diff options
Diffstat (limited to 'docs/angular_frequency.rst')
| -rw-r--r-- | docs/angular_frequency.rst | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/docs/angular_frequency.rst b/docs/angular_frequency.rst new file mode 100644 index 0000000..5636135 --- /dev/null +++ b/docs/angular_frequency.rst @@ -0,0 +1,34 @@ +.. _angular_frequency: + + +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: + +.. code-block:: python + + >> from pint import UnitRegistry + >>> ureg = UnitRegistry() + >>> frequency = ureg('60rpm') + >>> frequency.to('Hz') + <Quantity(6.28318531, 'hertz')> + +pint follows the convetions of SI. The SI BIPM Brochure (Bureau International des Poids et Mesures) states: + +.. note:: + + The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is + radian per second, and the SI unit of activity is becquerel, implying counts per second. + Although it is formally correct to write all three of these units as the reciprocal second, the + use of the different names emphasizes the different nature of the quantities concerned. It is + especially important to carefully distinguish frequencies from angular frequencies, because + by definition their numerical values differ by a factor1 of 2π. Ignoring this fact may cause + an error of 2π. Note that in some countries, frequency values are conventionally expressed + using “cycle/s” or “cps” instead of the SI unit Hz, although “cycle” and “cps” are not units + in the SI. Note also that it is common, although not recommended, to use the term + frequency for quantities expressed in rad/s. Because of this, it is recommended that + quantities called “frequency”, “angular frequency”, and “angular velocity” always be given + explicit units of Hz or rad/s and not s−1 |