Answer
The angle the wheel will turn is $0.6$ radians, or $34^\circ$.
Work Step by Step
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: $$\theta=0.6\times\frac{180^\circ}{\pi}\approx34^\circ$$
