Question

what is the ratio of angular velocities of hour hand of a clock and the spin motion of the earth ?

Answer 1

we know that the angular velocity = 2π/T

The hour hand of a clock takes 12 hrs to complete one revolution

=> Time period = 12 hours = 12 x 3600 sec

=> angular velocity = 2π/T

= 2π/12x3600

The earth completes one revolution in 24 hours

=> Time period = 24 hrs = 24x3600 sec

Hence angular velocity = 2π/T

= 2π/24x3600

Hence ratio of their angular velocity;

= (2π/12x3600)/2π/24x3600

= 2/1

= 2:1

Hence ratio of their angular velocity is 2:1