Calculating the Diameter of a Car’s Wheel: A Comprehensive Analysis

When discussing the engineering and mechanics of a car, understanding the relationship between speed, revolutions per minute (RPM), and the diameter of the wheels is crucial. This article will delve into the calculations needed to determine the diameter of a car's wheel, using a specific example to illustrate the process. By the end, you will have a clear understanding of how to calculate the diameter using the given data and relevant concepts.

Understanding the Given Data

The problem statement provided is: "A car travels 2.5km in 12 minutes and the revolution of the wheels of the car is 7.5 revolutions per second. What is the diameter of the wheel?" This means that the car covers a distance of 2.5 kilometers in 12 minutes, and each second, the wheels make 7.5 revolutions. Here's a breakdown of the numerical values:

Distance traveled 2.5 km 2500 meters Time taken 12 minutes 720 seconds Revolutions per second (RPM) 7.5

Converting the Speed to Kilometers per Hour (KPH)

To start the analysis, we need to convert the speed from kilometers per 12 minutes to kilometers per hour (KPH). The formula to convert distance traveled in a specific time period to KPH is as follows:

Speed (KPH) (Distance (meters) / Time (seconds)) * 3600

Plugging in the values:

Speed (KPH) (2500 / 720) * 3600

Speed (KPH) 12.5 KPH

Determining the Circumference of the Wheel

Now that we have the speed in KPH, we can calculate the circumference of the wheel. The relationship between the revolutions per second, the distance traveled, and the circumference of the wheel is given by:

Circumference (C) Distance (meters) / Total revolutions

The total number of revolutions in 12 minutes is:

Total revolutions 7.5 rev/sec * 720 sec 5400 revolutions

Using this data, we can find the circumference:

C 2500 meters / 5400 revolutions ≈ 0.463 meters

Calculating the Diameter of the Wheel

The relationship between the circumference (C) of a circle and its diameter (D) is given by the formula:

C πD

Solving for D:

D C / π ≈ 0.463 / 3.1416 ≈ 0.1474 meters

Converting meters to centimeters:

D ≈ 14.74 cm

Discussion and Conclusion

The diameter of the wheel calculated is 14.74 cm. This is a small diameter for a car wheel, which is consistent with the information provided that the RPM is high in relation to the distance traveled. If the average speed of the car were at least 40 KPH, then the diameter of the wheels would be more realistic.

Further Reading and Applications

Engineers and mechanics often use similar calculations to understand the performance of vehicles. By knowing the RPM and the distance traveled, they can optimize the performance and efficiency of the vehicle. This knowledge also helps in troubleshooting and diagnosing issues related to wheel mechanics.

For a deeper understanding, consider exploring the following topics:

Engine RPM and its impact on vehicle performance Wheel diameter and its relationship with vehicle speed control systems Design and optimization of car wheels for different speeds and terrains