Revolution of a wheel

Revolution of a Wheel

A wheel's revolution is a full 360-degree turn of the wheel about its central axis. Every full revolution allows the wheel to travel a distance equal to its circumference. This concept is widely used in calculating distances covered by vehicles, conveyor belts, and rotating machinery.

Understanding Circumference

To solve problems involving wheel revolutions, it is essential to know the circumference of the wheel — the distance traveled in a single complete rotation. The circumference (C) of a circle is calculated using the formula:

C = π × d
  

where:

• π (pi): Approximately 3.1416
• d: Diameter of the wheel

Concept of Revolution and Distance

When a wheel completes one full revolution, it travels a distance equal to its circumference. Therefore, for multiple revolutions, the total distance (D) is:

D = Number of revolutions × Circumference
  

Problem 1

i) The diameter of a wheel is 12.6 m. What is the distance covered in 500 revolutions?

Solution:

• Diameter (d) = 12.6 m
• Number of revolutions = 500
• Circumference = π × d = 3.1416 × 12.6 ≈ 39.584 m
• Total Distance = 500 × 39.584 ≈ 19,792 m or 19.792 km

Problem 2

ii) A car is moving at a speed of 66 km/hr. What distance will it travel in 10 minutes? If the diameter of the wheel is 56 cm, how many revolutions will it take to travel that distance?

Solution:

• Speed = 66 km/hr
• Time = 10 minutes = 10/60 = 1/6 hour
• Distance = Speed × Time = 66 × (1/6) = 11 km = 11,000 meters
• Diameter of the wheel = 56 cm = 0.56 m
• Circumference = π × d = 3.1416 × 0.56 ≈ 1.7593 m
• Revolutions = Total Distance / Circumference = 11,000 ÷ 1.7593 ≈ 6251.6
• Approximate number of revolutions = 6252

Conclusion

The concept of wheel revolution provides a simple yet powerful way to calculate distances and movement in mechanical and automotive contexts. By understanding how the circumference of a wheel relates to distance traveled, you can efficiently solve a variety of practical problems.