Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 73

Answer

The angular speed is 551 rpm.

Work Step by Step

We can find the speed of the string after 1.0 meter of string has been unwound: $v^2 = v_0^2+2ax = 0 +2ax$ $v =\sqrt{2ax} = \sqrt{(2)(1.5~m/s^2)(1.0~m)}$ $v = 1.73~m/s$ We can find the angular speed; $\omega = \frac{v}{r} = \frac{1.73~m/s}{0.030~m}$ $\omega = 57.7~rad/s$ We can express the angular speed in units of rpm: $\omega = (57.7~rad/s)(\frac{60~s}{1~min})(\frac{1~rev}{2\pi~rad})$ $\omega = 551~rpm$ The angular speed is 551 rpm.
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