If the length ratio of the hour hand, minute hand and second hand of the clock is 1:1.5:2, the ratio of the angular velocity at the end of the hour hand, minute hand and second hand to the linear velocity is

If the length ratio of the hour hand, minute hand and second hand of the clock is 1:1.5:2, the ratio of the angular velocity at the end of the hour hand, minute hand and second hand to the linear velocity is

(1) Ratio of angular velocity
Because:
The angular velocity is equal to the angle (2pi) corresponding to one revolution of the pointer on the dial divided by the time of one revolution
So:
Clockwise angular velocity = 360 / (12 * 60 * 60) = 1 / 120
Minute hand angular velocity = 360 / (60 * 60) = 1 / 10
Second hand angular speed = 360 / 60 = 60
The ratio of angular velocity of w [hour hand], w [minute hand] and w [second hand] = (1 / 120): (1 / 10): 60 = 10:120:7200 = 1:12:720
(2) Ratio of linear velocity
Because:
Length times angular velocity equals linear velocity
And because:
The length ratio of hour hand, minute hand and second hand is 1:1.5:2
So:
The linear speed ratio of w [hour hand], w [minute hand] and w [second hand] is 1:12 × 1.5:720 × 2 = 1:18:1440
A: the ratio of angular velocity at the end of the hour, minute and second hand is 1:12:720, and the ratio of linear velocity is 1:18:1440