A truck with 30-in-diameter wheels is traveling at 60mi/h. Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes: square rad/min How many revolutions per minute do the wheels make? square rpm Round your answers to 1 decimal place.

# Brief Explanations:<br />To find the angular speed in radians per minute, we need to convert the linear speed from miles per hour to inches per minute and then use the relationship between linear speed and angular speed. For the revolutions per minute, we use the angular speed and convert it to revolutions.<br /><br /># Answer:<br />1. **Angular Speed in rad/min:**<br /> - Convert 60 mi/h to inches per minute:<br /> \[<br /> 60 \text{ mi/h} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{1 \text{ h}}{60 \text{ min}} = 63,360 \text{ in/min}<br /> \]<br /> - The circumference of the wheel is:<br /> \[<br /> \pi \times 30 \text{ in} = 94.2 \text{ in}<br /> \]<br /> - Angular speed (ω) is given by:<br /> \[<br /> \omega = \frac{\text{linear speed}}{\text{radius}} = \frac{63,360 \text{ in/min}}{15 \text{ in}} = 4,224 \text{ rad/min}<br /> \]<br /><br />2. **Revolutions per minute (rpm):**<br /> - Convert angular speed to revolutions per minute:<br /> \[<br /> \text{Revolutions per minute} = \frac{\omega}{2\pi} = \frac{4,224 \text{ rad/min}}{2\pi} \approx 672.4 \text{ rpm}<br /> \]<br /><br /># Answer:<br />1. Angular Speed: \( 4,224.0 \) rad/min<br />2. Revolutions per minute: \( 672.4 \) rpm