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