The bicycle

How a bicycle works
When you pedal a bicycle, you cause the rear wheel to turn. How is the motion of your feet converted into forward motion of the bicycle? The moving parts of the bicycle that connect the pedals to the wheel are called the drive train. Read the text aloud
The crank is a lever integrated into a wheel-and-axle simple machine. Pushing down the pedal provides the input force and the output force turns the front gear. The mechanical advantage of the bicycle crank is the ratio of the radius of the pedal to the radius of the front gear, or MAcrank = rp / rf. Read the text aloud
The back wheel is another wheel-and-axle simple machine, but this time the input force turns the back gear (the axle) and the output force is exerted by the tire on the outside of the wheel. The mechanical advantage of the back wheel is the ratio of the radius of the back gear to the radius of the wheel, or MAwheel = rb / rw. Read the text aloud
The chain connects the front gear to the back gear such that the force is the same everywhere in the chain. Thus the combined mechanical advantage of a bicycle is the product of the mechanical advantages of the crank and the back wheel:
M A bicycle =M A crank ×M A wheel = r p r f × r b r w
Since the teeth are the same size on the front and back gears—the same chain runs over both gears!—the ratio of the radii of the back gear to the front gear, rb / rf , is the same as the ratio of their number of teeth. We can substitute the number of teeth for the ratio of the gear radii to get the mechanical advantage of a bicycle: Read the text aloud
M A bicycle = pedal radius wheel radius × number of back gear teeth number of front gear teeth Mechanical advantage
of a bicycle
The mechanical advantage of a bicycle depends on the ratio of the number of teeth in the back and front gears. Now we can see why most modern road bicycles have more than one gear! When you change gears on a bicycle, you are changing its mechanical advantage. Read the text aloud Show Gear ratio
  1. Calculate the mechanical advantage for the road bike in the illustration at the top of the page if the front gear were to be on the large chainring (53 teeth) while the back gear were to be on the smallest gear of the cassette (12 teeth).
  2. Compare this mechanical advantage to the example in the illustration at the top of the page, which used the small chainring for the front gear (39 teeth) and the largest gear on the back cassette (25 teeth). Which has a larger mechanical advantage?
  3. In what situations would you want to use each of these gear combinations? Why?
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