Calculate Angular Speed of Hour Hand of a Clock
Calculating the angular speed of the hour hand of a clock is crucial for understanding the mechanics of timekeeping devices. It helps in designing and maintaining clocks, as well as in educational settings to teach physics and mathematics concepts.
- Enter the number of hours and minutes on the clock.
- Enter the radius of the clock face in centimeters.
- Click the ‘Calculate’ button.
The angular speed (ω) of the hour hand can be calculated using the formula:
ω = (360° / (12 × 60)) × (hours + minutes / 60)
The calculator uses this formula to determine the angular speed in degrees per minute.
| Hours | Minutes | Radius (cm) | Angular Speed (°/min) |
|---|---|---|---|
| 3 | 30 | 20 | 0.5 |
| 6 | 15 | 25 | 0.375 |
| 9 | 45 | 30 | 0.75 |
| Time (HH:MM) | Angular Speed (°/min) |
|---|---|
| 00:00 | 0 |
| 01:00 | 0.5 |
| 02:00 | 1 |
| 03:00 | 1.5 |
- To find the angular speed in degrees per second, multiply the result by 60.
- For a 12-hour clock, the hour hand moves 30° per hour and 0.5° per minute.
- Adjust the radius input to account for different clock sizes.
What is the angular speed of the hour hand at 12:00?
The angular speed of the hour hand at 12:00 is 0°/min, as it is stationary.
How does the radius of the clock face affect the angular speed?
The radius of the clock face does not affect the angular speed of the hour hand. It only affects the linear speed of the hour hand’s tip.
For more information, see the following authoritative sources: