page_title: Centrifuge
section_title: Mathematical description
hierarchical_section_title: Centrifuge / Mathematical description
caption_attribution_description: 19th century centrifuge, held at the Deutsches Apotheken-Museum, Heidelberg
context_page_description: A centrifuge is a piece of equipment that puts an object in rotation around a fixed axis, applying a force perpendicular to the axis of spin that can be very strong. The centrifuge works using the sedimentation principle, where the centrifugal acceleration causes denser substances and particles to move outward in the radial direction. At the same time, objects that are less dense are displaced and move to the center. In a laboratory centrifuge that uses sample tubes, the radial acceleration causes denser particles to settle to the bottom of the tube, while low-density substances rise to the top.
  There are three types of centrifuge designed for different applications. Industrial scale centrifuges are commonly used in manufacturing and waste processing to sediment suspended solids, or to separate immiscible liquids. An example is the cream separator found in dairies. Very high speed centrifuges and ultracentrifuges able to provide very high accelerations can separate fine particles down to the nano-scale, and molecules of different masses.
  Large centrifuges are used to simulate high gravity or acceleration environments.
context_section_description: Protocols for centrifugation typically specify the amount of acceleration to be applied to the sample, rather than specifying a rotational speed such as revolutions per minute.  This distinction is important because two rotors with different diameters running at the same rotational speed will subject samples to different accelerations. During circular motion the acceleration is the product of the radius and the square of the angular velocity , and the acceleration relative to "g" is traditionally named "relative centrifugal force" (RCF). The acceleration is measured in multiples of "g" (or × "g"), the standard acceleration due to gravity at the Earth's surface, a dimensionless quantity given by the expression:
  where
   is earth's gravitational acceleration,
   is the rotational radius,
   is the angular velocity in radians per unit time
  This relationship may be written as
  or
  where
   is the rotational radius measured in millimeters (mm), and
   is rotational speed measured in revolutions per minute (RPM).
  To avoid having to perform a mathematical calculation every time, one can find nomograms for converting RCF to rpm for a rotor of a given radius. A ruler or other straight edge lined up with the radius on one scale, and the desired RCF on another scale, will point at the correct rpm on the third scale.  Based on automatic rotor recognition, modern centrifuges have a button for automatic conversion from RCF to rpm and vice versa.
caption: A 19th-century hand cranked laboratory centrifuge.
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