Why are radians dimensionless? According to https://en.wikipedia.org/wiki/Dimensionless_quantity, "A dimensionless quantity is a quantity to which no physical dimension is applicable." The article then explains, a few sentences later, that time, as an example, is a quantity with dimension.
https://en.wikipedia.org/wiki/SI_derived_unit states that "the International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr)."
Why are radians "dimensionless" if a unit like seconds aren't? I feel like angle measures have more of a "physical dimension" aspect to them than seconds.

The circumference $C$ of a circle is related to its radius $r$ as $C=2\pi r$; hence, $C/r$ corresponds to an angle of $2\pi$ radians. But circumference and radius both have units of length, so their ratio is dimensionless. (To generalize this, consider a circular arc of radius $r$ and angle $\theta$ having arc length $s=r\theta$.) Hence a unit of angle must be dimensionless.
