How Fast Does a Car's Wheel Rotate at 132 km/h with a Wheel Diameter of 0.35 m?

The question often arises in physics and engineering how many times a car's wheel rotates per minute when traveling at a specific speed. In this case, we are given a speed of 132 km/h and a wheel diameter of 0.35 meters. Let's break down the problem step-by-step to find the solution.

Conversion and Calculation Steps

First, we need to convert the car's speed from kilometers per hour (km/h) to meters per minute (m/min).
132 km/h 132/60 km per minute 2.2 km per minute 2200 meters per minute

Next, we need to calculate the circumference of the wheel. The circumference C of a circle is given by the formula:

C π × d, where d is the diameter of the wheel.

In this case, the diameter d is 0.35 meters, and π is approximately 3.14159. So, the circumference is:

C 3.14159 × 0.35 1.0995565 meters (approximately 1.1 meters)

Now, we can determine the number of rotations per minute by dividing the total distance traveled per minute by the circumference of the wheel:

2200 meters / 1.0995565 meters ≈ 2000.8 rotations per minute

Alternative Calculation Methods

Let's consider a few alternative methods to confirm our result:

Using Units Directly in km/h

Alternatively, we can directly use the speed in km/h to calculate the number of rotations:

132 km/h 132/60 km per minute 2.2 km per minute 2200 meters per minute
2200 meters / (π × 0.35) 2200 / 1.0995565 ≈ 2000.9 rotations per minute

Revisiting the Original Answer

Albeit with a slightly different approach, the original answer considers the radius of the wheel, which is half the diameter (0.175 meters). So, the circumference would be:

C π × 0.175 × 2 0.35 × π ≈ 1.0996 meters (consistent with previous method)

And again, we divide the total distance by the circumference:

2200 meters / 1.0996 meters ≈ 2000.8 turns per minute

This confirms that the original answer is correct.

Alternative Calculation with Slightly Different Diameter

Another perspective, as mentioned by Ashley Launn, if the diameter is considered 0.35 meters, the circumference would be approximately 1.0675 meters, and the calculation would be:

2200 meters / 1.0675 meters ≈ 2060.8899 turns per minute

This result is slightly higher and depends on the precise measurement of the wheel diameter.

Regardless of the minor differences due to rounding, the main conclusion remains: the car's wheel rotates approximately 2000 to 2060 times per minute at 132 km/h with a 0.35-meter diameter wheel.

This detailed breakdown provides a clear understanding of the concepts and calculations involved in determining the wheel rotation frequency of a car at a specific speed and wheel diameter.