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Difficulty: MediumGears and Gear Ratios

A commercial dough mixer utilizes a three-gear sequence to rotate its mixing hook. The main motor turns the first gear (24 teeth) clockwise at 240 rpm240\text{ rpm}. This gear meshes directly with a smaller intermediate gear (12 teeth), which subsequently drives the final hook gear (72 teeth). What is the resulting rotational speed and direction of the final hook gear?

  1. A
    720 rpm720\text{ rpm}, clockwise
  2. B
    80 rpm80\text{ rpm}, counter-clockwise
  3. 80 rpm80\text{ rpm}, clockwiseAnswer
  4. D
    720 rpm720\text{ rpm}, counter-clockwise

Answer

The final hook gear rotates at 80 rpm80\text{ rpm} in a clockwise direction.
The intermediate gear acts as an idler. Therefore, the overall speed ratio depends only on the first (24 teeth) and final (72 teeth) gears. The driven gear is three times larger than the driving gear, so it will rotate at one-third the speed: 240/3=80 rpm240 / 3 = 80\text{ rpm}. Regarding direction, meshing gears rotate in opposite directions. The first gear is clockwise, the second is counter-clockwise, and the third is clockwise.

Step-by-Step Solution

1
Determine the effect of the intermediate gear on the final speed.
The intermediate gear acts as an idler gear.
An idler gear placed between a driving and driven gear changes the direction of rotation but does not affect the final speed ratio.
2
Calculate the final rotational speed.
Final speed is 80 rpm80\text{ rpm}.
The speed is calculated using the ratio of the first and last gears: Speed=240×2472=240×13=80 rpm\text{Speed} = 240 \times \frac{24}{72} = 240 \times \frac{1}{3} = 80\text{ rpm}.
3
Determine the final direction of rotation.
The final gear rotates clockwise.
Gear 1 is clockwise, so Gear 2 is counter-clockwise, meaning Gear 3 is clockwise.

Key Concept

Idler Gears and Gear Ratios
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Topics

Gears and Gear Ratios

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