What the ASVAB is testing
Gear and wheel-and-axle questions are ratio problems dressed up in mechanical clothing. You need to know two things: how to compute the gear ratio, and what that ratio means for speed and torque.
The test presents scenarios — motor driving a gear train, bicycle sprocket and rear cassette, hand crank connected to a drum — and asks you to find output speed, output torque direction, or mechanical advantage.
Gear ratio fundamentals
When a small gear drives a large gear, the large gear turns slower and produces more torque. When a large gear drives a small gear, the result is higher speed and less torque. The gear ratio tells you exactly how much:
Gear ratio = driven teeth ÷ driver teeth
A ratio greater than 1 means speed reduction and torque multiplication. A ratio less than 1 means speed increase and torque reduction.
The speed formula avoids confusion about which gear is which:
Driver RPM × driver teeth = Driven RPM × driven teeth
Plug in three known values and solve for the fourth.
Direction of rotation
Meshing gears counter-rotate. If the top gear rotates clockwise, the gear it meshes with rotates counterclockwise. Add a third gear between them (an idler) and the final gear rotates the same direction as the first.
Idler gears appear on the ASVAB to test this. An idler doesn't change the gear ratio between the first and last gear — it only changes the final rotation direction.
Wheel and axle
A wheel and axle is a lever wrapped around an axis. The wheel is the long arm; the axle is the short arm. You apply force at the wheel rim and get amplified torque at the axle — or vice versa for speed.
MA = wheel radius ÷ axle radius
A steering wheel, a doorknob, a winch crank, and a screwdriver handle all work on this principle.
Belt and chain drives
Pulleys connected by a belt or chain follow the same math as gear teeth — just use pulley circumference or diameter instead of tooth count. A large driven pulley gives you torque multiplication; a small driven pulley gives you speed multiplication.
Quick test strategy
Identify the driver (power source side) and the driven (output side). Compute the ratio. If ratio > 1: output is slower, torque is up. If ratio < 1: output is faster, torque is down. Rotation direction: opposite for direct mesh, same for belt or idler.