Mechanical Abilities · Free Study Guide
Gears are the most common mechanical reasoning topic on UA aptitude tests. Learn the ratio rule, the direction rule, and the torque trade-off — you'll have every gear question on the test covered. Free to read; no signup.
Meshing gears turn in opposite directions. The gear ratio tells you how much faster or slower the driven gear spins. Press play below to watch the rotation — notice the larger gear turns slower.
Driver
12 teeth
Driven
18 teeth
Gear Ratio = Driven teeth ÷ Driver teeth = 18 ÷ 12 = 1.5 : 1
Adjacent meshing gears always rotate in opposite directions.
Question
A driver gear has 15 teeth and meshes with a driven gear that has 45 teeth. If the driver turns at 120 RPM, how fast does the driven gear turn?
Find the gear ratio: Ratio = Driven ÷ Driver = 45 ÷ 15 = 3:1
Apply the ratio: Driven RPM = Driver RPM ÷ Ratio = 120 ÷ 3
Answer: 40 RPM
Tip: More teeth = slower rotation but more torque. The driven gear direction is always opposite the driver. Count the meshing points in a gear train — odd number of meshes means opposite direction, even means same.
| Concept | Formula | What to Remember |
|---|---|---|
| Gear Ratio | Ratio = Driven teeth ÷ Driver teeth | More teeth on driven = slower but more torque. |
| Gear Direction | Adjacent = opposite direction | Same shaft = same direction. Count meshes for direction. |
| Output RPM | RPMout = RPMin ÷ Ratio | Faster input doesn't help if the ratio slows it. |
| Torque Trade-off | More teeth = less speed, more torque | Same trade as every simple machine: force vs. distance. |
Drill timed gear questions with scenario-specific diagrams. Inside the practice page, pick the Gears sub-skill to focus just on this topic.
The other study guides (pulleys, levers, reading, figure visualization, etc.) are unlocked with a free account or a paid tier. Gears stays free for everyone.