## College Physics (4th Edition)

To create an effective gravitational field of $2.0~g$, the angular speed should be $11.7~rad/s$
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 $11.7~rad/s$