Pinion gear speed from a gear proportion

Aviation Mechanic General (AMG) practice question 3 of 25 on Mathematics. ACS element AM.I.H.K4 · difficulty: applied. Want to answer it in a timed quiz? Use the Aviation Mechanic General (AMG) practice mode.

Question bank updated 2026-09-22

QUESTIONA pinion gear with 10 teeth is driving a spur gear with 40 teeth. If the spur gear rotates at 160 rpm, what is the speed of the pinion gear?

A40 rpm
B1,600 rpm
C640 rpm

Show the answer and explanation

Correct answer: C. 640 rpm

A — incorrect Dividing 160 by 4 treats the smaller gear as the slower one; the gear with fewer teeth turns faster.
B — incorrect This multiplies 160 by the pinion's 10 teeth instead of applying the 40:10 tooth ratio, which is 4:1.
C — correct Teeth in pinion ÷ teeth in spur = speed of spur ÷ speed of pinion; 10/40 = 160/SP, so SP = (40 × 160) ÷ 10 = 640 rpm.

BACKGROUND

When two gears mesh, the gear with fewer teeth turns faster, so the speed ratio is the inverse of the gear ratio. The handbook sets this up as a proportion: teeth in pinion gear / teeth in spur gear = speed of spur gear / speed of pinion gear. With 10 teeth, 40 teeth and a spur speed of 160 rpm, the proportion is 10/40 = 160/SP. Multiplying along the diagonal (40 × 160 = 6,400) and dividing by the remaining number (10) gives a pinion speed of 640 rpm.

STUDY TIP

Set the proportion up with teeth on one side and speeds on the other, inverted, then cross-multiply and divide.

KEY POINTS

Teeth ratio and speed ratio are inverses.
10/40 = 160/SP, so SP = 40 × 160 ÷ 10.
Pinion speed = 640 rpm.

SOURCES

FAA-H-8083-30B ch03 "Aviation Applications" (pinion gear speed example)

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