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Bicycle physics

Was given formula IMA(1) = (r of rear sprocket/r of front sprocket) * (r of pedal/r of wheel)

If Rear sprocket = r of 5.37cm; circum. of 33.75cm

Front sprokcet = r of 5.57cm; circum of 35cm

Radius of pedal = 9cm

Radius of wheel = 33cm

Calculated IMA(1) to be 0.28

was given formula IMA(2) = distance of pedal/distance of wheel
or Circum. of pedal/Circum. of wheel

1) How would you calculate the distance the wheel would travel using these figures?
2) How would you calculate the average speed of the gears if cyclist turns pedals at 90rpm's?

Solution Preview

1. Distance traveled will be equal to the circumference of the wheel times the number of the rotation of the wheels. Note that rear wheel is attached to the rear sprocket so they have the same angular velocity w. Rear sprocket is connected to front sprocket via chain. ...