# Centripetal Acceleration and period of rotation

1. Sep 26, 2007

### Heat

1. The problem statement, all variables and given/known data

In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 7.7m.

What must the period of rotation be so that the centripetal acceleration has a magnitude of 3.7g ?

What must the period of rotation be so that the centripetal acceleration has a magnitude of 10g?

2. Relevant equations
F=ma
w=ma
4pi^2r/T

3. The attempt at a solution

Ok I started by converting 3.7g, by doing this 9.8*3.7 = 36.26

4pi^2(7.7)/ 36.26

but it is wrong, how would I solve this?

2. Sep 26, 2007

### hage567

This isn't right, check the units. It's supposed to be acceleration, right? Did you derive it yourself?

3. Sep 26, 2007

### Heat

I've been told it has something to do with the equation, although I don't think I am using properly.

what would you do in the following situation?

4. Sep 26, 2007

### hage567

Well, start with the equation for centripetal acceleration, a = v^2/r. You need to relate it to the period. You can do that by the velocity term. What's a way to express the velocity of an object moving in a circle?

5. Sep 26, 2007

### Heat

velocity would be distance/time.

v=2pir/t ?

6. Sep 26, 2007

### hage567

That's right. Now put that together with the a=v^2/r and you should come up with the equation you need.

7. Sep 26, 2007

### Heat

a = 4pi^2r / t^2

?

8. Sep 26, 2007

### hage567

Yes. So solve that for t and use it to find the period.

9. Sep 26, 2007

### Heat

ok got it. thank you