Impulse & Momentum
J = FΔt = Δp — before/after view with momentum change computed.
Key Notes
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.
Formulas
Impulse (constant F)
Force × time, vector.
Impulse (variable F)
Area under F-t graph.
Impulse-momentum theorem
Change in momentum equals impulse.
Average force
Useful when only Δp and Δt are known.
Important Points
Same impulse can be delivered by big force × short time, or small force × long time — design choice.
Catching a ball: gentle deceleration (long Δt) ⇒ smaller peak force on your hand.
Cricket: a batsman 'follows through' to extend Δt for maximum momentum transfer.
Airbags: extend collision time from milliseconds to ~0.1 s, dropping peak force ~10-50×.
F-t graph area = impulse. Useful when F isn't constant (collisions).
Impulse-momentum theorem is just Newton's 2nd law integrated: ∫F dt = ∫dp ⇒ J = Δp.
Impulse & Momentum notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.