Physics (10th Edition)

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

Chapter 5 - Dynamics of Uniform Circular Motion - Problems - Page 141: 57

Answer

a) $a_c=3\times10^5m/s^2$ b) $a_c=3.06\times10^4g$

Work Step by Step

a) Turbine blades rotate at $617rev/s$, so the period of rotation is $T=1/617=1.62\times10^{-3}s$ We also have $r=0.02m$ We know that $$T=\frac{2\pi r}{v}=\frac{2\pi r}{\sqrt{a_cr}}=\frac{2\pi\sqrt r}{\sqrt{a_c}}$$ $$\sqrt{a_c}=\frac{2\pi\sqrt r}{T}$$ $$a_c=\frac{4\pi^2r}{T^2}$$ Plug $T$ and $r$: $$a_c=3\times10^5m/s^2$$ b) $a_c=\frac{3\times10^5m/s^2}{9.8m/s^2}g=3.06\times10^4g$
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