Physics

The key is connecting angular motion to linear motion using the radius as your bridge. Since the rim moves in a circle, each complete rotation carries a point a distance equal to the circumference; angular velocity tells you how many radians (and thus what fraction of circles) happen per second. Multiply angular velocity by time to get total angle swept, then use $s = r\theta$ to find the arc length traveled.

The key is connecting angular motion to linear motion using the radius as your bridge. Since the rim moves in a circle, each complete rotation carries a point a distance equal to the circumference; angular velocity tells you how many radians (and thus what fraction of circles) happen per second. Multiply angular velocity by time to get total angle swept, then use $s = r\theta$ to find the arc length traveled.