The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Arc length, sector perimeter and rolling distance
Choose the requested arc and use compatible length units.
Distinguish curved length, sector perimeter and full-circle boundary.
Translate rolling or rotational descriptions into total swept angles.
Use \(s=r\theta\) with \(\theta\) in radians. A proper sector, \(0<\theta<2\pi\), has \(P=r\theta+2r\). A full disk has no exposed radial edges. For rolling without slipping, distance equals radius times total swept angle.