Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 387: 100


Angular speed $\omega=\frac{1}{8}\,rad/s$ Linear speed $v=\frac{1}{4}\,m/s$

Work Step by Step

Identify the given: $s=5 \text{ m}$ $t=20 \text{ s}$ $r=2\text{ m}$ Solve for $\theta$ using the formula $\theta =\frac{s}{r}$ to obtain: $$\theta=\frac{5\,m}{2\,m}=\frac{5}{2}\text{ rad} = 2.5\text{ rad}$$ Solve for the angular speed using the formula $\omega=\frac{\theta}{t}$ to obtain: $$\omega=\frac{2.5\text{ rad}}{20\text{ s}}=\frac{1}{8}\text{ rad/s}$$ Therefore, the linear speed $v=r\omega=2\,m\times\frac{1}{8}\text{ rad/s}=\frac{1}{4}\text{ m/s}$
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