In a gear drive with a 2-tooth driver gear and an 8-tooth driven gear, if the driver torque is 2.5 ft-lbs, the torque of the driven gear is ______ ft-lbs.

• A. 3.75
• B. 10
• C. 5
• D. 20

Answer: (B)

Torque in a gear train scales with the gear ratio. The drive and driven gears share the same tangential force at their teeth, and torque is that force times the gear’s radius. The driven gear has four times as many teeth as the driver (8 vs 2), so its pitch radius is four times larger. With the same tangential force, the driven gear’s torque becomes four times the driver’s: 2.5 ft-lbs × 4 = 10 ft-lbs. In an ideal system, this also means the driven gear spins at a quarter of the driver’s speed, while power stays the same (ignoring losses). So the driven torque is 10 ft-lbs.