# Would this be a correct explanation on denser molecules end up further away from axis of rotation in a centrifuge?

Here's my following explanation for why denser molecules end up further away from axis of rotation in a centrifuge (i got this from my other account on physics stack exchange - yug)

A centrifuge separates dense molecules from less dense molecules in the following manner.

The centrifuge provides a certain amount of centripetal force, y. centripetal force is given by m * centripetal acceleration. The only way to increase the centripetal force is to increase mass (the magnitude of centripetal acceleration is a constant value provided by the power level of the centrifuge).

Therefore, the heavier the mass = the greater centripetal force needed. Now we also know that centripetal force is the force that pulls something inward in a centrifuge.

However the "y" centripetal force is not enough to provide for the centripetal force required by heavier mass. Therefore, there is not enough inward pull for the heavier mass and so, the heavier mass stays the furthest away in the test tube from the axis of rotation. This is how centrifuges work in separating substances of different densities.

Is this explanation correct? because other sites said the phenomenon occured due to heavier molecules having a greater tangential velocity. I have a feeling I went wrong when I assumed centripetal force to be constant...

• Also, if you have more than one account on PSE, then you should merge your accounts. Cheers. Aug 18, 2021 at 4:54
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– ACB
Aug 22, 2021 at 10:24

Note that centrifugal force (centrifugal force is equal in magnitude to centripetal force but acts away from the center of a circular path) can be expressed in terms of both angular and tangential velocity. That is $$\tag 1 {\bf F}=\frac{m{\bf v}^2}{r}$$

So the magnitude of the centrifugal force depends both on the square of the tangential velocity $$\bf v$$, but also note that since $${\bf v}={\bf \omega} r$$ where $$\bf \omega$$ is the angular velocity, we could just as well write equation (1) as $$\tag 2 {\bf F}=m{\bf\omega}^2 r$$

So in equations (1) and (2), we have two equivalent ways to write the centrifugal force, one in terms of the square of the angular velocity and one in terms of the square of the tangential velocity. Either way, how the components separate will be determined mainly by their masses (densities).

These components are free to move in an outward radial direction because they have mass. It's not that the centrifugal force is greater as such (since for a fixed value of $$r$$ the centripetal and centrifugal forces are equal but in opposite directions), but because this is a natural response to a changing velocity (the inward acceleration) - ie., centrifugal force is an inertial force.

I have a feeling I went wrong when I assumed centripetal force to be constant...

Assuming the distance $$r$$ is fixed, and we have a constant $$\bf \omega$$ (which means a constant value for $$\bf v$$) then the force will be constant.