Equilibrium needs Στ = 0, not just ΣF = 0
The mistake
Balancing forces but forgetting the torque condition.
Why it feels right
If the forces add to zero, it looks like the object is done.
How to catch it
A rigid body with ΣF = 0 that could still spin.
The first principle
A rigid body in equilibrium needs both ΣF = 0 and Στ = 0 about any axis. Two equal forces can have zero net force yet a non-zero couple.
worked mini-example
A beam on a pivot held by a rope — is force balance enough?
Common wrong move
Yes, set ΣF = 0.
Correct
No — also set Στ = 0 about the pivot to fix the rope tension.
Test the repair ROT-01 · transfer
Make a fresh prediction before referring to the worked example.