Choose the system before applying conservation
The mistake
Applying conservation without defining what's inside the system.
Why it feels right
The objects named in the prompt can look like the system even when a different boundary makes the conservation law usable.
How to catch it
Your 'conserved' quantity depends on forces that are external to your chosen system.
The first principle
Define the system first. A force internal to one choice is external to another — that decides whether momentum is conserved.
worked mini-example
A gun fires a bullet. Is momentum conserved?
Common wrong move
No — the bullet speeds up.
Correct
For the gun+bullet system, yes: total momentum stays zero (recoil).
Test the repair MOM-04 · transfer
Make a fresh prediction before referring to the worked example.