Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 8 - Rotational Kinematics - Problems - Page 213: 23


a) $\omega_0=117.2rad/s$ b) $t=141s$

Work Step by Step

We have: final speed $\omega=137rad/s$, acceleration $\alpha=0.14rad/s^2$ and angular displacement $\theta=2870rev\times\Big(\frac{2\pi rad}{1rev}\Big)=1.8\times10^4rad$ a) The turbine's initial velocity is $$\omega^2=\omega_0^2+2\alpha\theta$$ $$\omega_0^2=\omega^2-2\alpha\theta=13729$$ $$\omega_0=117.2rad/s$$ b) The amount of time elapsed is $$t=\frac{\omega-\omega_0}{\alpha}=141s$$
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