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 8 - Dynamics II: Motion in a Plane - Exercises and Problems: 10

Answer

To provide normal gravity, the rotation period should be 44.9 seconds.

Work Step by Step

We can set the centripetal acceleration equal to $g$, the acceleration due to gravity on earth. $a_c = \frac{v^2}{r} = g$ $v = \sqrt{g~r}$ We can find the period $P$ of the space station. $P = \frac{2\pi~r}{v}$ $P = \frac{2\pi~r}{\sqrt{g~r}}$ $P = 2\pi~\sqrt{\frac{~r}{g}}$ $P = 2\pi~\sqrt{\frac{500~m}{9.80~m/s^2}}$ $P = 44.9~s$ To provide normal gravity, the rotation period should be 44.9 seconds.
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