# Rotating Space Station

1. Dec 4, 2011

### Becca93

The problem statement, all variables and given/known data
A proposed space station includes living quarters in a circular ring 62.0 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth?

The attempt at a solution

I assumed that to do this problem, Fcp had to equal the force of gravity.

Fcp = Fg

mv^2 / r = mg
v^2 / r = g
v = √(rg)
v = √(62g)
v = 24.65

v = ωr
ω = v/r
ω = 24.65 / 62

This isn't correct.

Does anyone have any advice on what to do differently? Any help would be greatly appreciated.

2. Dec 4, 2011

### cepheid

Staff Emeritus
I don't see anything wrong with your physics. The problem may lie with your math. What value of g did you use? Using g = 9.81 N/kg, I get v = 24.66 m/s (to two decimal places).

3. Dec 4, 2011

### Becca93

I tried both, but when whittled down to the required three sigfigs, the answer is still 0.398 rad/s.

I'm at a loss as to what to do differently.

4. Dec 4, 2011

### cepheid

Staff Emeritus
Oh.

62.0 m is the diameter of the space station, not its radius.

It helps if you read the problem carefully (and I apply this advice to you and me both!).

5. Dec 4, 2011

### Becca93

Do you ever have one of those moments where you just can't believe you mixed up something really simple?

Thank you very much for pointing that out. I feel a bit foolish, but I do have the right answer now.