Momentum and collisions.
Momentum is mass in motion. It's conserved in every closed system — which is what makes collision problems solvable from a single equation, no matter how messy the geometry.
Linear momentum
A vector quantity: mass times velocity.
p = m · vUnits: kg · m/s. The direction of p matches the direction of v. A 1500 kg car moving at 20 m/s has p = 30,000 kg·m/s, eastward. Slow it down to 10 m/s and p drops to 15,000 — the impulse (change in momentum) is 15,000 kg·m/s.
Impulse
A force applied over a time changes momentum. The change is the impulse.
J = F · Δt = ΔpWhy airbags save lives: a crash that would change momentum by 30,000 kg·m/s in 0.1 s needs 300,000 N of force. Spread it over 0.5 s and the force drops to 60,000 N — survivable. The momentum change is the same; only the time and the force change.
Conservation of momentum
In a closed system — no external forces — total momentum is constant. This is one of the deepest facts in physics, and it works whether the objects stick together, bounce apart, explode, or do anything in between.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂The u's are initial velocities; the v's are final. One equation, two unknowns, and you can solve the whole collision.
Worked example
A 2 kg cart moving at 3 m/s collides with a stationary 1 kg cart and they stick together. What's their final velocity?
(2)(3) + (1)(0) = (2 + 1) vf 6 = 3 vf vf = 2 m/sTotal mass tripled; velocity dropped by a third. Momentum in = momentum out: 6 = 6. ✓
Flashcard · Unit 4
Linear momentum — mass times velocity.
Check your understanding
A 0.5 kg ball moving at 8 m/s hits a wall and bounces back at 6 m/s. What is the magnitude of the impulse on the ball?