Rotational Frequency (ν) ○◂ Entries

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Rotational Frequency (ν) ○◂｜Definition｜1st｜20251119205401-00-⌔

Rotational frequency - Wikipedia

Rotational frequency

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Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s${}^{-1}$); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).¹²³

Rotational frequency can be obtained dividing angular frequency, ω, by a full turn (2 π radians): ν =ω/(2π rad). It can also be formulated as the instantaneous rate of change of the number of rotations, N, with respect to time, t: n =d N/d t (as per International System of Quantities).⁴ Similar to ordinary period, the reciprocal of rotational frequency is the rotation period or period of rotation, T = ν${}^{-1}$ = n${}^{-1}$, with dimension of time (SI unit seconds).

Rotational velocity is the vector quantity whose magnitude equals the scalar rotational speed. In the special cases of spin (around an axis internal to the body) and revolution (external axis), the rotation speed may be called spin speed and revolution speed, respectively.

Rotational acceleration is the rate of change of rotational velocity; it has dimension of squared reciprocal time and SI units of squared reciprocal seconds (s${}^{-2}$); thus, it is a normalized version of angular acceleration and it is analogous to chirpyness.

Printed 2026-06-28.

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Footnotes

1. Atkins, Tony; Escudier, Marcel (2013). A Dictionary of Mechanical Engineering. Oxford University Press. ISBN 9780199587438. ↩

2. “The rotational frequency n of a rotating body is defined to be the number of revolutions it makes in a time interval divided by that time interval [4: ISO 80000-3]. The SI unit of this quantity is thus the reciprocal second (s${}^{-1}$). However, as pointed out in Ref. [4: ISO 80000-3], the designations “revolutions per second” (r/s) and “revolutions per minute” (r/min) are widely used as units for rotational frequency in specifications on rotating machinery.”${}^{[2]}$ ↩

3. “The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is radian per second, and the SI unit of activity is becquerel, implying counts per second. Although it is formally correct to write all three of these units as the reciprocal second, the use of the different names emphasizes the different nature of the quantities concerned. It is especially important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor [see ISO 80000-3 for details] of 2π. Ignoring this fact may cause an error of 2π. Note that in some countries, frequency values are conventionally expressed using “cycle/s” or “cps” instead of the SI unit Hz, although “cycle” and “cps” are not units in the SI. Note also that it is common, although not recommended, to use the term frequency for quantities expressed in rad/s. Because of this, it is recommended that quantities called “frequency”, “angular frequency”, and “angular velocity” always be given explicit units of Hz or rad/s and not s${}^{-1}$.”${}^{[3]}$ ↩

4. “ISO 80000-3:2019 Quantities and units — Part 3: Space and time” (2 ed.). International Organization for Standardization. 2019. Retrieved 2019-10-23. [2] (11 pages) ↩

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