Balanced Configurations of Multislot Centrifuges

In molecular biology, centrifuges are used in procedures involving isolation and purification of proteins and nucleic acids. Often these processes are performed with small, benchtop microcentrifuges which hold multiple 1.5 mL to 2.0 mL tubes and can spin with centrifugal forces as high as 13,000 to 15,000 g. In such experiments, sample tubes of identical weight must be placed in appropriate rotor slots to ensure that the centrifuge is balanced.
This Demonstration considers centrifuges containing a varying number of slots. In order for the centrifuge to be balanced, the center of gravity of the assembly of tubes must fall in the center. This can be determined by representing each slot occupied by a tube as one of the 6, 12 or 24 complex roots of unity. If these add to zero, for example,
,
then the centrifuge is balanced.
  • Contributed by: Amy Blinder
  • (Department of Molecular & Integrative Physiology, University of Michigan Medical School)
  • and
  • S. M. Blinder

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DETAILS

For the case of 5 tubes in 24 slots, a balanced configuration is a combination of the equilateral triangle {1, 9, 17} and the pair {7,19}. For 7 tubes, a balanced combination is {1, 9, 17}, {3,15} and {11,23}.
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