Answer
To create an effective gravitational field of $2.0~g$, the angular speed should be $11.7~rad/s$
Work Step by Step
We can find the required radial acceleration:
$\sqrt{a_r^2+g^2} = 2.0~g$
$a_r^2+g^2 = 4.0~g^2$
$a_r^2 = 3.0~g^2$
$a_r = \sqrt{3.0~g^2}$
$a_r = \sqrt{3.0}~g$
To create an effective gravitational field of $2.0~g$, the radial acceleration should be equal to $\sqrt{3.0}~g$. We can find the required angular speed:
$\omega^2~r = \sqrt{3.0}~g$
$\omega = \sqrt{\frac{\sqrt{3.0}~g}{r}}$
$\omega = \sqrt{\frac{(\sqrt{3.0})~(9.80~m/s^2)}{0.125~m}}$
$\omega = 11.7~rad/s$
To create an effective gravitational field of $2.0~g$, the angular speed should be $11.7~rad/s$
