Rotational frequency

Rotational frequency
Angular speed ω (in radians per second), is greater than rotational frequency ν (in Hz), by a factor of 2π.
Other names	rotational speed, rate of rotation
Common symbols	${\displaystyle \nu }$, 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	${\displaystyle {\mathsf {T}}^{-1}}$

Part of a series on
Classical mechanics
${\displaystyle {\textbf {F}}=m{\textbf {a}}}$ Second law of motion
History Timeline Textbooks
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical mechanics
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Koopman–von Neumann mechanics
Core topics Damping Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational frequency Angular acceleration / displacement / frequency / velocity
Scientists Kepler Galileo Huygens Newton Horrocks Halley Maupertuis Daniel Bernoulli Johann Bernoulli Euler d'Alembert Clairaut Lagrange Laplace Poisson Hamilton Jacobi Cauchy Routh Liouville Appell Gibbs Koopman von Neumann
Physics portal  Category
v t e

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][a][b]

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).^[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.

Cite error: There are <ref group=lower-alpha> tags or {{efn}} templates on this page, but the references will not show without a {{reflist|group=lower-alpha}} template or {{notelist}} template (see the help page).