A cyclist is turning the pedals of his bicycle at a speed of 60RPM while exerting a torque of 1 lb-ft. The input sprocket has 40 teeth. What is the number of teeth on the output sprocket, if the driven wheel is rotating at 240 RPM?

10

Explanation:

The speed of the chain is the same for both sprockets.

vᵢ = vₒ

ωᵢ rᵢ = ωₒ rₒ

The sprockets have the same pitch, so the radius is proportional to the number of teeth.  So we can say:

ωᵢ nᵢ = ωₒ nₒ

Plugging in values:

(60 rpm) (40) = (240 rpm) nₒ

nₒ = 10

The output sprocket has 10 teeth.  This makes sense, if the output sprocket is 4 times smaller, it will turn 4 times faster than the input sprocket.

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