Calculating Velocity for Burn Patients on a Rotating Space Station

[IamatWork]

consider a rotating doughnut shaped space station used to treat burn patients. the patients are located on the outer perimeter of the station at a distance of 200 meters from the axis of rotation. calculate the period of rotation that would produce a radial acceleration equal to 1/10 the acceleration due to gravity (.98 meters/second2).

this appears to me as a centripetal acceleration problem...a=v2/r, because the acceleration is directed toward the center, but how do i get my velocity? am i going in the right direction? thanks

 

[arildno]

You are on the right track.
Now, you have gotten that $$\frac{v^{2}}{R}=\frac{g}{10}$$
This has only 1 unknown, v.

Secondly, how is v related to the period?

 

[IamatWork]

well, velocity is m/s. if i solve this equation i get v2=.0049/s2, which is no good!

 

[arildno]

What are you talking about?
You get $$v=\sqrt{\frac{gR}{10}}$$

 

[IamatWork]

which gives you a velocity of 14 m/s. however, that does not help you find the period using centripetal accelaration

 

[arildno]

Sure it does: What is the relation between the velocity you found and the period?

 

[IamatWork]

velocity is 14m/s and one period is 2pi...therefore the period is equal to 87.9 seconds

 

[IamatWork]

never mind that doesn't work

 

[IamatWork]

i got it..one period equals 2 pi and the lenth of arc s/r equals the circumference of the station...thanks for your help