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