Equilibrium needs Στ = 0, not just ΣF = 0

01
The tempting model
Balancing forces but forgetting the torque condition.
02
Why it feels right
If the forces add to zero, it looks like the object is done.
03
Where it breaks · how to catch it
A rigid body with ΣF = 0 that could still spin.
04
The correct model
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.
05
Repair · see it, then test it
worked example A beam on a pivot held by a rope — is force balance enough?
Tempting move
Yes, set ΣF = 0.
Correct move
No — also set Στ = 0 about the pivot to fix the rope tension.
Test the repair ROT-01 · transfer

Two equal and opposite forces act at different points on a free rigid body. What can their net effect be?
Zero force and zero torque only Zero force but nonzero torque Nonzero force but zero torque only No motion under any condition

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R31Beam torque equilibriumadds: Static rigid bodies need both force and torque balance.