Everything you learned about motion along a line has a twin that turns, and the twins share one shape. Meet the cast. $\theta$ — theta — is the angle a body has turned through, measured in radians: one radian is the angle whose arc is exactly one radius long, and a full turn is $2\pi \approx 6.283$ rad. $\omega$ — omega — is angular velocity, how fast it turns, in $\mathrm{rad/s}$. $\alpha$ — alpha — is angular acceleration, how fast that turning rate itself changes, in $\mathrm{rad/s^2}$.

Two relations carry the whole lesson. Read aloud: omega equals theta over t — $\omega = \dfrac{\theta}{t}$, the angle swept shared out over the time $t$ in seconds it took. And alpha equals delta-omega over t — $\alpha = \dfrac{\Delta\omega}{t}$, where $\Delta$ is the Greek capital delta and simply means change in: the final $\omega$ minus the starting $\omega_0$ (say it omega-nought), divided by the seconds between them. Whichever letter the question leaves blank is the one you solve for.

The third relation is the bridge between the two worlds: $v = \omega r$, v equals omega r. $v$ is the linear speed of a point on the body, in $\mathrm{m/s}$, and $r$ is that point's radius from the axis, in metres. The radius is the exchange rate: it converts an angle into a length. This is also why radians are worth the trouble — $v = \omega r$ is only that clean when $\omega$ is in radians per second. Degrees would drag a conversion factor into every line you write.