Motion in a Circle

Angular measure

An angle in radians is the arc length divided by the radius: $\theta = s/r$. One complete circle is $2\pi$ radians. Angular speed $\omega$ is the rate of change of angle:

$$\omega = \dfrac{\Delta\theta}{\Delta t} = \dfrac{2\pi}{T} = 2\pi f$$

The linear (tangential) speed is related by $v = r\omega$.