The RPM of "D" is 500 and hobbed with 42...

Question 1 of 270705eccefa3bacbc34ba4d47cd6

The RPM of "D" is 500 and hobbed with 42 teeth. If gears "A", "B", and "C" have 42, 60, and 32 teeth respectively, the RPM of "A" 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 RPM and number of teeth (for meshing gears, speed is inversely proportional to teeth). • How a compound gear train works when two gears (B and C) are fixed to the same shaft and therefore have the same RPM. • Writing an overall speed ratio from gear D (known RPM) through gears C and B to gear A (unknown RPM).

💭 Think About

• From the sketch, which gears are actually meshing with each other, and which gears are on the same shaft? • If gear D turns at 500 RPM, how do you use the tooth counts of D and C to find the RPM of C, and what does that tell you about the RPM of B? • Once you know the RPM of B, how do the tooth counts of gears A and B tell you whether A must turn faster or slower than 500 RPM, and by roughly what factor?

✅ Before You Answer

• Use the meshing-gear relation N₁ × T₁ = N₂ × T₂ (RPM × teeth) for each pair of gears that mesh (D with C, then B with A). • Remember that gears B and C share a shaft, so their RPMs are equal before you move the calculation from C to B. • Before choosing an answer, check whether your final RPM for gear A makes sense based on the relative sizes (tooth counts) of D, C, B, and A (should A be the fastest or slowest gear in the train?).