A Ferns wheel at a carnival has a diameter of 54 feet.Suppose a passenger is traveling at 4 miles per hour. (A useful fact 1mi=5280ft , (a) Find the angular speed of the wheel in radians per minute. (b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.) Do not round any intermediate computations , and round your answer to the nearest whole number. (a) Angular speed: square radians per minute (b) Number of revolutions perho

(a) To find the angular speed of the wheel in radians per minute, we need to first convert the linear speed from miles per hour to feet per minute.<br /><br />Given:<br />Diameter of the wheel = 54 feet<br />Linear speed = 4 miles per hour<br /><br />Step 1: Convert the linear speed to feet per hour.<br />Linear speed in feet per hour = 4 miles/hour * 5280 feet/mile = 21120 feet/hour<br /><br />Step 2: Convert the linear speed to feet per minute.<br />Linear speed in feet per minute = 21120 feet/hour / 60 minutes/hour = 352 feet/minute<br /><br />Step 3: Calculate the angular speed in radians per minute.<br />Angular speed = Linear speed / Radius<br />Radius = Diameter / 2 = 54 feet / 2 = 27 feet<br />Angular speed = 352 feet/minute / 27 feet = 13.04 radians/minute<br /><br />Rounding to the nearest whole number, the angular speed is 13 radians per minute.<br /><br />(b) To find the number of revolutions the wheel makes per hour, we need to use the formula:<br /><br />Number of revolutions = Total distance traveled / Circumference of the wheel<br /><br />Step 1: Calculate the circumference of the wheel.<br />Circumference = π * Diameter = π * 54 feet = 169.65 feet<br /><br />Step 2: Calculate the total distance traveled in one hour.<br />Total distance traveled = Linear speed * Time<br />Total distance traveled = 21120 feet/hour * 1 hour = 21120 feet<br /><br />Step 3: Calculate the number of revolutions.<br />Number of revolutions = Total distance traveled / Circumference of the wheel<br />Number of revolutions = 21120 feet / 169.65 feet = 124.5 revolutions<br /><br />Rounding to the nearest whole number, the wheel makes 125 revolutions per hour.<br /><br />Therefore, the answers are:<br />(a) Angular speed: 13 radians per minute<br />(b) Number of revolutions per hour: 125