The ratio of the speeds of the sprockets is the __________ of the sprocket ratio.

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Multiple Choice

The ratio of the speeds of the sprockets is the __________ of the sprocket ratio.

Explanation:
When two sprockets are connected by a chain, the chain moves at the same linear speed on both sprockets, so ω1 r1 = ω2 r2. Since the radius is proportional to the number of teeth, r ∝ N, this gives ω1/ω2 = N2/N1. If the sprocket ratio is defined as N1/N2 (driving to driven), the speed ratio becomes N2/N1, which is the inverse of the sprocket ratio. In other words, a larger sprocket (more teeth) must rotate more slowly to keep the chain’s linear speed constant, so the ratio of speeds is the inverse of the sprocket ratio.

When two sprockets are connected by a chain, the chain moves at the same linear speed on both sprockets, so ω1 r1 = ω2 r2. Since the radius is proportional to the number of teeth, r ∝ N, this gives ω1/ω2 = N2/N1. If the sprocket ratio is defined as N1/N2 (driving to driven), the speed ratio becomes N2/N1, which is the inverse of the sprocket ratio. In other words, a larger sprocket (more teeth) must rotate more slowly to keep the chain’s linear speed constant, so the ratio of speeds is the inverse of the sprocket ratio.

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