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Bicycle Wheel The sprockets and chain of a bicycle are shown in the figure. The pedal sprocket has a radius of 4 in. the wheel sprocket a radius of 2 in.. and the wheel a radius of 13 in. The cyclist pedals at 40 rpm. (a) Find the angular speed of the wheel sprocket. (b) Find the speed of the bicycle. (Assume that the wheel turns at the same rate as the wheel sprocket.) | Numerade

SOLVED: Now let's consider the rotational motion of two bicyclesprockets that are connected to each other by a chain.Specifically, we want to find how the angular speeds of the twosprockets in (Figure 1) are related to their respectivenumbers of teeth, NANA and NBNB.SOLUTIONSET UP AND SOLVE The chain does not slipor stretch; therefore, it moves at the same tangentialspeed vv on both sprockets. We use therelationship v=rωv=rω for each sprocket and equate thetwo tangential speeds:v=rAωA=rBωBv=rAωA

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