In a belt drive, the velocity ratio ω1/ω2 equals which of the following?

• A. ω1/ω2 = D1/D2
• B. ω2/ω1 = D2/D1
• C. ω1/ω2 = D2/D1
• D. ω1 ω2 = D1 D2

Answer: (C)

In a belt drive, the belt’s linear speed is the same around both pulleys, so the angular speeds must scale with the pulley sizes. The belt speed relation is v = ω1(D1/2) = ω2(D2/2). Solving for the ratio of angular speeds gives ω1/ω2 = D2/D1. This means the velocity ratio is determined by the diameter of the driven pulley relative to the driver pulley. In RPM terms, N1/N2 also equals D2/D1. The setup where the ratio would equal D1/D2 or where it would be a product of speeds and diameters doesn’t fit the belt-speed equality, so the correct interpretation is that the driver-to-driven speed ratio matches the inverse of the diameter ratio, i.e., the driven diameter over the driver diameter.