University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.3 - Trigonometric Functions - Exercises - Page 27: 4


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: $$\theta=0.6\times\frac{180^\circ}{\pi}\approx34^\circ$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.