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Difficulty: EasyGears and Gear Ratios

In a simple mechanical drive system, a small driving gear with 10 teeth meshes directly with a larger driven gear that has 30 teeth. If the driving gear is spinning clockwise at 120 RPM120\text{ RPM}, what is the rotational speed and direction of the driven gear?

  1. 40 RPM40\text{ RPM}, counterclockwiseAnswer
  2. B
    360 RPM360\text{ RPM}, counterclockwise
  3. C
    40 RPM40\text{ RPM}, clockwise
  4. D
    360 RPM360\text{ RPM}, clockwise

Answer

The driven gear will rotate at 40 RPM40\text{ RPM} in a counterclockwise direction.
The correct answer accurately applies both fundamental rules of simple two-gear trains: speed reduction and direction reversal. Because the driven gear has three times as many teeth (30 vs 10), it turns at one-third the speed (40 RPM). Because it meshes directly with the clockwise-turning driving gear, it must turn counterclockwise.

Step-by-Step Solution

1
Determine the direction of rotation for the driven gear.
Counterclockwise
When two external gears mesh directly, they rotate in opposite directions. Since the driving gear rotates clockwise, the driven gear must rotate counterclockwise.
2
Calculate the speed ratio and the output speed.
40 RPM40\text{ RPM}
The speed of the driven gear is inversely proportional to its number of teeth. The ratio of driving teeth to driven teeth is 10/30 (or 1/3). Multiplying the input speed (120 RPM120\text{ RPM}) by this ratio gives 120×(1/3)=40 RPM120 \times (1/3) = 40\text{ RPM}.

Key Concept

Two adjacent meshing gears always rotate in opposite directions, and a larger driven gear turns slower than a smaller driving gear in direct proportion to their tooth counts.
Estimated Time:45s
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Topics

Gears and Gear Ratios

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