A car is moving at a rate of 55 miles per hour. The diameter of its wheels is 2.5 feet. (Round your answers to three decimal places.)
Find the number of revolutions per minute the wheels are rotating.
616.850.  now find the angular speed of the wheels in radians per minute.

 


To find the angular speed of the wheels in radians per minute, we need to first recall the relationship between linear speed, angular speed, and the radius of the wheel. The angular speed \( \omega \) in radians per minute can be calculated using the formula:

\[
\omega = \frac{v}{r}
\]

where:
- \( v \) is the linear speed of the car in feet per minute,
- \( r \) is the radius of the wheel in feet.

### Step 1: Convert the speed of the car from miles per hour to feet per minute

We know:
- 1 mile = 5280 feet
- 1 hour = 60 minutes

So, the speed of the car in feet per minute is:

\[
v = 55 \text{ miles/hour} \times 5280 \text{ feet/mile} \times \frac{1}{60} \text{ hour/minute}
\]

\[
v = 4840 \text{ feet/minute}
\]

### Step 2: Calculate the radius of the wheel
Given that the diameter of the wheel is 2.5 feet, the radius \( r \) is:

\[
r = \frac{2.5}{2} = 1.25 \text{ feet}
\]

### Step 3: Calculate the angular speed
Now, use the formula for angular speed:

\[
\omega = \frac{v}{r} = \frac{4840 \text{ feet/minute}}{1.25 \text{ feet}} = 3872 \text{ radians/minute}
\]

Thus, the angular speed of the wheels is **3872 radians per minute**.

Would you like further details or have any other questions?

Here are 5 related questions for you to consider:
1. How would the angular speed change if the diameter of the wheels was doubled?
2. What is the linear speed of the car if the wheels make 500 revolutions per minute?
3. How many revolutions per minute would the wheels make if the car was moving at 70 miles per hour?
4. What would be the angular speed in radians per second instead of radians per minute?
5. How would the number of revolutions per minute change if the car's speed is reduced by half?

**Tip:** Always remember that the angular speed in radians per minute can be found by dividing the linear speed by the radius of the circular path.

A car is moving at a rate of 55 miles per hour. The diameter of its wheels is 2.5 feet. (Round your answers to three decimal places.) Find the number of revolutions per minute the wheels are rotating. Now find the angular speed of the wheels in radians per minute.

Learn how to calculate the angular speed of car wheels in radians per minute given a car speed of 55 miles per hour and a wheel diameter of 2.5 feet. This problem involves key concepts such as linear speed, angular speed, and unit conversions, suitable for students in Grades 9-11.

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