6.1.2 Angular Velocity

Consider an object moving from A to B along the circular arc in 1 second.

You can describe its speed as 3.0 cm s^-1. This called the linear velocity v. Or you can describe it as 45° per second, or π/4 rad s^-1. This is called the angular velocity ω (the Greek symbol omega, not the english alphabet double-u). Got it? v is distance per unit time whereas ω is angular displacement per unit time.

Starting from $s=r\theta$ , we can obtain the formula the relationship between v and ω.

$\displaystyle \begin{aligned}\frac{{ds}}{{dt}}&=\frac{{d(r\theta )}}{{dt}}\\\frac{{ds}}{{dt}}&=r\frac{{d\theta }}{{dt}}\\v&=r\omega \end{aligned}$

If the circular motion is repetitive then it has a period T. Remember that one revolution corresponds to an angular displacement of 2π rad. So we have another useful identity

$\displaystyle \omega =\frac{{2\pi }}{T}=2\pi f$