Understanding the Speed Ratio Between the Second and Hour Hands of a Clock

Introduction

Understanding the speed ratio between the second and hour hands of a clock is an interesting and practical knowledge, especially for students and teachers explaining the workings of analog clocks. This article will delve into the calculation of this ratio, providing clear explanations and mathematical steps to help readers comprehend the relationship between the speeds of these clock hands.

The Speed of the Hour Hand

The hour hand of a clock is one of the slowest moving components. It completes a full revolution around the clock face in 12 hours, which is a total of 720 minutes or 43,200 seconds. To find the speed of the hour hand in degrees per second, we can follow these steps:

The hour hand completes a full revolution of 360 degrees in 43,200 seconds. Therefore, the speed of the hour hand is calculated as follows:

Speed of the hour hand 360 degrees / 43,200 seconds 0.00833 degrees per second

The Speed of the Second Hand

The second hand is much quicker. It completes a full revolution in 60 seconds, which is 360 degrees. To find the speed of the second hand in degrees per second:

The second hand completes a full revolution of 360 degrees in 60 seconds. Therefore, the speed of the second hand is:

Speed of the second hand 360 degrees / 60 seconds 6 degrees per second

Comparing the Speeds

To determine how many times faster the second hand is compared to the hour hand, we can use the following calculation:

Ratio Speed of the second hand / Speed of the hour hand

Ratio 6 degrees per second / 0.00833 degrees per second ≈ 720

Therefore, the second hand is approximately 720 times faster than the hour hand.

Additional Insights

For further understanding, it is important to note the following points:

The Hour Hand and the 12-Hour Period

The hour hand completes 1 full revolution in 12 hours, and during the same period, the minute hand completes 60 revolutions (1 revolution per hour).

Frequency of the second hand 3600 revolutions in 12 hours.

Therefore, the second hand is 3600 times faster than the hour hand.

Mathematical Calculation

When the hour hand moves 30 degrees (which is 1 hour), the second hand moves:

720 * 30 degrees 21600 degrees.

This means the second hand moves 21600 degrees in the time it takes the hour hand to move 30 degrees. To find the number of times faster, we divide:

720 * 30 degrees / 30 degrees 720 times faster.

In conclusion, the second hand of a clock is approximately 720 times faster than the hour hand of a clock, making it an essential concept in understanding the mechanics of analog clocks.