Gear "D" hobbed with 42 teeth and rotates at...

Question 1 of 270705eccefa3bacbc34ba4d47cd3

Gear "D" hobbed with 42 teeth and rotates at a speed of 700 RPM. 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 speed and number of teeth (speed ratio = inverse of tooth ratio) for two gears in mesh • How a compound gear train works when two gears are fixed on the same shaft (they have the same RPM) • Direction of solving: start from known gear D (42 teeth, 700 RPM) and work back through gears C, B, then to A

💭 Think About

• From the illustration, which gears are clearly meshed together, and which gears appear to be mounted on the same shaft so they must turn at the same RPM? • When you know the speed and teeth of gear D, how can you use the tooth ratio with gear C to find the RPM of C, and then carry that result through gear B to gear A? • After you compute the RPM of gear A, how can you quickly estimate whether the result should be higher or lower than 700 RPM, based on whether the gear train overall is a step-up or step-down?

✅ Before You Answer

• Identify correctly which gears are compound (same shaft, same RPM) and which are only in mesh — misreading this will give a wrong answer even with correct math. • Use the formula for gears in mesh: \(N_1/N_2 = T_2/T_1\), where N is RPM and T is teeth, and apply it twice: once for the D–C pair, and once for the B–A pair. • After calculating, compare your final RPM of A against 700 RPM and check whether the overall tooth ratios you multiplied together logically lead to a speed increase or decrease.