The RPM of "A" is 100 and hobbed with 76...

Question 1 of 270705eccefa3bacbc34ba4d47ce2

The RPM of "A" is 100 and hobbed with 76 teeth. If gears "B", "C", and "D" have 60, 32, and 42 teeth respectively, the RPM of "D" in the gear train illustration is __________. See illustration MO-0088.

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Question 1 of 27070

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🔍 Key Concepts

• Relationship between gear teeth and RPM in a simple/compound gear train (teeth × RPM is constant between meshing gears) • How to handle a compound gear where two gears (B and C) are rigidly connected on the same shaft, sharing the same RPM • Overall speed ratio from first driver (A) to final driven gear (D) by multiplying the intermediate gear ratios

💭 Think About

• Between two meshing gears, if you know the teeth and RPM of one gear, how can you calculate the RPM of the other? Write that as a formula. • Look at the drawing: which gears are on the same shaft, and what does that tell you about their RPMs? How does that affect the step-by-step calculation from A → B → C → D? • After you compute the RPM of gear B (and therefore C), how do you use the teeth and RPM of C to find the RPM of D? What direction does the speed change go when the driven gear has more or fewer teeth than the driver?

✅ Before You Answer

• Be sure you are using teeth of driver vs. driven in the correct positions in the ratio (don’t invert the fraction). • Confirm that gears B and C have the same RPM because they are on the same shaft in the illustration. • After finding the theoretical RPM of D, compare with the choices and check that your result is reasonable in magnitude (is the final gear expected to turn faster or slower than A, given each step’s ratio?).