The RPM of "A" is 100 and hobbed with 88...

Question 1 of 270705eccefa3bacbc34ba4d47ce4

The RPM of "A" is 100 and hobbed with 88 teeth. If gears "B", "C", and "D" have 66, 22, and 48 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

• For external spur gears, speed ratio is inversely proportional to the number of teeth (more teeth = slower RPM). • In a compound gear train, gears on the same shaft (like B and C) turn at the same RPM, so their speed is a link between the first and last gears. • Overall speed ratio is the product of each meshing pair’s ratios from A→B and then C→D.

💭 Think About

• First, ignore gears C and D and find the RPM of gear B from A using their tooth counts. Is gear B faster or slower than A? Why? • Once you know the RPM of B, remember B and C are on the same shaft. How does that help you get the RPM of C? • Now treat C driving D as a simple gear pair. Use their tooth counts to find D’s RPM from C’s RPM, then combine all your steps into one expression.

✅ Before You Answer

• Make sure you are using inverse ratios: $N_1 T_1 = N_2 T_2$ for each meshing pair (speed × teeth = constant). • Confirm that gears B and C have the same RPM because they share a shaft; don’t apply a tooth ratio between B and C. • Before choosing an answer, check your combined expression looks like RPM(A) × (teeth of driven / teeth of driver) for each stage, multiplied together, and that the final RPM is reasonable (not wildly higher than all intermediate steps).