The center of mass ignores internal forces

01
The tempting model
Trying to change a system's center-of-mass motion using only internal pushes.
02
Why it feels right
Internal forces can make parts move dramatically, so they seem able to move the whole system.
03
Where it breaks · how to catch it
A person jumping inside a boat changes the boat/person center-of-mass velocity without an external horizontal force.
04
The correct model
For a system, M a_cm = F_external. Internal forces rearrange parts but cannot accelerate the center of mass.
05
Repair · see it, then test it
worked example Two skaters push off from rest on frictionless ice. What happens to their total center of mass?
Tempting move
It moves toward the heavier skater.
Correct move
It remains fixed because no external horizontal force acts.
Test the repair NL-17 · transfer

An astronaut floating far from external forces throws a tool. What happens to the astronaut-tool center of mass?
It accelerates toward the astronaut It accelerates toward the tool It continues at constant velocity It stops

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R21Explosion momentumadds: Internal energy can increase kinetic energy without changing total momentum.R25Center-of-mass velocityadds: The center-of-mass velocity is total momentum over total mass.