Space Station-Artificial Gravity

[ariol]

Determind the minimum diameter of a space station that would simulate an artificial G of 10 m/s^2 at a rotation rate of 1 rpm.



I was not given an equation, it was one of them 'try to figure it out yourself equations' but I think it is:
r=9.81g?(pie * rpm/30)^2

at least that is the equation I got from wiki...




My attempt at a solution:
r=9.81(10 m/s^2)/ (pie *1rpm/30)^2
r =981/.0109
r =90,000

then I doubled the ratius to get the diameter:
d=180,000

that seems pretty large. i don't know what I am doing wrong. if you could help that would be great. thanks.

 

[Cyosis]

Where does the 9.81 come from? We are not on Earth we're in space there is no gravitational acceleration.

Instead of finding some formula on wikipedia, are you familiar with the centripetal force?

 

[ariol]

Yes. I am familiar with it.

 

[Cyosis]

Then you can answer this question without having to look up a formula on wiki by using F=ma. Can you see how?

 

[ariol]

Oh okay. Wow, I didn't realize it was that simple. Thanks.