Definition
Torque
(M5.3.1) M5.3 · Torque →Statement
The cross product of the position vector (from the axis to the point of application) and the force, with magnitude rF sin θ.
Symbols and units
| torque | N·m | |
| position from axis to force | m | |
| applied force | N | |
| angle between r and F | degrees |
When it applies
Any force and any choice of axis or reference point.
Derivation
Only the component of force perpendicular to r produces rotation; this is exactly what the cross product extracts:
Worked examples
Torque from a wrench
A 40 N force applied 0.25 m from a bolt, at 90° to the wrench:
Watch out for
A force directed straight through the axis (θ = 0 or 180°) produces zero torque, no matter how large it is.
Connects to