Energy and momentum are not interchangeable
The mistake
Conserving kinetic energy in an inelastic collision (or momentum via energy).
Why it feels right
Both are 'conserved quantities', so they seem to travel together.
How to catch it
You set ½mv² conserved in a collision where objects stick or deform.
The first principle
Momentum is conserved in all collisions (no external impulse); kinetic energy is conserved only in elastic ones. Use the right invariant.
worked mini-example
Two clay balls collide and stick. Which is conserved?
Common wrong move
Kinetic energy.
Correct
Momentum — KE is lost to deformation/heat.
Test the repair MOM-02 · transfer
Make a fresh prediction before referring to the worked example.