1. The problem statement, all variables and given/known data The cylindrical space station, d = 280m in diameter, rotates in order to provide artificial gravity of g for the occupants. How much time does the station take to complete one rotation? 2. Relevant equations velocity= (2*pi*r)/period acceleration = v^2/r 3. The attempt at a solution It's a multiple choice problem, so the possible answers are 34s, 38s, 24s, and 4s. I'm thinking that to provide it's own gravity, the acceleration should be about equal to the earth's acceleration due to gravity (9.8 m/s^2). Thus, I've found the acceleration that'll occur for each time. a(38s)=[(2pi140m)/38s]^2/140m a(38s) = 3.83 m/s^2 a(34s)=[(2pi140m)/34s]^2/140m a(34s) = 4.78 m/s^2 a(24s)=[(2pi140m)/34s]^2/140m a(24s) = 9.60 m/s^2 a(4s)=[(2pi140m)/34s]^2/140m a(4s) = 345 m/s^2 Now, when the period is four seconds, the acceleration is far greater than the earth's acceleration due to gravity, so it must generate it's own gravitational field, right? So would the answer be four seconds? Also, if I'm given this problem in the future on a free response, how do I do it without plugging in the given periods to the formula?