As the hands of a clock travel steadily around the clock face, their velocity is constantly changing. The minute hand travels round ${360^ \circ }$ or $2p$ radians in 3600 seconds.
Although its velocity is changing, we can say that its angular speed is constant, because it moves through the same angle each second:

$\begin{array}{l}
anglular\,speed = \frac{{anglular\,displacement}}{{time\,taken}}\\
\omega  = \frac{{\Delta \theta }}{{\Delta t}}
\end{array}$

where $\Delta \theta $ is the change in angle and $\Delta t$ is the change in time.
We use the symbol $\omega $ (Greek letter omega) for angular velocity, measured in radians per second (rad s−1).
For the minute hand of a clock, we have $\omega  = \frac{{2\pi }}{{3600}} \approx 0.00175\,rad\,{s^{ - 1}}$.

A particularly useful example of the equation $\omega  = \frac{{\Delta \theta }}{{\Delta t}}$ is when a single revolution is considered. The time to make one revolution is referred to as the period (T), the angle through which the object rotates in one revolution is $2\pi $ radians. So, substituting in the equation:

$\omega  = \frac{{2\pi }}{T}$

Relating speed and angular speed

Think again about the second hand of a clock. As the hand goes round, each bit of the hand has the same angular speed. However, different bits of the hand have different velocities. The tip of the hand moves fastest; points closer to the centre of the clock face move more slowly.
This shows that the speed v of an object travelling around a circle depends on two quantities: its angular speed $\omega $ and its distance from the centre of the circle r. We can write the relationship as an equation:

$\begin{array}{l}
speed = angular\,speed \times radius\\
v = \omega r
\end{array}$

Worked example 2 shows how to use this equation.