The center of mass ignores internal forces
The mistake
Trying to change a system's center-of-mass motion using only internal pushes.
Why it feels right
Internal forces can make parts move dramatically, so they seem able to move the whole system.
How to catch it
A person jumping inside a boat changes the boat/person center-of-mass velocity without an external horizontal force.
The first principle
For a system, M a_cm = F_external. Internal forces rearrange parts but cannot accelerate the center of mass.
worked mini-example
Two skaters push off from rest on frictionless ice. What happens to their total center of mass?
Common wrong move
It moves toward the heavier skater.
Correct
It remains fixed because no external horizontal force acts.
Test the repair NL-17 · transfer
Make a fresh prediction before referring to the worked example.