To determine the angular velocity of an hour hand, we need to know the time it takes for the hand to complete one revolution (360 degrees or 2π radians) and divide it by that time.
The standard clock has 12 hours, so it takes 12 hours (or 720 minutes) for the hour hand to complete a full revolution. Since there are 60 minutes in an hour, the hour hand takes 12 * 60 = 720 minutes to complete one revolution.
To convert minutes to hours, we divide by 60:
720 minutes ÷ 60 = 12 hours
To convert hours to seconds, we multiply by 60 * 60:
12 hours * 60 minutes * 60 seconds = 43,200 seconds
Finally, we divide the angle of a full revolution (2π radians) by the time in seconds:
Angular velocity = 2π radians / 43,200 seconds
Simplifying the expression:
Angular velocity ≈ 0.000145 radians/second
Therefore, the angular velocity of an hour hand is approximately 0.000145 radians per second.