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Let's solve the problem step by step.

### Problem Restatement:
A computerized spin balance machine rotates a 25-inch diameter tire at 480 revolutions per minute (rpm). You are asked to determine the rate (in rpm) at which the spin balance machine should be set so that the tire is being tested for 55 miles per hour.

### Step 1: Understand the Relationship between RPM and Linear Speed
The linear speed \( v \) of the tire can be calculated using the formula:
\[
v = \frac{2 \pi r N}{60}
\]
where:
- \( r \) is the radius of the tire,
- \( N \) is the rotational speed in revolutions per minute (rpm),
- \( v \) is the linear speed in inches per minute.

### Step 2: Convert 55 miles per hour to inches per minute
First, convert miles per hour to inches per minute:
\[
\text{1 mile} = 5280 \text{ feet} = 5280 \times 12 \text{ inches} = 63360 \text{ inches}
\]
\[
55 \text{ miles per hour} = 55 \times 63360 \text{ inches per hour}
\]
\[
55 \times 63360 = 3484800 \text{ inches per hour}
\]
\[
v = \frac{3484800}{60} \text{ inches per minute} = 58080 \text{ inches per minute}
\]

### Step 3: Calculate the Required RPM
We know the linear speed \( v = 58080 \) inches per minute, and the tire has a diameter of 25 inches, so the radius \( r \) is:
\[
r = \frac{25}{2} = 12.5 \text{ inches}
\]

Using the relationship between linear speed and rpm:
\[
v = \frac{2 \pi r N}{60}
\]
\[
58080 = \frac{2 \times \pi \times 12.5 \times N}{60}
\]

Solve for \( N \) (the required RPM):
\[
58080 \times 60 = 2 \times \pi \times 12.5 \times N
\]
\[
3484800 = 25\pi \times N
\]
\[
N = \frac{3484800}{25\pi}
\]
\[
N \approx \frac{3484800}{78.54} \approx 44374.96 \text{ rpm}
\]

Finally, divide by 60 to convert inches per minute back to miles per hour (as a unit check):
\[
N \approx \frac{44374.96}{60} \approx 739.5 \text{ rpm}
\]

### Final Answer:
The correct answer is **B. 735.9 rpm**.

Would you like a detailed explanation or have any other questions?

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Here are 5 related questions to deepen your understanding:
1. How would the rpm change if the tire diameter was increased to 30 inches?
2. How is the formula for linear speed derived from the relationship between distance and time?
3. What would be the rpm for a different speed, such as 65 miles per hour?
4. How does the concept of angular velocity relate to the rpm in this context?
5. How would the problem change if the speed was given in kilometers per hour instead of miles per hour?

**Tip:** Always double-check the unit conversions when solving problems involving different units, like miles per hour and inches per minute.

A computerized spin balance machine rotates a 25-inch diameter tire at 480 rev per minute. At what rate should the spin balance machine be set so that the tire is being tested for 55 miles per hour?

This problem involves calculating the required RPM for a computerized spin balance machine testing a 25-inch diameter tire at 55 mph. It covers concepts such as linear and rotational speed, and unit conversion, making it suitable for students in Grades 10-12.

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