FirstPrinciplesa Physoly project
ROT-09rotationtrap · Dimensional inconsistency

Radius and diameter are not interchangeable

  1. 01

    The tempting model

    Using diameter where a rolling or torque relation requires radius.

  2. 02

    Why it feels right

    Both describe the size of a wheel, and diagrams often label the full width.

  3. 03

    Where it breaks · how to catch it

    Your v = ωR calculation uses the wheel's diameter.

  4. 04

    The correct model

    Rotational constraints use distance from the axis to the contact point: radius R, not diameter 2R.

  5. 05

    Repair · see it, then test it

    worked example A wheel of diameter 0.60 m rolls at ω = 10 rad/s. Speed?

    Tempting move

    v = ωd = 6.0 m/s.

    Correct move

    R = 0.30 m, so v = ωR = 3.0 m/s.

    Test the repair ROT-09 · transfer
    include m/s

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R34Rolling constraint v = ωRadds: Rolling without slipping links translation and rotation.R39Rolling down an inclineadds: Rolling inertia reduces translational acceleration.