\(\omega_{mh} = \text{Angular speed of minute hand}\)

\(\omega_{hh} = \text{Angular speed of hour hand}\)

\[ \omega_{mh} = \frac{2\pi}{60m} = \frac{2\pi}{60 \times 60} \mathrm{rad}\,\mathrm{s}^{-1} \] \[ \omega_{hh} = \frac{2\pi}{12h} = \frac{2\pi}{12 \times 60 \times 60} \mathrm{rad}\,\mathrm{s}^{-1} \]

\(\frac{\omega_{mh}}{\omega_{hh}} = \frac{\frac{2\pi}{60 \times 60}}{\frac{2\pi}{12 \times 60 \times 60}} = \frac{1}{1} \times \frac{12}{1}\)

\(\omega_{mh} : \omega_{hh} \Rightarrow 12 : 1\)