Rotational frequency

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=dN/dt (as per International System of Quantities). 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.

Related quantities

Tangential speed ${\displaystyle v}$ (Latin letter v), rotational frequency ${\displaystyle \nu }$, and radial distance ${\displaystyle r}$, are related by the following equation: $${\displaystyle \begin{array}{cc}v& =2\pi r\nu \\ v& =r\omega .\end{array}}$$

An algebraic rearrangement of this equation allows us to solve for rotational frequency: $${\displaystyle \begin{array}{cc}\nu & =v/2\pi r\\ \omega & =v/r.\end{array}}$$

Thus, the tangential speed will be directly proportional to ${\displaystyle r}$ when all parts of a system simultaneously have the same ${\displaystyle \omega }$, as for a wheel, disk, or rigid wand. The direct proportionality of ${\displaystyle v}$ to ${\displaystyle r}$ is not valid for the planets, because the planets have different rotational frequencies.