University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 9 - Rotation of Rigid Bodies - Problems - Exercises - Page 295: 9.11

Answer

(a) $t = 24.0~s$ (b) The blade turns 68.8 revolutions.

Work Step by Step

(a) $\omega = \alpha ~t$ $t = \frac{\omega}{\alpha}$ $t = \frac{36.0~rad/s}{1.50~rad/s^2}$ $t = 24.0~s$ (b) $\theta = \frac{1}{2}~\alpha~t^2$ $\theta = \frac{1}{2}(1.50~rad/s^2)(24.0~s)^2$ $\theta = 432~rad$ Let $n$ be the number of revolutions. $n = \frac{\theta}{2 \pi ~rad/rev} = \frac{432~rad}{2 \pi~rad/rev}$ $n = 68.8~revolutions$ The blade turns 68.8 revolutions.
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