A belt drive uses a 4-inch driver pulley to drive a 12-inch driven pulley. What is the speed ratio of driven to driver?

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Multiple Choice

A belt drive uses a 4-inch driver pulley to drive a 12-inch driven pulley. What is the speed ratio of driven to driver?

Explanation:
In a belt drive, the belt’s constant linear speed means the rotational speeds are inversely proportional to the pulley diameters: ω_driven/ω_driver = D_driver/D_driven. With a 4-inch driver and a 12-inch driven pulley, the driven speed is ω_driven = ω_driver × (4/12) = ω_driver/3. So the speed ratio (driven to driver) is 1/3, which is about 0.333.... This ratio makes sense: a much larger driven pulley rotates more slowly than the driver. If you had a driven pulley of 16 inches, the ratio would be 0.25; if it were 8 inches, the ratio would be 0.5; and if both pulleys were the same size, the ratio would be 1.

In a belt drive, the belt’s constant linear speed means the rotational speeds are inversely proportional to the pulley diameters: ω_driven/ω_driver = D_driver/D_driven. With a 4-inch driver and a 12-inch driven pulley, the driven speed is ω_driven = ω_driver × (4/12) = ω_driver/3. So the speed ratio (driven to driver) is 1/3, which is about 0.333....

This ratio makes sense: a much larger driven pulley rotates more slowly than the driver. If you had a driven pulley of 16 inches, the ratio would be 0.25; if it were 8 inches, the ratio would be 0.5; and if both pulleys were the same size, the ratio would be 1.

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