Answer
To simulate the Earth's gravitational field, the angular speed should be $7.0~rad/s$
Work Step by Step
To simulate the Earth's gravitational field, the radial acceleration should be equal to $g$. We can find the required angular speed:
$\omega^2~r = g$
$\omega = \sqrt{\frac{g}{r}}$
$\omega = \sqrt{\frac{9.80~m/s^2}{0.20~m}}$
$\omega = 7.0~rad/s$
To simulate the Earth's gravitational field, the angular speed should be $7.0~rad/s$.
