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 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.
