Answer to Question #289697 in Physics for Lily

Question

1. When a wheel is rotated through an angle of 35°, a point on the circumference travels through an arc length of 2.5 m. When the wheel is rotated through angles of 35 rad and 35 rev, the same point travels through arc lengths of 143 m and 9.0 × 102 m, respectively. What is the radius of the wheel?(See Sample Problem 7A.)

Answer 1

The arc length depends on the radius of a circle and arc angle by an equation

$$l=\alpha R$$

Hence

$$R=\frac{l}{\alpha}=\frac{143\:\rm m}{35\:\rm rad }=4.1\:\rm m$$