor.
Why does spreading the stop over more time help?
Because impulse is force times time, so the same impulse at a longer duration means a smaller force. Halving the force doubles the time, and since acceleration is force over mass, the acceleration — which is what causes injury — halves too.
Does momentum have a direction?
Yes, it points the same way as the velocity, which makes it a vector. In a head-on collision the momenta partly cancel, so the combined momentum can be far smaller than either one alone, and the impulse needed to stop the pair is correspondingly smaller.
Is momentum conserved in a car crash?
For the two vehicles considered together, yes, over the short duration of the impact — external forces like tyre friction are small by comparison. It is not conserved for one vehicle alone, because the other vehicle and the road apply impulse to it.
How is this different from kinetic energy?
Momentum is mass times velocity and is conserved in a closed system; kinetic energy is half of mass times velocity squared and is not conserved in an inelastic collision. In a crash, momentum is preserved while a large share of the kinetic energy becomes deformation and heat.
More Comparisons
- Kinetic Energy vs Potential Energy
Kinetic energy comes from motion; gravitational potential energy comes from height. A 10 kg mass 5 m up holds 490.33 J, and hitting the ground at 9.9 m/s it carries the same 490.33 J — the interchange is the whole of a pendulum.
- Average vs Median
The average uses every value; the median uses the middle one. On five incomes where one is an outlier, the average moves 8.65 and the median moves 1.5 — here is why that matters.
Sources
- Momentum and the impulse-momentum theorem — The Physics Classroom
- Momentum, impulse and collisions — NASA begin guide — NASA Glenn Research Center
- Crashworthiness and occupant protection research — National Highway Traffic Safety Administration
Both methods sit in Science.