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

Asked by Mr_Saturn512 (305 ) July 25th, 2013

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.

Observing members: 0 Composing members: 0

## 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.

CWOTUS (19552 )

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.

Mr_Saturn512 (305 )

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.

CWOTUS (19552 )

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

PhiNotPi (11627 )

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

Mr_Saturn512 (305 )

## Answer this question

or

#### Join

to answer.

This question is in the General Section. Responses must be helpful and on-topic.

Your answer will be saved while you login or join.
Have a question? Ask Fluther!
What do you know more about?
or
Knowledge Networking @ Fluther