Which is greater the angular velocity of hour hand of a watch or angular velocity of earth around its own axis ? Calculate their ratio ?

Explanation

The hour hand completes one rotation in 12 hours. Its angular speed is
`:. omega_(1) = (theta)/(t) = ( 2 pi rad)/(12 h)`
`= (2 pi rad)/( 12 xx 60 xx 60s)`
`= (pi)/( 21600) rad s^(-1)`
The earth completes one rotation about its axis in 24 hours. Its angular speed is
` :. omega_(2) = (theta)/(t) = ( 2 pi rad)/( 24 h)`
`= ( 2 pi rad)/( 24 xx 60 xx 60)`
`= (2pi)/( 86400)`
` = (pi)/(43200) rad s^(-1)`
Clearly , `omega_(1) gt omega_(2) and omega _(1) : omega_(2) = 2 : 1 `