## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

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 as; $P = \frac{2\pi~r}{v}$ $P = \frac{2\pi~r}{\sqrt{g~r}}$ $P = 2\pi~\sqrt{\frac{~r}{g}}$ $P = 2\pi~\sqrt{\frac{500~m}{9.80~m/s^2}}$ $P = 44.9~s$ To provide normal gravity, the rotation period should be 44.9 seconds.