A car with a 44inch diameter wheel is traveling at 55 mph. (Round the answer to three decimal places.) find the angular speed of the wheels in rad/min

To find the angular speed of the wheels in radians per minute, we'll use the following approach:

1. **Convert the car's speed from miles per hour to inches per minute.**
2. **Calculate the wheel's circumference in inches.**
3. **Determine the number of wheel rotations per minute.**
4. **Convert the rotations per minute to angular speed in radians per minute.**

Let's go through each step.

### Step 1: Convert the car's speed from miles per hour to inches per minute

1 mile = 5280 feet  
1 foot = 12 inches

So, 1 mile = \( 5280 \times 12 = 63360 \) inches.

The car's speed is 55 mph, which is:

\[
\text{Speed in inches per minute} = 55 \times 63360 \, \text{inches per hour} \div 60 = \frac{55 \times 63360}{60} \, \text{inches per minute}
\]

### Step 2: Calculate the wheel's circumference in inches

The diameter of the wheel is 44 inches, so its circumference \( C \) is:

\[
C = \pi \times \text{diameter} = \pi \times 44 \, \text{inches}
\]

### Step 3: Determine the number of wheel rotations per minute

The number of rotations per minute \( N \) is given by:

\[
N = \frac{\text{Speed in inches per minute}}{\text{Circumference}} = \frac{\frac{55 \times 63360}{60}}{\pi \times 44}
\]

### Step 4: Convert the rotations per minute to angular speed in radians per minute

Since one full rotation corresponds to \( 2\pi \) radians, the angular speed \( \omega \) in radians per minute is:

\[
\omega = N \times 2\pi
\]

Let's calculate this step-by-step.The angular speed of the wheels is \( 2640.000 \) radians per minute.

Would you like more details or have any questions? Here are some related questions to consider:

1. How would the angular speed change if the wheel diameter increased?
2. What would be the angular speed if the car's speed were different?
3. How can you convert angular speed from radians per minute to revolutions per second?
4. What is the relationship between linear speed and angular speed?
5. How would this calculation change if the units were in metric (e.g., kilometers per hour)?

**Tip:** Angular speed in radians per minute can provide insights into mechanical stress and wear on rotating parts.

Learn how to calculate the angular speed of wheels when a car with a 44-inch diameter wheel travels at 55 mph. Detailed step-by-step solution converting speed units, calculating circumference, and determining rotations per minute. Suitable for high school students studying physics and circular motion.

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