As their booster rockets separate, space shuttle astronauts typically feel accelerations up to $3 g,$ where $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ . In their training, astronauts ride in a device in which they experience such an acceleration as a centripetal acceleration. Specifically, the astronaut is fastened securely at the end of a mechanical arm that then turns at constant speed in a horizontal circle. Determine the rotation rate, in revolutions per second, required to give an astronaut a centripetal acceleration of 3.00$g$ while in circular motion with radius 9.45 $\mathrm{m}$ .
