## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 132: 48

#### Answer

The angular speed of the larger pulley is 4.36 rad/s The angular speed of the smaller pulley is 8.18 rad/s

#### Work Step by Step

We can find the angular speed of the larger pulley: $\omega = \frac{\theta}{t}$ $\omega = \frac{(2\pi~rad)(25)}{36~s}$ $\omega = 4.36~rad/s$ We can find the linear speed of the larger pulley: $v = \omega ~r$ $v = (4.36~rad/s)(15~cm)$ $v = 65.4~cm/s$ Since the same belt goes around both pulleys, we know that both pulleys have the same linear speed. We can find the angular speed of the smaller pulley: $\omega = \frac{v}{r}$ $\omega = \frac{65.4~cm/s}{8~cm}$ $\omega = 8.18~rad/s$

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