Cycles per second in the context of "Rotational frequency"

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⭐ Core Definition: Cycles per second

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.

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Cycles per second in the context of Turn (unit)

The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r). Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm). The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Divisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.

In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and a full turn. It is represented by the symbol N. (See below for the formula.)

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Cycles per second in the context of Nyquist frequency

In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second (Hz). Conversely, the Nyquist rate for sampling a 22050 Hz signal is 44100 samples/second.

When the highest frequency (bandwidth) of a signal is less than the Nyquist frequency of the sampler, the resulting discrete-time sequence is said to be free of the distortion known as aliasing, and the corresponding sample rate is said to be above the Nyquist rate for that particular signal.

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Cycles per second in the context of Rotational speed

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).

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