To find the angular velocity of an hour hand in radians per second (rad/s), we need to know the time it takes for the hour hand to complete one full revolution or cycle.
In a 12-hour analog clock, the hour hand completes one revolution in 12 hours or 720 minutes (since 1 hour = 60 minutes). To convert this time to seconds, we multiply by 60:
720 minutes × 60 seconds/minute = 43,200 seconds
Therefore, it takes the hour hand 43,200 seconds to complete one full revolution.
The angle covered in one full revolution is 360 degrees or 2π radians. Therefore, the angular velocity (ω) can be calculated as:
ω = angle covered / time taken
ω = 2π radians / 43,200 seconds
Simplifying:
ω ≈ 0.000145 rad/s
Hence, the angular velocity of the hour hand is approximately 0.000145 rad/s.