Add cycles per second to units

[BrandonConder]

Cycles per second is a really powerful unit to include. In theory the definition of "Hertz" as a unit is the same as cycles per second, but in practice it is sometimes not.

In my field (electronics) cycles per second can simplify most of my calculations:

• 1 cycle = 2π radians

For example, calculating impedance of an inductor, cycles per second avoids an arbitrary factor of 2π in my equations.

With Hertz:

using Unitful: nH, Ω, MHz
L = 200nH  # Inductance
f = 10MHz  # Frequency
ω = 2π*f  # Angular frequency
Z = uconvert(Ω, im*ω*L)

ω is 62.8e6/s which is required for calculations but illegible to humans

With cycles per second:

using Unitful: nH, Ω, Mcps
L = 200nH  # Inductance
ω = 10Mcps  # Angular frequency
Z = uconvert(Ω, im*ω*L)

ω is 10e6 cyc/s, which is legible to humans and converts to the correct value in Ohms

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So why not make the unit of Hertz equal to cycles per second?

In electromagnetics (and probably other domains) there's a problem: it's standard to use wavelength (units: meters) instead of angular wavelength (units: meters/cycle).
As an example, CB radio operates around the 11 meter band, which corresponds to a frequency around 25 MHz. The conversion from wavelength to frequency requires frequency to be in units of "per second":

julia> using Unitful: m, c0, MHz, Mcps

julia> λ = 11m;  # CB radio wavelength

julia> @show ω = uconvert(Mcps, c0/λ);  # Not conventional
ω = uconvert(Mcps, c0 / λ) = 4.33758650839722 Mcps

julia> @show f = uconvert(MHz, c0/λ);  # Conventional units
f = uconvert(MHz, c0 / λ) = 27.253859818181816 MHz

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Similarly you may want to consider creating the "Revolution" unit for the RPM and RPS units:

@unit rev     "rev"     Revolution       2π*rad                  false

[codecov-io]

Codecov Report

Merging #420 (a91cb3f) into master (9126cc5) will not change coverage.
The diff coverage is n/a.

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Impacted Files	Coverage Δ
src/pkgdefaults.jl	30.00% <ø> (ø)

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[sostock]

Note that there is already the unit Hz2π which is equal to cps.

[giordano]

And "cycle" is already in UnitfulAngles.jl as "turn"