Arc length

A length, in meters, not an angle. It answers how far the point actually went, while $\theta$ answers how far around it went.

It is on every sheet, in a box people skip. All four booklets, AP Physics 1, AP Physics 2, C: Mechanics and C: Electricity and Magnetism, print $s = r\theta$ in the GEOMETRY AND TRIGONOMETRY table, sitting under Circle beside $A = \pi r^2$ and $C = 2\pi r$, with a diagram labelling $s$, $r$ and $\theta$. That table is separate from the mechanics equations, which is where a search for it tends to stop.

The CED gives the same relation as a change. EK 5.2.A.1: for a point at a distance $r$ from a fixed axis of rotation, the linear distance $s$ travelled by the point as the system rotates through an angle $\Delta\theta$ is $\Delta s = r\,\Delta\theta$. EK 5.2.A.2 then lists $s = r\theta$ with $v = r\omega$ and $a_T = r\alpha$.

Radians only. The relation is a definition of the radian, so degrees break it silently. Check it against a full turn: $\theta = 2\pi$ gives $s = 2\pi r$, the circumference, which is the same formula wearing a different name.

Distance, not displacement. Walk halfway around a circle of radius $r$ and the arc length is $\pi r$ while the straight-line displacement is $2r$. The two only converge for small angles.

Same angle, different arcs. Points on one rigid body share $\Delta\theta$, so the arc length scales with distance from the axis. The rim of a wheel covers more ground than a spoke's midpoint in the same turn, which is what makes $v = r\omega$ work.