Understanding Angular Velocity

* Angular velocity is the rate at which an object rotates or revolves around a central point. It's measured in radians per second (rad/s) or degrees per second (°/s).

Calculating the Angular Velocity of the Hour Hand

1. Full Circle: The hour hand completes a full circle (360 degrees) in 12 hours.

2. Degrees Per Hour: Therefore, the hour hand moves 360 degrees / 12 hours = 30 degrees per hour.

3. Radians Per Hour: To convert degrees to radians, use the conversion factor: 180 degrees = π radians. So, the hour hand moves (30 degrees/hour) * (π radians / 180 degrees) = π/6 radians per hour.

4. Radians Per Second: To get radians per second, divide the radians per hour by the number of seconds in an hour: (π/6 radians/hour) / (3600 seconds/hour) = π/21600 radians/second

Therefore, the angular velocity of the hour hand of a clock is approximately π/21600 radians per second.