04 / CHAPTER 02
Torque and rotational dynamics
Choose a pivot and calculate how forces change rotation.
ANCHOR EQUATION
Torque
In symbols: τ = r×F
Torque measures the tendency of a force to change rotation about a pivot.
Torque is the turning component of force
A force changes rotation only through its perpendicular lever arm. Pushing directly toward a hinge can require large force and produce zero torque; pushing at right angles is mechanically effective.
Take the moment of a force
For position r from pivot to application point, torque is τ = r × F, with magnitude τ = rF sinφ. The factor r sinφ is the perpendicular distance from pivot to the force line. Rotational Newton’s law for a rigid body is Στ = Iα.
A 40 N force applied 0.25 m from a shaft at 60° gives τ = 0.25(40)sin60° = 8.66 N·m. If the force is radial, φ = 0 and the torque vanishes.
Torque depends on pivot
The same force can have different moments about different points. Choose the pivot that makes unknown forces or reaction torques disappear, but state the point explicitly.
Work it: A 2 m wrench is pulled by 100 N at 30° to the handle. Find torque about the bolt. What angle maximizes torque for the same force and length?