Question on circular motion involving astronauts and g force?

[Tangeton]

The question is: If an astronaut who can physically withstand acceleration up to 9 times that of free fall (9g) is being rotated in an arm of length 5.0m what is the maximum number of revolutions per second permissible.

I approached this by considering 9g to be the centripetal acceleration (because as there is no other acceleration in circular motion).

I've worked out the time for one revolution many times, but I don't know how to do this the other way around. What equations should I use?

I know I haven't fallowed the strict guide to homework questions but I don't know the equations I could use other than that for centripetal acceleration, a = v^2/r, but that doesn't tell me anything about the maximum number of revolutions per second.

Can someone push me in the right direction for the start? I just look at the question and all equations related to circular motion and just nothing comes to my head.

 

[Doc Al]

The time of one revolution is the period (usually symbolized by T) and you want the frequency. How are period and frequency related?

 

[Tangeton]

The time of one revolution is the period (usually symbolized by T) and you want the frequency. How are period and frequency related?

Oh frequency... F = 1/T. I do remember working out the Time T but I don't know if I was right about how I done it. I used the acceleration and so a = v²/r, 9g = v²/r. I then used this to find the v, v = sqrt of 9gr = 21ms^-1 . And so now I guess I can work out the time T using v = 2∏r/T so T = 2∏r/v = (2∏ x 5.0)/21 = 10∏/21 = 1.50 s.

So F = 1/T = 1/ 1.50 = 0.67 (2sf), is this correct?

EDIT: Is 0.67Hz the final answer? Should I just say it needs to be less than 0.67 of a turn per second?

 

[Doc Al]

Looks good. Express like they asked: The maximum number of revolutions per sec is 0.67.