diff --git a/docs/user/angular_frequency.rst b/docs/user/angular_frequency.rst index 4fbb7bdce..58e126a9c 100644 --- a/docs/user/angular_frequency.rst +++ b/docs/user/angular_frequency.rst @@ -1,12 +1,43 @@ .. _angular_frequency: -Angular Frequency +Angles and Angular Frequency ================= +Angles +------ + +pint treats angle quantities as `dimensionless`, following the conventions of SI. The base unit for angle is the `radian`. +The SI BIPM Brochure (Bureau International des Poids et Mesures) states: + +.. note:: + + Plane and solid angles, when expressed in radians and steradians respectively, are in effect + also treated within the SI as quantities with the unit one (see section 5.4.8). The symbols rad + and sr are written explicitly where appropriate, in order to emphasize that, for radians or + steradians, the quantity being considered is, or involves the plane angle or solid angle + respectively. For steradians it emphasizes the distinction between units of flux and intensity + in radiometry and photometry for example. However, it is a long-established practice in + mathematics and across all areas of science to make use of rad = 1 and sr = 1. + + +This leads to behavior some users may find unintuitive. For example, since angles have no dimensionality, it is not possible to check whether a quantity has an angle dimension. + +.. code-block:: python + + >>> import pint + >>> ureg = pint.UnitRegistry() + >>> angle = ureg('1 rad') + >>> angle.dimensionality + + + +Angular Frequency +----------------- + `Hertz` is a unit for frequency, that is often also used for angular frequency. For example, a shaft spinning at `60 revolutions per minute` will often be said to spin at `1 Hz`, rather than `1 revolution per second`. -By default, pint treats angle quantities as `dimensionless`, so allows conversions between frequencies and angular frequencies. The base unit for angle is the `radian`. This leads to some unintuitive behaviour, as pint will convert angular frequencies into frequencies by converting angles into `radians`, rather than `revolutions`. This leads to converted values `2 * pi` larger than expected: +Since pint treats angle quantities as `dimensionless`, it allows conversions between frequencies and angular frequencies. This leads to some unintuitive behaviour, as pint will convert angular frequencies into frequencies by converting angles into `radians`, rather than `revolutions`. This leads to converted values `2 * pi` larger than expected: .. code-block:: python @@ -16,7 +47,7 @@ By default, pint treats angle quantities as `dimensionless`, so allows conversio >>> angular_frequency.to('Hz') -pint follows the conventions of SI. The SI BIPM Brochure (Bureau International des Poids et Mesures) states: +The SI BIPM Brochure (Bureau International des Poids et Mesures) states: .. note::