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  4. The ratio of angular speeds of minute hand and hour hand of a watch is

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Q. The ratio of angular speeds of minute hand and hour hand of a watch is

Motion in a Plane

Solution:

$\omega_{ mh }=$ Angular speed of minute hand
$\omega_{ hh }=$ Angular speed of hour hand
$\omega_{ mh }=\frac{2 \pi}{60\, m }=\frac{2 \pi}{60 \times 60} rad\, s ^{-1}$
$\omega_{ hh }=\frac{2 \pi}{12\, h }=\frac{2 \pi}{12 \times 60 \times 60} rad\, s ^{-1}$
$\frac{\omega_{ mh }}{\omega_{ hh }}=\frac{\frac{2 \pi}{60 \times 60}}{\frac{2 \pi}{12 \times 60 \times 60}}=\frac{1}{1} \times \frac{12}{1}$
$\omega_{ mh }: \omega_{ hh } \Rightarrow 12: 1$