Angular frequency

Symbol $\omega$, units radians per second. The AP Physics C: Mechanics equation sheet lists $\omega$ in its table of symbols as angular frequency or angular speed, and prints $T = \frac{2\pi}{\omega} = \frac{1}{f}$. Rearranged, that is $\omega = 2\pi f$.

Radians, not cycles. This is where the marks go. A 2.0 Hz oscillator has $f = 2.0$ cycles per second and $\omega = 4\pi \approx 12.6$ rad/s. Same motion, different number. Anything sitting inside a sine or cosine as $\omega t$ wants radians.

Where it appears. C: Mechanics writes SHM as $x = x_{\text{max}}\cos(\omega t + \phi)$ (EK 7.3.A.3), with $\phi$ the phase angle fixing where the object is at $t = 0$. From that come $a = -\omega^2 x$, $v_{\text{max}} = A\omega$ and $a_{\text{max}} = A\omega^2$ (EK 7.3.A.3.i and ii). AP Physics 2 prints the same $\omega$ in its wave equation $x(t) = A\cos(\omega t) = A\cos(2\pi f t)$.

One symbol, two quantities. In rotation, $\omega$ is angular speed, $d\theta/dt$ for a body actually turning. In oscillation it is a phase rate for something that is not going anywhere. The units match and the algebra rhymes, but a block on a spring has no angular displacement.

$\omega = 2\pi f$ is not itself printed on any of the four sheets; it falls out of the printed period relation.