Understanding Hour Hand Rotation on a Clock: A Detailed Analysis
In this article, we will delve deep into the rotation of the hour hand on a clock, specifically calculating the degrees it rotates when the time changes from 5:00 PM to 9:15 PM. This analysis will be broken down into several steps, providing a clear and easy-to-understand method for anyone interested in the mechanics of a clock.
Calculating the Time Interval
To determine how many degrees the hour hand rotates from 5:00 PM to 9:15 PM, we first need to calculate the total time interval:
From 5:00 PM to 9:00 PM is 4 hours. From 9:00 PM to 9:15 PM is an additional 15 minutes. Total time 4 hours 15 minutes 4.25 hours.Calculating Degrees Rotated per Hour
The hour hand completes a full 360 degrees in 12 hours. To find out how many degrees it rotates per hour, we use the following formula:
(360 degrees / 12 hours) 30 degrees/hour
Calculating the Total Rotation
Now, we need to calculate the total rotation of the hour hand over the 4.25 hours:
(4.25 hours) × (30 degrees/hour) 127.5 degrees
Therefore, the hour hand will rotate 127.5 degrees from 5:00 PM to 9:15 PM.
Additional Analysis
For those looking for additional clarity, we can break down the calculation even further:
In an Hour or 60 Minutes:
The hour hand moves by 30 degrees. In one minute, the hour hand moves by 30/60 0.5 degrees.From 5:00 to 9:15:
The hour hand moves 4 hours (120 degrees) at 9:00 PM. For the additional 15 minutes, the hour hand moves 15 × 0.5 7.5 degrees. Total rotation: 120 degrees 7.5 degrees 127.5 degrees.This detailed breakdown confirms the initial calculation that the hour hand rotates 127.5 degrees from 5:00 PM to 9:15 PM. The mechanics of a clock and the precise calculations involved offer a fascinating glimpse into the mathematics behind time measurement.
Conclusion
The rotation of the hour hand on a clock is an interesting aspect of timekeeping, involving simple yet precise mathematical calculations. Whether you are a student, teacher, or simply curious about the mechanisms of time, understanding these details can provide a deeper appreciation for the systems that keep us on track throughout our day.
Frequently Asked Questions (FAQs)
Q1: How many degrees does the hour hand rotate per hour?A1: The hour hand rotates 30 degrees per hour. Q2: How many degrees does the hour hand rotate in 15 minutes?
A2: The hour hand rotates 7.5 degrees in 15 minutes. Q3: How do you calculate the degrees rotated by the hour hand?
A3: First, determine the time interval. Then, use the formula (degrees/hour) × (time interval in hours). Finally, add any additional degrees for the remaining minutes.
Related Topics
Interested in learning more about clock mechanics or the math behind timekeeping? Explore related topics such as angles in geometry, military time conversions, or the history of clocks and timekeeping devices.