Understanding Angular Velocity
* Angular velocity (ω) is the rate at which an object rotates or revolves around a central point. It's measured in radians per second (rad/s).
* Radians are a unit of angular measurement. A full circle is 2π radians.
Calculations
1. Time for one full rotation: The hour hand of a watch completes one full rotation in 12 hours.
2. Converting time to seconds: 12 hours * 3600 seconds/hour = 43200 seconds
3. Calculating angular velocity:
* Angular velocity (ω) = (2π radians) / (43200 seconds)
* ω ≈ 0.000145 rad/s
Therefore, the angular velocity of an hour hand on a watch (regardless of its length) is approximately 0.000145 radians per second.
Note: The length of the hour hand doesn't affect its angular velocity. Angular velocity only depends on the time it takes to complete a full rotation.
