Impulse & Momentum

Impulse J is the integral of force over time: J = ∫F·dt. Equal to the change in momentum: J = Δp.

For constant force: J = F·Δt. For variable force: J = average F × Δt = area under F-t curve.

Units: N·s = kg·m/s (same as momentum).

Impulse-momentum theorem: Δp = J. Useful when force varies (collisions, hammer blows).

Long contact time, small force ⇒ same impulse as short contact time, large force.

Engineering use: airbags, crumple zones, gloves, padding extend Δt to reduce peak F for the same Δp.

Impulse is a VECTOR — both magnitude and direction matter.

Impulsive force: very large F acting for very short Δt (impacts, gunshots). Gravity is negligible during such events.