Speed of Rotation to Experience X Acceleration

[Hisui]

Homework Statement

How fast (in rpm) must a centrifuge rotate if a particle 9.00cm from the axis of rotation is to experience an acceleration of 115,000 g's?

Homework Equations

Either v=2(pi)r/T or v=(square root)(ar) ...not knowing which of these to use is possibly my first problem...

The Attempt at a Solution

First, I converted the g's to m/s^2 and got 11,734.7m/s^2 and the radius to 0.09m... I tried solving for v with both equations above and (obviously) got two completely different answers... my notes make it look like my professor was using both, but surely for different things...?

Also, I can't seem to be able to convert this into rpm... I got the circumference to be 0.57m, so I tried to use that as one rotation, then tried using v=2(pi)r/T where T is 60s (I figured this would make it rpm)... but that gave me 0.0095m/s... which left me again with trying to figure out how to convert it into rpm... but I still don't think that's right, because the actual answer is supposed to be 3.38 x 10^4 rpm...

 

[learningphysics]

"v=(square root)(ar)" (you can't use the other equation because you don't know T... T is not 60)

solve for v here... remember to convert r to m.

then find the angular velocity. v = rw where w is angular velocity.

then convert to rpm.