Rotational frequency (also known as rotational speed or rate of rotation) of an object rotating around an axis is the

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...

of rotation of the object. Its unit is revolution per minute (rpm), cycle per second (cps), etc. The symbol for rotational frequency is

\nu

(the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

lowercase letter nu).

Tangential speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantit ...

''v'', rotational frequency

\nu

, and radial distance ''r'', are related by the following equation: :

v = 2\pi r\nu

v = r\omega

An algebraic rearrangement of this equation allows us to solve for rotational frequency: :

\nu = v/2\pi r

\omega = v/r

Thus, the tangential speed will be directly proportional to ''r'' when all parts of a system simultaneously have the same ''ω'', as for a wheel, disk, or rigid wand. The direct proportionality of ''v'' to ''r'' is not valid for the

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...

s, because the planets have different rotational frequencies. Rotational frequency can measure, for example, how fast a motor is running. ''Rotational speed'' is sometimes used to mean angular frequency rather than the quantity defined in this article. Angular frequency gives the change in

angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ...

per time unit, which is given with the unit radian per second in the SI system. Since 2π radians or 360 degrees correspond to a cycle, we can convert angular frequency to rotational frequency by :

\nu = \omega/2\pi ,

where *

\nu\,

is rotational frequency, with unit cycles per second *

\omega\,

is angular frequency, with unit radian per second or degree per second For example, a stepper motor might turn exactly one complete revolution each second. Its angular frequency is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational frequency is 60 rpm. Rotational frequency is not to be confused with

tangential speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantit ...

, despite some relation between the two concepts. Imagine a merry-go-round with a constant rate of rotation. No matter how close or far you stand from the axis of rotation, your rotational frequency will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.

References

{{DEFAULTSORT:Rotational frequency Kinematic properties Temporal rates

See also

References