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Since the radian is a dimensionless unit in the SI, the radian per second is dimensionally equivalent to the hertz—both can be expressed as reciprocal seconds, s −1. So, context is necessary to specify which kind of quantity is being expressed, angular frequency or ordinary frequency.
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).
cycle per second: cps ≡ 1 Hz = 1 cps = 1 Hz degree per second: deg/s ≡ 1 °/s ≡ 1/360 Hz = 0.002 7 Hz hertz (SI unit) Hz ≡ One cycle per second = 1 Hz = 1/s radian per second: rad/s ≡ 1/(2π) Hz ≈ 0.159 155 Hz: revolution per minute: rpm ≡ One rpm equals one rotation completed around a fixed axis in one minute of time. ≈ 0.104 ...
The hertz is defined as one per second for periodic events. The International Committee for Weights and Measures defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" [3] [4] and then adds: "It follows that the hyperfine splitting in the ground state of the ...
The SI unit of frequency is the hertz (Hz), [4] named after the German physicist Heinrich Hertz by the International Electrotechnical Commission in 1930. It was adopted by the CGPM (Conférence générale des poids et mesures) in 1960, officially replacing the previous name, cycle per second (cps).
The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m 2), the SI derived unit of area; and the kilogram per cubic metre (kg/m 3 or kg⋅m −3), the SI derived unit of density.
The Heaviside step function, often denoted by u(t): = {, <, the impulse function, often denoted by δ(t), and also the sinusoidal input function: = or =, where A is the amplitude of the forcing function, f is the frequency in Hertz, and ω = 2π f is the frequency in radians 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 ...