Rolling without slipping links v and ω
The mistake
Treating translation and rotation as independent while rolling.
Why it feels right
Linear and angular motion are taught as separate chapters.
How to catch it
You have v and ω as free variables for a rolling body.
The first principle
Rolling without slipping is a constraint: v = ωR (and a = αR). The contact point is instantaneously at rest.
worked mini-example
A wheel of radius R rolls without slipping at speed v. Its ω is?
Common wrong move
Independent of v.
Correct
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.