The hour hand and minute hand of a mechanical watch can be regarded as rotating at a constant speed. How long does it take for the hour hand and minute hand to coincide from the first time to the second time?

The hour hand and minute hand of a mechanical watch can be regarded as rotating at a constant speed. How long does it take for the hour hand and minute hand to coincide from the first time to the second time?

According to ω = 2 π T, we know that the ratio of the angular velocity of the hour hand and the minute hand is 1:12. When the hour hand and the minute hand overlap from the first time to the second time, t + 2 π = ω min T., then t = 2 π ω min − ω H = 2 π 1112 ω min = 2 π 11122 π t min