Physics
Momentum, impulse & collisions — quick study summary
Momentum p = mv (a vector). Newton's second law in its general form is F = dp/dt — force equals the rate of change of momentum. Impulse J = FΔt = Δp. Conservation of momentum: in any isolated system, total momentum before = total momentum after a collision. Elastic collisions also conserve kinetic energy (think billiard balls); inelastic collisions don't (think clay sticking together).
Key points
- p = mv (vector)
- F = dp/dt; impulse J = FΔt = Δp
- Total momentum is conserved in any isolated collision
- Elastic: KE also conserved. Inelastic: KE lost to heat/deformation
- Perfectly inelastic: objects stick together after collision
Practice quiz
Click each question to reveal the answer.
1. A 2 kg ball moves at 5 m/s. What's its momentum?
- 2.5 kg·m/s
- 7 kg·m/s
- 10 kg·m/s
- 25 kg·m/s
Answer: 10 kg·m/s
p = mv = 2 × 5 = 10 kg·m/s.
2. A 1 kg ball travelling at 3 m/s hits and sticks to a stationary 2 kg ball. What's their combined velocity after?
Answer: 1 m/s
Conservation of momentum: (1)(3) + (2)(0) = (1+2)v → v = 1 m/s. Perfectly inelastic — KE is lost to heat/sound.
3. Why do airbags reduce injury in a car crash?
Answer: They increase the time over which the impulse acts, reducing the peak force
Impulse J = FΔt is fixed (set by your momentum change). Longer Δt → smaller F. Same idea as bending knees when landing.
Last reviewed: May 2026