Final answer:
The angular speed of the wheels in rad/min is 139.938 rad/min, and the number of revolutions per minute is 33.82 rev/min.
Step-by-step explanation:
(a) To find the angular speed of the wheels in rad/min, we need to convert the linear speed of the truck to angular speed. The linear speed can be converted to meters per second by dividing 45 mi/h by 2.237 (1 mile = 1609 meters and 1 hour = 3600 seconds). Now, to find the angular speed, we divide the linear speed by the radius of the wheels. The radius is half of the diameter, so the radius is 9 inches or 0.2286 meters. The angular speed in rad/min is given by:
Angular speed = Linear speed / Radius
Angular speed = (32.0 m/s) / (0.2286 m) = 139.938 rad/min
(b) To find the number of revolutions per minute that the wheels make, we divide the linear speed by the circumference of the wheels. The circumference of the wheels is given by 2 * pi * radius, where pi is approximately 3.14159. The number of revolutions per minute is then given by:
Revolutions per minute = Linear speed / Circumference
Revolutions per minute = (32.0 m/s) / ((2 * 3.14159 * 0.2286 m) / 60 s) = 33.82 rev/min