Angular speed of minute hand,
$\omega_{ m }=360^{\circ} \text { per hour } $
$=\left(360 \times \frac{\pi}{180}\right) \text { per hour }=\frac{2 \pi}{3600} rad / s $
$\left[\because 1^{\circ} =\frac{\pi}{180} rad \text { and } 1 \text { hour }=3600 s \right]$
Angular speed of second hand,
$\omega_{s}=360^{\circ}$ per minute $=\frac{2 \pi}{60} rad / s$
$\therefore $ Difference between angular speeds of minute hand and second hand of a clock
$=\omega_{ m }-\omega_{ s }=\frac{2 \pi}{3600}-\frac{2 \pi}{60}=-\frac{59 \pi}{1800}$
So, difference between $\omega_{m}$ and $\omega_{s}$ is $\frac{59 \pi}{1800} rad / s$