Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.1 - Angles and Radian Measure - Exercise Set - Page 533: 75


The angular speed of $6\text{ revolutions per second}$ is $\frac{12\pi \ \text{radians}}{\text{second}}$.

Work Step by Step

The angular speed conversion relation between revolutions per second to radians per second is: $\frac{1\text{ revolution}}{\text{second}}=\frac{2\pi \text{ radians}}{\text{second}}$ Multiply both sides by $6$. $\begin{align} & 6\left( \frac{1\text{ revolutions}}{\text{second}} \right)=6\left( \frac{2\pi \text{ radians}}{\text{second}} \right) \\ & 6\text{ revolutions/second}=\frac{12\pi \text{ radians}}{\text{second}} \end{align}$ Therefore, the angular speed of $6\text{ revolutions per second}$ is $\frac{12\pi \ \text{radians}}{\text{second}}$.
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