# Rotational frequency

## Number of rotations per unit time / From Wikipedia, the free encyclopedia

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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).^{[1]}^{[lower-alpha 1]}^{[lower-alpha 2]}

**Quick Facts**Other names, Common symbols ...

Rotational frequency | |
---|---|

Other names | rotational speed, rate of rotation |

Common symbols | $\nu$, n |

SI unit | Hz |

Other units | rpm, cps |

In SI base units | s^{-1} |

Derivations from other quantities | ν=ω/(2π rad), n=dN/dt |

Dimension | ${\mathsf {T}}^{-1}$ |

Rotational frequency can be obtained dividing *angular frequency*, ω, by a full turn (2π 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

*, respectively.*

**revolution speed****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*.