FirstPrinciplesa Physoly project
ROT-04rotationtrap · Constraint missed

Rolling without slipping links v and ω

  1. 01

    The tempting model

    Treating translation and rotation as independent while rolling.

  2. 02

    Why it feels right

    Linear and angular motion are taught as separate chapters.

  3. 03

    Where it breaks · how to catch it

    You have v and ω as free variables for a rolling body.

  4. 04

    The correct model

    Rolling without slipping is a constraint: v = ωR (and a = αR). The contact point is instantaneously at rest.

  5. 05

    Repair · see it, then test it

    worked example A wheel of radius R rolls without slipping at speed v. Its ω is?

    Tempting move

    Independent of v.

    Correct move

    ω = v/R, fixed by the no-slip constraint.

    Test the repair ROT-04 · 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.