If a gear pair has a 4-tooth driver and an 16-tooth driven gear and the driver torque is 5 ft-lbs, the driven torque is ______ ft-lbs.

• A. 10
• B. 20
• C. 25
• D. 40

Answer: (B)

In a gear pair, torque scales with the gear ratio: the driven gear gains torque as it has more teeth and turns more slowly than the driver. Here, the driven gear has 16 teeth and the driver has 4, giving a gear ratio of 16/4 = 4:1. That means the driven torque is four times the driver torque. With a driver torque of 5 ft-lbs, the driven torque becomes 5 × 4 = 20 ft-lbs. In an ideal gear system (ignoring losses), that’s the exact result; real gears will be a bit lower due to inefficiencies.