FirstPrinciplesa Physoly project
ROT-02rotationtrap · Rotation / torque-arm error

Torque uses the perpendicular lever arm

  1. 01

    The tempting model

    Writing τ = F·r regardless of the force's direction.

  2. 02

    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.

  3. 03

    Where it breaks · how to catch it

    You used the full distance without projecting onto the perpendicular.

  4. 04

    The correct model

    τ = r·F·sin φ = F × (perpendicular lever arm). A force along the line to the pivot produces no torque.

  5. 05

    Repair · see it, then test it

    worked example Force F at the end of a wrench of length L, at 30° to the handle. Torque?

    Tempting move

    τ = F·L.

    Correct move

    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.

    Then practise it on the ladder

    R32Torque arm projectionadds: Torque uses the perpendicular lever arm.