The relative angular speed of hour hand and minute hand of clock is

Question

TestHub · Accepted Answer

The angular speed of the minute hand is the angle covered in one revolution divided by the time taken (1 hour = 3600 s):

$ω_{m} = \frac{2 π}{3600} = \frac{π}{1800}$ rad/s

The angular speed of the hour hand is the angle covered in one revolution divided by the time taken (12 hours = $12 \times 3600$ s = 43200 s):

$ω_{h} = \frac{2 π}{43200} = \frac{π}{21600}$ rad/s

The relative angular speed of the minute hand with respect to the hour hand is the difference between their angular speeds:

$ω_{re l} = ω_{m} - ω_{h}$

$ω_{re l} = \frac{π}{1800} - \frac{π}{21600}$

$ω_{re l} = \frac{12 π - π}{21600} = \frac{11 π}{21600}$ rad/s

Answer: $\frac{11 π}{21600}$

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