The case of the disappearing angle units, or "the dangle of the angle"

[ijabbott]

(08-01-2019 01:41 AM)Geoff Wrote:  A radian is not an independent unit as you are using it above. It is a dimensionless name.

In the ASTM SI-10 document a radian in base units is m/m (from Table 4), which self cancels out.

Quoting from clause 3.4.4.1 of SI-10 (2016) :

The coherent SI unit of plane angle is the number one; thus, the coherent SI units of the quantities angle, angular velocity, and angular acceleration are, respectively, 1, 1/s, and 1/s^2 . However, it is often convenient to use the special name radian (rad) instead of the number 1 when expressing the values of these quantities.

Note: ASTM SI-10 is titled the American National Standard for Metric Practice.

They could have really put the cat amongst the pigeons and defined the unit of plane angle as the number \(\mathrm{e}^\mathrm{i}\).

(Yes, I know that doesn't really work as a unit as multiplication of the unit wouldn't work as expected.)