The Earth's radius is 6378.1 kilometers. A mad scientist has come up with the simultaneously awesome and terrifying plan to increase the speed of the Earth's rotation until people at the Earth's equator experience a centripetal (radial) acceleration with a magnitude equal to g (9.81 m/s2 ), eectively making them experience weightlessness. If the mad scientist succeeds in their dastardly plan, what would be the new period of the Earth's rotation?