In a centrifuge, a_c should be constant. If m increases, the r will increase in order to maintain a constant a_c. Constant centripetal acceleration is given by a_c = v² / r and a_c = omega² * r. But the conflict between these two equations arises when we increase r. In the first equation - if we increase r, v should increase so that a_c remains constant. But in the second equation - since omega is constant in a centrifuge, if we increase r then a_c is no longer constant. I don't understand how this is happening and would appreciate any help. I have also looked at other similar questions on this site but they do not answer to this conflict. This is not a duplicate. Also, does anyone know how to mathematically show that radius increases when mass increases?