Answer:
each rotation of the smaller wheel will show 84.382-75.3982=8.9838 inches more than the actual distance
Explanation:
d = Diameter of the wheel
The distance traveled in one rotation of the wheel is the circumference of the wheel
[tex]\pi d=\pi\times 27\\ =84.823\ inch[/tex]
When diameter is 24 inches
[tex]\pi d=\pi\times 24\\ =75.3982\ inch[/tex]
Therefore, each rotation of the smaller wheel will show 84.382-75.3982=8.9838 inches more than the actual distance
The odometer will show 12.12 inches more per revolution.
Given that the bicycle odometer is calibrated for 27 inches wheel. So for each rotation, it will consider the total distance traveled by the wheel in one complete rotation which is equal to the circumference of the wheel.
The circumference of the 27-inch wheel:
C = πd
here d = 27in is the diameter of the wheel
C = 3.14 × 27 in
C = 87.48 in
Now, the circumference of the 24-inch wheel:
C' = πd'
here d' = 24in is the diameter of the wheel
C = 3.14 × 24 in
C = 75.36 in
The odometer is calibrated to show distance equivalent to one revolution of the 27-inch wheel, so when it is used with a 24-inch wheel it will show
87.48 - 75.36 = 12.12 inches more.
Learn more about circumference:
https://brainly.com/question/4268218?referrer=searchResults
