If the diameter of the space station is 730 m, how many revolutions per minute are needed for the "artificial gravity" acceleration to be 9.80m/s2?

For circular motion we know that

F=ma=v^2/r

Therefore:

v = sqrt (rma)

Also, for cicular motion:

rev/min. = 60v / (2r*pi)

So your equation is:

rev./min = 60sqrt (rma) / (2pi*r)

For the mass (m) we can just use 1 kg.

rev./min = 60sqrt (730*1*9.8) / (2pi*730) = 60sqrt (7154) / (4584.4)

rev./min = 60sqrt (7154) / (4584.4) = 1.11 rev/min

the answer is 1.11 rev/min