In a simple gear train, if the driver gear has a smaller radius than the driven gear, how does the driven gear's speed compare to the driver's?

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Multiple Choice

In a simple gear train, if the driver gear has a smaller radius than the driven gear, how does the driven gear's speed compare to the driver's?

Explanation:
Gears that mesh share the same linear speed at the contact point. So the tangential velocity v = ω r is the same for both gears. If the driver has a smaller radius than the driven gear, keeping the same v means the driven gear must spin more slowly: ω_driven = ω_driver × (r_driver / r_driven), and since r_driver < r_driven, the ratio is less than one. Therefore, the driven gear rotates slower than the driver.

Gears that mesh share the same linear speed at the contact point. So the tangential velocity v = ω r is the same for both gears. If the driver has a smaller radius than the driven gear, keeping the same v means the driven gear must spin more slowly: ω_driven = ω_driver × (r_driver / r_driven), and since r_driver < r_driven, the ratio is less than one. Therefore, the driven gear rotates slower than the driver.

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