Question

what is the ratio of angular speed of minute hand and second hands in a watch

Answer 1

second hand goes through 2π radians in 1 minutes , or 2π radian /60 seconds , so angular speed (w) = π/30 radian

Answer 2

The ratio of angular speed of minute hand and second hands in a watch is 12:1

Solution:

The minute hand of a watch covers 360 degrees in 60 minutes or it can be said as 6 degree/minute.

Because $(\frac{360}{60} = \frac{6}{1} )$

The hour hand of a watch covers 30 degrees in 60 minutes or 0.5 degree/minute.

Because $(\frac{30}{60} = \frac{1}{5} = 0.5 )$

The ratio of the angular speed of the minute to the hour hand is $\frac{6}{0.5} = 12:1$