# How can I find "r" in this equation?

You don’t really need to know much about what this is for, just how the math works, because the square root is annoying me. And crap. . how do I express square root on my keyboard? Oh well, let me explain it best I can.

RPM = square root (RCF/1.119×10^-5 x r)

RPM and RCF are speeds, and r is the radius of the center of the sample to the center of the centrifuge, in centimeters I believe.

I know for a fact that in this centrifuge, 25,000 RCF is equal to 14,500 RPM. So knowing that, I want to find out the radius so that I can figure out how much 20,000 RCF is in RPMs. But when I try to solve for r, I just get a useless, tiny number that is wrong, becuase I end up dividing a small number by a big number. And I tried it also knowing in another centrifuge that 2989.406 = square root (750/1.119×10^-5×7.5). So I tested how I did it by solving for r in there knowing what r was, but I still got a wrong number. So I’m definitely doing something wrong and it probably has to do with how to deal with the square root.

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## 5 Answers

I think that you’re writing your formula incorrectly. Take a look at this link.

As it is written there, the basic equation seems to be:

g = (1.118 × 10^-5) R S^2

Where g is the relative centrifugal force (RCF), S is the speed of the centrifuge in RPM, and R is the radius from the center of the rotor to the sample. Restating your equation with the known values:

25000 = (1.118×10^-5) x R x 14,500 ^ 2

In order to isolate for R you need to divide both sides by 14,500 ^ 2, then divide by (1.118×10^-5).

Dividing the big number (25000) by a very big number (14500 ^ 2) will give a small number, and dividing that by the very small (1.118×10^-5) should give you the reasonably sized number that you expect.

Mmmmm, still doesn’t seem to work. I tried it and got 1542.16270. When I tested it out with 750 and 2989.406 (or you could just round to 2990) I don’t get 7.5 or anywhere near 7.5. So something is still off. I got that original equation off the company’s official worksheet thing. And to be definite, it IS in cm, the radius. I double checked.

I have a little crappy Casio scientific calculator. I might want to do it again on one of my co-worker’s more elaborate, comfortable calculator when she gets here.

It still seems to me like your basic arithmetic is off.

25,000 ÷ (14,500^2) = 0.00011891

1.118×10^-5 = 0.00001118

Dividing the first number by the second gives me 10.63605.

Check your math.

There is an error in the parentheses in the original question.

The formula is given as

RPM = sqrt (RCF/1.119×10^-5 x r)

but it should be

RPM = sqrt (RCF/(1.119×10^-5 x r))

sqrt (750/1.119×10^-5×7.5) = 0.2242, which is wrong

sqrt (750/(1.119×10^-5×7.5)) = 2989.406, which is matches the expected result

Anyways,

25,000 RCF is equal to 14,500 RPM, which gives:

20,000 RCF is equal to 12,969.1943 RPM

r = RCF / (1.118 × 10^-5) / RPM^2

Soooo this whole thing was avoided anyway when my co-worker showed me a chart they have hidden in the lab for all the centrifuges in the building. So all I needed to do was look at it to find the appropriate RPM for the centrifuge.

wa wa waaaaaaa

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