Question 966857
the front wheel has a radius of 10 inches.
the front pedal has a radius of 7 inches.
the rear wheel has a radius of 6 inches.


one revolution of the rear wheel is exactly equal to the circumference of the rear wheel.


this is equal to 2 * pi * 6 which is equal to 12 * pi.


the circumference of the pedal is equal to 2 * pi * 7 which is equal to 14 * pi.


the pedal will actually be traveling the same distance as the rear wheel.


however, that same distance represents 12 * pi / 14 * pi = 6/7 of the circumference of the pedal.


the rear wheel will have traveled 360 degrees.


the pedal will have traveled 6/7 * 360 = 308.5714286 degrees.


the formula to calculate the arc length of 308.5714286 degrees is:


arc length = 308.5714286 / 360 * 2 * pi * 7 which is equal to 12 * pi.


that's the same distance of travel as the rear wheels did in one complete revolution.


i belive that answers your question.


let me know if you think otherwise.