In a gear pair, if one gear has 30 teeth and rotates at 90 rpm and the mating gear has 20 teeth, what is the rpm of the mating gear?

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Study for the Mechatronics End-of-Pathway (EOP) Test. Explore flashcards and multiple-choice questions, each with hints and explanations. Prepare confidently for your exam!

Multiple Choice

In a gear pair, if one gear has 30 teeth and rotates at 90 rpm and the mating gear has 20 teeth, what is the rpm of the mating gear?

Explanation:
When gears mesh, the tangential speed at the pitch circles is the same for both gears. With the same gear pitch, the pitch radii are proportional to the number of teeth, so the speed relation is ω_driving / ω_driven = N_driven / N_driving. The driven gear’s rpm is the driving rpm multiplied by the ratio of the driving gear’s teeth to the driven gear’s teeth. Here, with 30 teeth driving at 90 rpm and 20 teeth in the driven gear, the ratio is 30/20 = 1.5. So the driven gear spins at 90 × 1.5 = 135 rpm. The driven gear will rotate faster and in the opposite direction, as expected for external gears.

When gears mesh, the tangential speed at the pitch circles is the same for both gears. With the same gear pitch, the pitch radii are proportional to the number of teeth, so the speed relation is ω_driving / ω_driven = N_driven / N_driving. The driven gear’s rpm is the driving rpm multiplied by the ratio of the driving gear’s teeth to the driven gear’s teeth.

Here, with 30 teeth driving at 90 rpm and 20 teeth in the driven gear, the ratio is 30/20 = 1.5. So the driven gear spins at 90 × 1.5 = 135 rpm. The driven gear will rotate faster and in the opposite direction, as expected for external gears.

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