Reciprocal second in the context of Rate of rotation

The cycle per second is a once-common English name for the unit of frequency now known as the hertz (Hz). Cycles per second may be denoted by c.p.s., c/s, or, ambiguously, just "cycles" (Cyc., Cy., C, or c). The term comes from repetitive phenomena such as sound waves having a frequency measurable as a number of oscillations, or cycles, per second.

With the organization of the International System of Units in 1960, the cycle per second was officially replaced by the hertz, or reciprocal second, "s" or "1/s". Symbolically, "cycle per second" units are "cycle/second", while hertz is "Hz" or "s". For higher frequencies, kilocycles (kc), as an abbreviation of kilocycles per second were often used on components or devices. Other higher units like megacycle (Mc) and less commonly kilomegacycle (kMc) were used before 1960and in some later documents. These have modern equivalents such as kilohertz (kHz), megahertz (MHz), and gigahertz (GHz). Following the introduction of the SI standard, use of these terms began to fall off in favor of the new unit, with hertz becoming the dominant convention in both academic and colloquial speech by the 1970s.

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); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).

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=n, with dimension of time (SI unit seconds).

In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the ordinary frequency, defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the angular frequency, defined as the phase angle divided by time (in radians per second).

In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.