Momentum is conserved only when external impulse is negligible

01
The tempting model
Applying conservation of momentum with a large external force present.
02
Why it feels right
'Momentum is conserved' is stated so often it feels unconditional.
03
Where it breaks · how to catch it
You conserved momentum across an interval with significant external force × time.
04
The correct model
Δp = external impulse. Momentum of a system is conserved only when the net external impulse ≈ 0 — true for brief collisions, not over long gravity-driven intervals.
05
Repair · see it, then test it
worked example Is momentum conserved for a ball during a 2 s fall?
Tempting move
Yes — momentum is always conserved.
Correct move
No — gravity delivers external impulse mgΔt, so p changes.
Test the repair MOM-01 · transfer

During takeoff, is the momentum of a jumper alone conserved?
Yes, because momentum is always conserved Yes, because gravity is small No, because the floor and Earth provide external impulse No, because kinetic energy increases

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R27Classify the collisionadds: Momentum conservation does not imply kinetic-energy conservation.R28External impulse estimateadds: Momentum conservation is an approximation when external impulse is small.