Torque uses the perpendicular lever arm
The mistake
Writing τ = F·r regardless of the force's direction.
Why it feels right
The abbreviated form τ = Fr is valid only when the force is perpendicular to the radius, but that condition is easy to omit.
How to catch it
You used the full distance without projecting onto the perpendicular.
The first principle
τ = r·F·sin φ = F × (perpendicular lever arm). A force along the line to the pivot produces no torque.
worked mini-example
Force F at the end of a wrench of length L, at 30° to the handle. Torque?
Common wrong move
τ = F·L.
Correct
τ = F·L·sin 30° = F·L/2.
Test the repair ROT-02 · transfer
include N·m
Make a fresh prediction before referring to the worked example.