Rotation period of a space station

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1. Feb 3, 2015

ross moldvoer

1. The problem statement, all variables and given/known data
To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of
If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 2 g? of 5g?

2. Relevant equations
T=2*pi*r/v

3. The attempt at a solution
i tried solving for v using a=v^2/r and then plugging it in but i got the wrong answer

2. Feb 3, 2015

haruspex

Please post your working, or we can't tell if or where you went wrong.
(Are you sure it asks for a centripetal acceleration of that magnitude, not a net g-force corresponding to it?)

3. Feb 3, 2015

ross moldvoer

i did 9.8=v^2/6.75, v^2=(9.8)(6.75)=66.15 v=8.13
then i plugged v into the equation i gave above

4. Feb 4, 2015

haruspex

It says 2g and 5g, not 1g.

5. Feb 4, 2015

dean barry

You need to introduce T into the root equation.
You have a = v ² / r
But v = ( 2 * π * r ) / T

6. Feb 4, 2015

ross moldvoer

then what equation should i use to solve for v since i dont know T?

7. Feb 4, 2015

haruspex

I think dean barry is suggesting you eliminate v between the two equations so that you can go straight to finding T without having to calculate v. That's good advice generally, since it serves to reduce accumulation of rounding errors, but I don't think it matters here.
Do you have a response to my post #4?

8. Feb 4, 2015

ross moldvoer

i did accidently forget to do 2g instead of just 9.8.

9. Feb 4, 2015

haruspex

So does that resolve your issue, or do you still have the wrong answer?

10. Feb 4, 2015

ross moldvoer

that fixed it. thanks a ton

11. Feb 4, 2015

ross moldvoer

so after solving for omega i plug it into T=2*pi*r/v? i get 407 when i do this and this seeems a little high

12. Feb 4, 2015

haruspex

13. Feb 5, 2015

dean barry

Take: a = v ² / r
You know:
v = ( 2 * π * r ) / T
( which introduces T into the game )
You get: a = ( ( 2 * π * r ) / T ) ² ) / r
Transpose for T