Final answer:
The angular speed of the truck's wheels is 4755.654 rad/min and it makes approximately 756.4 revolutions per minute (rpm).
Step-by-step explanation:
To calculate the angular speed in rad/min of a truck wheel, we need to start with the given speed of the truck in miles per hour (mph) and convert it into inches per minute. Then, using the diameter of the wheel, we can find out how many inches the wheel travels in one revolution to eventually calculate the angular speed.
First Step: Convert 45 mi/hr to in/min
- 1 mile = 63,360 inches (1 mile = 5280 feet, 1 foot = 12 inches)
- 45 mi/hr = 45 * 63,360 inches/hr
- 45 mi/hr = 2,851,200 inches/hr
- Since there are 60 minutes in an hour, we divide by 60 to convert to minutes:
- 2,851,200 inches/hr = 47,520 inches/min
Second Step: Calculate the circumference of the wheel
- Circumference (C) = π * diameter
- C = π * 20 inches
- C = 62.83185307179586 inches (using π ≈ 3.14159)
Third Step: Find the angular speed in revolutions per minute (rpm)
- 47,520 inches/min divided by one wheel circumference (62.83185307179586 inches) gives us the revolutions per minute:
- RPM = 47,520 in/min / 62.83185307179586 in/rev
- RPM = 756.3995776646093
Fourth Step: Convert rpm to angular speed in rad/min
- 1 rev = 2π rad
- Angular speed = RPM * 2π rad
- Angular speed = 756.3995776646093 rev/min * 2π
- Angular speed = 4755.654083342531 rad/min
So, the angular speed of the wheels is 4755.654 rad/min and the wheels make approximately 756.4 revolutions per minute (rpm).