Engineers and science fiction writers have proposed designing space stations in the shape of a rotating wheel or ring, which would allow astronauts to experience a sort of artificial gravity when walking along the inner wall of the station's outer rim.

1. Imagine one such station with a diameter of 110 m, where the apparent gravity is 2.70 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute?

2. How fast would the space station have to rotate, in revolutions per minute, for the artificial gravity that is produced to equal that at the surface of the Earth, 9.80 m/s2?