Questions: Question 9 10 pts A truck with 22-in.-diameter wheels is traveling at 45 mi / h. Find the angular speed of the wheels in rad/min, hint convert miles to inches hours to minutes: rad/min How many revolutions per minute do the wheels make? rpm Round your answers to 1 decimal place.

Find the angular speed of the wheels in rad/min.

Convert the truck's speed from miles per hour to inches per minute.

First, convert 45 miles per hour to inches per hour: \[ 45 \, \text{mi/h} \times 5280 \, \text{ft/mi} \times 12 \, \text{in/ft} = 2,851,200 \, \text{in/h} \]

Next, convert inches per hour to inches per minute: \[ 2,851,200 \, \text{in/h} \div 60 \, \text{min/h} = 47,520 \, \text{in/min} \]

Calculate the circumference of the wheel.

The diameter of the wheel is 22 inches, so the radius \( r \) is: \[ r = \frac{22}{2} = 11 \, \text{in} \]

The circumference \( C \) of the wheel is: \[ C = 2 \pi r = 2 \pi \times 11 = 22 \pi \, \text{in} \]

Determine the angular speed in radians per minute.

The angular speed \( \omega \) in radians per minute is given by: \[ \omega = \frac{\text{linear speed}}{\text{radius}} \]

Using the linear speed in inches per minute and the radius: \[ \omega = \frac{47,520 \, \text{in/min}}{11 \, \text{in}} = 4320 \, \text{rad/min} \]

\(\boxed{4320.0 \, \text{rad/min}}\)

How many revolutions per minute do the wheels make?

Convert the angular speed from radians per minute to revolutions per minute.

One revolution is \( 2\pi \) radians. Therefore, the number of revolutions per minute \( N \) is: \[ N = \frac{\omega}{2\pi} = \frac{4320 \, \text{rad/min}}{2\pi} \approx 687.5 \, \text{rev/min} \]

\(\boxed{687.5 \, \text{rpm}}\)

\(\boxed{4320.0 \, \text{rad/min}}\)

\(\boxed{687.5 \, \text{rpm}}\)