Momentum and Impulse
Simple Explanation
Momentum (p = mv) measures how hard it is to stop a moving object — it combines both mass and velocity. Impulse is the change in momentum a force produces over time: impulse = FΔt = Δp. A given force produces a bigger change in momentum the longer it acts.
Why Do We Need It?
Momentum and impulse explain why crumple zones, airbags, and padded landing mats work — they all extend the TIME over which a collision happens, which reduces the force needed to produce the same change in momentum.
Formula
Momentum and Impulse
p = mv; impulse J = FΔt = Δp
Momentum measures how hard it is to stop a moving object — it combines mass and velocity. Impulse is the change in momentum a force produces, and equals that force multiplied by the time it acts for.
- p
- — momentum, in kilogram-metres per second (kg·m/s)
- m
- — mass, in kilograms (kg)
- v
- — velocity, in metres per second (m/s)
- J
- — impulse, in newton-seconds (N·s), numerically equal to kg·m/s
- F
- — force applied, in newtons (N)
- Δt
- — the time interval the force acts for, in seconds (s)
- Δp
- — the resulting change in momentum, in kg·m/s
When to use it: Whenever finding an object's momentum, or the change in momentum (impulse) produced by a force acting for a known time.
Worked Example
Find the impulse needed to stop a moving object
A 1200 kg car travelling at 20 m/s is brought to rest. Find the impulse required.
Why Does This Work?
Impulse is DEFINED as the change in momentum a force produces, so whenever an object's momentum changes by a known amount, the impulse that caused that change must equal exactly that change — no separate calculation of force and time is needed if only the impulse is wanted.
Real-Life Example
Why airbags reduce injury
A car crash brings a passenger's momentum to zero either way — with or without an airbag.
An airbag extends the time (Δt) over which that same change in momentum happens; since impulse = FΔt is fixed, a longer Δt means a much smaller force F on the passenger — reducing injury.
Practice
Find the momentum of a 3 kg object moving at 6 m/s.
EasyA force of 400 N acts on an object for 0.5 s. Find the impulse delivered.
MediumCommon mistake
Forgetting that impulse and momentum are vectors — a change of direction (like a ball bouncing straight back off a wall) involves a much bigger change in momentum than just stopping, since the velocity reverses sign.
Quick Review
- p = mv (momentum); J = FΔt = Δp (impulse).
- A longer contact time reduces the force needed for the same change in momentum.
- This is why crumple zones, airbags, and padded mats reduce injury.