Bicycle gears: (a) How is the angular velocity wR of the rear wheel of a bicycle related to the angular velocity of the front sprocket and pedals? Let NF and NR be the number of teeth on the front and rear sprockets, respectively, Fig. 8-53. The teeth are spaced the same on both sprocket: and the rear sprocket is firmly attached to the rear wheel, (b) Evaluate the ratio wR/wF when the front and rear sprockets have 52 and 13 teeth, respectively, and (c) when they have 42 and 28 teeth.
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(A) Let the spacing between the teeth on the front and rear wheel be d, and the number of teeth on the front and the rear wheel are and respectively.
Radii of the front and rear sprockets are .
Hence, we have
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As the chain moves uniformly with a speed v on both the sprockets, we have: