Rotation period of a space station

AI Thread Summary
To determine the rotation period of a centrifuge with a diameter of 13.5m that produces centripetal accelerations of 2g and 5g, the equations a = v²/r and v = (2 * π * r) / T are utilized. The user initially calculated velocity incorrectly by using 1g instead of the required 2g, leading to an incorrect answer. After correcting this mistake, they were advised to eliminate velocity from the equations to directly solve for the rotation period T. The discussion emphasizes the importance of careful calculations and the need to post all steps for accurate troubleshooting. Ultimately, the focus is on deriving T accurately to meet the specified acceleration requirements.
ross moldvoer
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Homework Statement


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?

Homework Equations


T=2*pi*r/v

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
 
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ross moldvoer said:

Homework Statement


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?

Homework Equations


T=2*pi*r/v

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
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?)
 
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
 
ross moldvoer said:
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
It says 2g and 5g, not 1g.
 
You need to introduce T into the root equation.
You have a = v ² / r
But v = ( 2 * π * r ) / T
 
then what equation should i use to solve for v since i don't know T?
 
ross moldvoer said:
then what equation should i use to solve for v since i don't know T?
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?
 
i did accidently forget to do 2g instead of just 9.8.
 
ross moldvoer said:
i did accidently forget to do 2g instead of just 9.8.
So does that resolve your issue, or do you still have the wrong answer?
 
  • #10
that fixed it. thanks a ton
 
  • #11
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
ross moldvoer said:
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
Yes, that's way too high. Please post all your steps.
 
  • #13
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
 
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