# Homework Help: Centrifuge Problem (Circular Motion)

1. Jan 20, 2014

### GoodOldLimbo

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

A Centrifuge rotates at 12000rpm. What is this in radians per second?

If the radius of this centrifuge is 150mm, what is the centripetal acceleration?

2. Relevant equations

v2 / r

v = rω

a = rω2

3. The attempt at a solution

First I converted the 12000rpm to 1256.64 rad/sec.

12000 / 60 = 200 Rev. per minute.

200 x 2∏ = 1256. 64 rad/sec

Onto the centripetal acceleration, I was given a = rω2

a = 0.15 x 1256.642

a= 236871.61 m/s2

I'm just a little thrown off by how incredibly large the number is and I don't really have any idea of how a centrifuge usually moves. Any help?

Would be much appreciated.

2. Jan 20, 2014

### Staff: Mentor

Welcome to the PF.

I only see one problem in your work, and it's just a simple typo that doesn't change the numbers. See where I fixed it in the quoted text above.

And yes, the acceleration does seem high, but after all that's what centrifuges are for. I used Google to look up some typical specs on labratory-grade centrifuges to see if the acceleration number you calculated is reasonable. The 12,000 rpm given number is pretty fast for the centrifuges that I looked up, but the size is in the typical range.

Convert your acceleration into the number of g's (g = 9.8m/s^2), and compare your answer to what you find on Google. Post what you find so we can see what you are getting...

3. Jan 20, 2014

### Staff: Mentor

That acceleration value is fine for a centrifuge. And it is still far away from their limits.