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# Rotational Motion and Biking

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As most of us know, a bicycle is ridden by turning pedals that rotate a chain which spins a gear that turns the back wheel, propelling bike and rider forward. This common set up immediately came to mind as an example of rotational motion, and I've discovered some interesting physics behind a process I had taken for granted. Studying only the back sprocket of a bike, and assuming the rider pedals at a constant rate, a clear difference can be seen between higher and lower gears. A lower gear is a disc with greater radius and larger circumference, meaning that according to the equation v = omega r tangential velocity is greater than that of a higher gear (smaller radius). The rider must pedal a greater distance for one complete rotation of the wheel than in a higher gear, making low gears good for uphills and starting. Another way of looking at this is through gear ratios. A gear ratio is the ratio of angular velocity of input gear (pedals) to output gear (low vs. high) A low gear has a lower gear ratio than a high gear, and a low gear ratio means lots of torque. This allows the rider to get up a hill more efficiently than with a high gear. This all gets very confusing, so if I've made a mistake please comment!

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