To find the angular speed of the truck's wheels in radians per minute, convert the linear speed to inches per minute and then calculate the number of wheel rotations per minute. Finally, convert the number of rotations to radians per minute.
To find the angular speed of the truck's wheels in radians per minute, we need to convert the linear speed from miles per hour to inches per minute, and then calculate the angular speed.
Given that the truck is moving at a rate of 60 miles per hour and the diameter of its wheels is 24 inches:
- Convert the linear speed from miles per hour to inches per minute: 60 miles/hour * 5280 feet/mile * 12 inches/foot * 1/60 hour/minute = 63360 inches/minute
- Calculate the circumference of the wheels: Circumference = π * diameter = π * 24 inches ≈ 75.4 inches
- Calculate the number of wheel rotations per minute: Rotations/minute = linear speed (inches/minute) / circumference (inches/rotation) = 63360 inches/minute / 75.4 inches/rotation ≈ 840 rotations/minute
- Convert the number of rotations to radians: Radians/minute = rotations/minute * 2π radians/rotation ≈ 840 rotations/minute * 2π radians/rotation ≈ 5280π radians/minute
Therefore, the angular speed of the truck's wheels is approximately 5280π radians per minute.