2. A spin balancer rotates the wheel of the car at 480 revolutions per min. if the diameter of the wheel is 26 in what road speed is being tested in the miles per hour? Round to the nearest tenth
To calculate the road speed in miles per hour (mph), we need to determine the circumference of the wheel. The formula for circumference is C = π * d, where C represents the circumference and d represents the diameter.
Step 1: Calculate the circumference
Given the diameter of the wheel is 26 inches, we can find the circumference by multiplying the diameter by π (pi).
C = 3.14159 * 26
C ≈ 81.68134 inches
Step 2: Convert the circumference to miles
Since the road speed is typically measured in miles per hour, we need to convert the circumference from inches to miles. There are 12 inches in a foot, and 5280 feet in a mile. By dividing the circumference by the number of inches in a mile (12 * 5280), we can convert it to miles.
C_miles = C / (12 * 5280)
C_miles ≈ 0.0012938 miles
Step 3: Calculate the distance traveled in one minute
Since the spin balancer rotates the wheel at 480 revolutions per minute, the distance traveled in one minute would be equal to the circumference multiplied by the number of revolutions.
Distance_per_minute = C_miles * 480
Distance_per_minute ≈ 0.6199 miles
Step 4: Convert minutes to hours
To convert the distance per minute to miles per hour, we need to multiply the distance by the number of minutes in an hour (60).
Road_speed = Distance_per_minute * 60
Road_speed ≈ 37.194 miles per hour
Therefore, the road speed being tested is approximately 37.2 miles per hour.