Calculating Bus Wheel Rotations: Understanding Speed and Distance
In this comprehensive guide, we will explore the process of calculating wheel rotations for a bus running at a specific speed. This article is designed to help understand the fundamental concepts of speed, distance, and rotations, providing a clear and detailed explanation for both educational and practical purposes.
Introduction to Speed and Distance
A bus is traveling at a speed of 33 km/hr. Our goal is to determine the number of rotations the bus's wheel makes per minute given its speed and the diameter of the wheel. This calculation involves converting units, understanding the relationship between distance and rotations, and applying basic mathematical formulas.
Step-by-Step Calculation
To begin, we need to convert the speed from kilometers per hour to centimeters per minute.
Speed of bus 33 km/hr 33000 m/60 min 550 m/min 550×100 55000 cm/min
The diameter of the wheel is given as 70 cm. The circumference of the wheel, which is the distance the wheel covers in one rotation, can be calculated using the formula for the circumference of a circle:
Circumference of wheel (C) π × diameter (D) 22/7 × 70 220 cm
The number of rotations the wheel makes per minute can be calculated by dividing the speed of the bus by the circumference of the wheel:
No. of rotations of wheel speed of the bus / circum. of Wheel 55000 cm/min ÷ 220 250
Therefore, the wheel of the bus makes 250 rotations per minute.
Alternative Calculations
For a fresh perspective, let's consider the same problem from different angles:
Alternate 1
The speed of the bus is 33 km/hr. First, we convert this speed to centimeters per minute:
Speed of bus :- 33 km/hr 3300000 cm/hr
Since the wheel has a diameter of 70 cm, the radius is 35 cm. The distance covered in one revolution is:
Distance covered in one revolution 2 × π × r 2 × 22 × 35 / 7 220 cm
The number of rotations the wheel makes is:
No of rotations wheel make 3300000 / 220 15000/hour 15000/60 250 revolutions/min
Alternate 2
A different approach involves converting the bus speed to a more direct form:
Speed of bus 33 km/hr 33000/60 m/min 550 m/min 550×100 55000 cm/min
The circumference of the wheel is calculated as:
Circumference of tyre distance done in one rotation 22/7 × 35/100 2.2 m 220 cm
The number of rotations per minute is:
No. of rotations per min 550 / 2.2 250
Conclusion
By using these calculations, it becomes evident that a bus running at 33 km/hr with a wheel diameter of 70 cm will make 250 rotations per minute. These detailed calculations provide a clear understanding of the relationship between speed, distance, and wheel rotations, which is crucial for various practical applications. Understanding these concepts can greatly assist in planning and optimizing transportation systems.
Keywords: bus speed calculation, wheel rotation, bus speed conversion