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Difficulty: EasyGears and Gear Ratios

A motor drives a small pinion gear with 10 teeth, which is meshed directly with a larger bull gear having 40 teeth. Compared to the small driving gear, which of the following correctly describes the output of the large driven gear?

  1. It will rotate slower and produce more torque.Answer
  2. B
    It will rotate faster and produce more torque.
  3. C
    It will rotate faster and produce less torque.
  4. D
    It will rotate slower and produce less torque.

Answer

The large driven gear will rotate slower and produce more torque compared to the small driving gear.
In a gear train, when a small gear drives a larger gear, the system is stepping down the speed. Because the driven gear has more teeth, it revolves less frequently than the driving gear. However, due to the conservation of energy (ignoring friction), this reduction in speed provides a mechanical advantage, meaning the output torque (turning force) is increased.

Step-by-Step Solution

1
Analyze the size relationship between the driving gear and the driven gear.
The driving gear has 10 teeth, and the driven gear has 40 teeth. The driven gear is larger.
Gear size determines the mechanical advantage and the speed ratio.
2
Determine the effect of size on rotational speed.
Because the driven gear is 4 times larger (40/10 = 4), it will take 4 revolutions of the smaller gear to turn the larger gear once. Therefore, the driven gear rotates slower.
A smaller gear must turn multiple times to advance the many teeth of a larger gear through one full rotation.
3
Determine the effect on torque (turning force).
The decrease in speed is accompanied by a proportional increase in torque. The torque is multiplied by 4.
In simple machines like gear trains, trading distance (or speed) results in a gain in force (or torque), conserving mechanical power.

Key Concept

Mechanical Advantage in Gears
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Topics

Gears and Gear Ratios

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