The Centrifuge: Circular Motion Turned Up to Thousands of g

Circular motion always needs an inward push

An object moving in a circle at constant speed is still accelerating - its velocity's direction is constantly changing even though its magnitude is not, and any change in velocity is by definition an acceleration. That acceleration always points toward the center of the circle, which is why it is called centripetal ("center-seeking") acceleration, and by Newton's second law it requires a real, physical force pointing the same way: the tube wall in a centrifuge, the string in a swung ball, gravity for an orbiting satellite. Remove that inward force and the object does not fly outward along the radius - it flies off along a straight tangent line, exactly as Newton's first law demands.

The formula, and where its steep RPM sensitivity comes from

a  =  ω² r  =  v² / r          (centripetal acceleration)
F  =  m ω² r                    (centripetal force, Newton's 2nd law)

ω = angular velocity (rad/s) = 2π · RPM / 60
r = radius from the rotation axis

RPM appears SQUARED in the acceleration
r appears LINEARLY

That squared dependence on RPM is the whole reason centrifuges are effective: doubling the rotational speed while keeping the radius fixed does not double the acceleration, it quadruples it, and tripling the speed multiplies it by nine. A modest increase on the speed dial produces a dramatic jump in the force felt by the sample - which is also why a centrifuge's speed control has to be handled carefully near its rated maximum, since a small speed increase near the limit corresponds to an outsized jump in stress on the rotor and tubes.

G-force: acceleration measured against gravity

RCF (relative centrifugal force, in "×g")  =  ω²r / g  =  1.118 × 10⁻⁵ × RPM² × r(cm)

example: a microcentrifuge rotor, r = 8 cm, at 13,000 RPM
RCF ≈ 1.118e-5 × 13000² × 8  ≈  15,100 × g

Laboratory centrifuges report their spin rate not just in RPM but in "×g" - the relative centrifugal force, the centripetal acceleration expressed as a multiple of standard Earth gravity (9.81 m/s²). This is the number that actually matters biologically and chemically: it is what determines how fast a given particle size sediments out of a suspension, following Stokes' law, regardless of which specific rotor or RPM combination produced that acceleration. A protocol that calls for "10,000 × g for 10 minutes" can be satisfied by many different RPM settings, one for each rotor radius, precisely because RCF is the physically meaningful, radius-independent quantity.

Why a small rotor beats a big wheel

Because acceleration scales with r only linearly but with RPM quadratically, the fastest route to extreme g-forces is to spin a small radius very fast, not a large radius modestly. A playground merry-go-round with a 3-meter radius spun at a brisk, still-safe 20 RPM produces only about 1.3 × g at the rim - barely noticeable. A laboratory ultracentrifuge with a rotor radius of just a few centimeters, spinning at 60,000+ RPM, reaches accelerations well over 100,000 × g, enough to separate viruses and even individual macromolecules by density. The engineering trade-off is exactly the inverse of the physics benefit: smaller, faster rotors demand far stronger materials to survive the enormous centripetal force the rotor itself must withstand without flying apart.

The "centrifugal force" everyone feels but nothing exerts

Anyone who has been pressed against the outer wall of a spinning ride swears an outward force is pushing them there. In the actual, non-rotating (inertial) frame of reference, no outward force exists at all: the wall is pushing inward on the rider, providing the centripetal force that keeps them moving in a circle instead of flying off in a straight line, and what the rider interprets as being "pushed outward" is really their own inertia resisting that inward turn. The outward-feeling centrifugal force only becomes a well-defined, calculable quantity if you choose to do your analysis from inside the rotating frame itself, where it appears as a fictitious force needed to make Newton's laws balance for an observer who is themselves accelerating. Both descriptions predict the same physical outcome; only one of them corresponds to a real, physical, Newton's-third-law-obeying force.

Frequently asked questions

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Everything above runs in your browser - open Centrifuge: Centripetal Force & G-Force and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.