Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 131: 42


$112880\pi$ cm per min

Work Step by Step

The formula for linear speed is $v=r\omega$ where $r$ is the radius and $\omega$ is the angular speed. The formula for angular speed $\omega$ is $\omega=\frac{\theta}{t}$. Since the point on the edge of the gyroscope rotates 680 times each minute, $\omega=\frac{\theta}{t}=\frac{2\pi\times680}{1}=1360\pi$ radians per min Substituting the values of $r$ and $\omega$ in the formula for linear speed: $v=rw=83(1360\pi)=112880\pi$ cm per min
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