Radius and diameter are not interchangeable
The mistake
Using diameter where a rolling or torque relation requires radius.
Why it feels right
Both describe the size of a wheel, and diagrams often label the full width.
How to catch it
Your v = ωR calculation uses the wheel's diameter.
The first principle
Rotational constraints use distance from the axis to the contact point: radius R, not diameter 2R.
worked mini-example
A wheel of diameter 0.60 m rolls at ω = 10 rad/s. Speed?
Common wrong move
v = ωd = 6.0 m/s.
Correct
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.