How Fast Should a Space Station Rotate to Mimic Earth's Gravity?

[Becca93]

Homework Statement
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
ω = 0.398 rad/s

This isn't correct.

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

 

[cepheid]

Homework Statement
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
ω = 0.398 rad/s

This isn't correct.

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

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).

 

[Becca93]

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).

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.

 

[cepheid]

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.

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!).

 

[Becca93]

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!).

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.