In the example with a 24-tooth driver and a 72-tooth driven, the driven torque is 1899 ft-lbs. Which statement is true about this example?

• A. The driven torque equals 1899 ft-lbs
• B. The driven torque equals 633 ft-lbs
• C. The driven torque equals 1266 ft-lbs
• D. The driven torque equals 453 ft-lbs

Answer: (A)

When torque is transmitted through gears, the torque on the driven gear scales with the gear ratio. For a driver with 24 teeth and a driven gear with 72 teeth, the gear ratio is 72/24 = 3. In an ideal gear train, power in equals power out, so the driven torque is three times the driver torque, and the driven speed is one-third of the driver speed.

In this example, the driven torque is stated as 1899 ft-lbs, which fits the 3:1 ratio. That means the corresponding driver torque would be 1899 ÷ 3 = 633 ft-lbs, which is consistent with the given numbers. The value 1899 ft-lbs on the driven side is therefore true. The other numbers would not align with the 3:1 ratio (they would correspond to driver-torque values or different ratios).