Question

On an analog clock, the hour hand rotates 30 degrees as the second hand rotates 21,600 degrees. Which equation correctly relates the variables defined below?

h: angular motion of the hour hand, in degrees

s: angular motion of the second hand, in degrees

Answer 1

Explanation:

the ratio is 30/21600 = 3/2160 = 1/720

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

FYI :

as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.