# Homework Help: How do i get my velocity?

1. Mar 17, 2005

### 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

2. Mar 17, 2005

### 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?

3. Mar 17, 2005

### IamatWork

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

4. Mar 17, 2005

### arildno

You get $$v=\sqrt{\frac{gR}{10}}$$

5. Mar 17, 2005

### IamatWork

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

6. Mar 17, 2005

### arildno

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

7. Mar 17, 2005

### IamatWork

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

8. Mar 17, 2005

### IamatWork

never mind that doesn't work

9. Mar 17, 2005

### 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