## University Physics with Modern Physics (14th Edition)

Published by Pearson

# Chapter 9 - Rotation of Rigid Bodies - Problems - Exercises - Page 295: 9.18

#### Answer

(a) The disk should turn at a rate of 1.91 rpm. (b) $\alpha = 0.980~rad/s^2$ (c) $\theta = 2.60~rad$ $\theta = 149^{\circ}$

#### Work Step by Step

(a) The radius $r$ of the disk is $1.25 ~m$ One revolution of the disk is a distance of $2\pi ~r$. $0.250~m/s$ is $15.0~m$ per minute. $rpm = \frac{15.0~m}{(2\pi)(1.25~m)}$ $rpm = 1.91$ The disk should turn at a rate of 1.91 rpm. (b) $\alpha = \frac{a}{r} = \frac{\frac{1}{8}~(9.80~m/s^2)}{1.25~m}$ $\alpha = 0.980~rad/s^2$ (c) $\theta = \frac{d}{r} = \frac{3.25~m}{1.25~m}$ $\theta = 2.60~rad$ We can convert this angle to degrees. $\theta = (2.60~rad)(\frac{180^{\circ}}{\pi ~rad})$ $\theta = 149^{\circ}$

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