University Calculus: Early Transcendentals (3rd Edition)

The angle the wheel will turn is $0.6$ radians, or $34^\circ$.
To find the angle, we need to employ the formula: $$s = r\theta$$ which means $$\theta=\frac{s}{r}$$ $s$: the length of the arc $r$: radius of the circle $\theta$: the central angle of the arc (in radians) Here we have the diameter of the wheel $d=1$ m. Also, rolling the wheel forward 30cm means the arc length $s=30cm=0.3m$ - The radius of the wheel is: $r=\frac{d}{2}=0.5$ m. So the angle the wheel turns would be (in radians): $$\theta=\frac{0.3}{0.5}=0.6$$ - In degrees: $$\theta=0.6\times\frac{180^\circ}{\pi}\approx34^\circ$$