Which of the following statements best describes the relationship between pulley sizes and the speed of the driven shaft in a belt drive?

• A. A larger driver relative to the driven increases the driven speed
• B. A larger driver relative to the driven decreases the driven speed
• C. Pulley size has no effect on speed
• D. The belt speed equals the average of pulley diameters

Answer: (A)

In a belt-drive system, the speed of the driven shaft is determined by the ratio of pulley diameters. The belt’s linear speed is set by how fast the driver pulley turns and its size, so v ≈ ω_driver × D_driver. The driven shaft converts that belt speed into rotational speed via ω_driven = v / D_driven, which simplifies to ω_driven = ω_driver × (D_driver / D_driven). This means when the driver is larger than the driven, the driven shaft spins faster because the diameter ratio is greater than one. If the driver were smaller, the driven speed would be slower. Pulley size clearly affects speed in belt drives; statements claiming no effect or that belt speed is the average of the diameters aren’t accurate because the speed is governed by the diameter ratio, not an average.