A truck with 36-inch diameter wheels is traveling 67 mph. How many revolutions per minute do the wheels make?

To find the number of revolutions per minute (RPM) that the truck's wheels make, we'll go through the following steps:

1. **Convert the speed from miles per hour (mph) to inches per minute:**

   - \( 1 \text{ mile} = 5280 \text{ feet} \)
   - \( 1 \text{ foot} = 12 \text{ inches} \)
   - \( 1 \text{ hour} = 60 \times 60 = 3600 \text{ seconds} \)

   So, convert 67 mph to inches per minute:

   \[
   67 \text{ mph} = 67 \times 5280 \times 12 \text{ inches per hour}
   \]
   \[
   \text{Inches per minute} = \frac{67 \times 5280 \times 12}{60} = 70,656 \text{ inches per minute}
   \]

2. **Calculate the circumference of the wheel:**

   The diameter of the wheel is 36 inches, so the circumference \( C \) is:

   \[
   C = \pi \times \text{diameter} = \pi \times 36 \approx 113.1 \text{ inches}
   \]

3. **Find the number of revolutions per minute (RPM):**

   The number of revolutions per minute is the speed in inches per minute divided by the circumference of the wheel:

   \[
   \text{RPM} = \frac{70,656 \text{ inches per minute}}{113.1 \text{ inches per revolution}} \approx 624.6 \text{ RPM}
   \]

So, the wheels make approximately **624.6 revolutions per minute**.

Would you like any further details or have any questions?

Here are five related questions:

1. How would the RPM change if the wheel diameter was increased to 40 inches?
2. What is the linear speed of a point on the edge of the wheel in feet per second?
3. How many revolutions per second do the wheels make?
4. If the truck were traveling at 100 mph, how many revolutions per minute would the wheels make?
5. How does the circumference of the wheel relate to the distance traveled in one revolution?

**Tip:** When dealing with rotational motion, always keep in mind the relationship between linear speed, angular speed, and the radius or diameter of the wheel.

Learn how to calculate the revolutions per minute (RPM) of 36-inch diameter wheels traveling at 67 mph. This problem involves converting speed units, calculating wheel circumference, and applying RPM formula. Suitable for high school students studying geometry, trigonometry, and physics.

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