A conveyor system uses a compound gear train to reduce motor speed. The driving motor turn… — Armed Services Vocational Aptitude Battery (ASVAB)

A conveyor system uses a compound gear train to reduce motor speed. The driving motor turns Gear A (20 teeth) clockwise at $240\text{ rpm}$ . Gear A meshes with Gear B (60 teeth). Gear B shares a solid axle with Gear C (10 teeth), meaning they rotate together. Gear C meshes with Gear D (40 teeth), which drives the conveyor belt. What is the rotational speed and direction of Gear D?

$20\text{ rpm}$ , clockwiseAnswer
B
$20\text{ rpm}$ , counter-clockwise
C
$120\text{ rpm}$ , counter-clockwise
D
$2880\text{ rpm}$ , clockwise

Answer

Gear D rotates at

20\text{ rpm}

, clockwise.

In a compound gear system, the total speed reduction is the product of the individual gear pair ratios. The first pair reduces the speed from

240\text{ rpm}

80\text{ rpm}

and reverses direction to counter-clockwise. The second pair reduces the

80\text{ rpm}

speed to

20\text{ rpm}

and reverses direction back to clockwise.

Step-by-Step Solution

Calculate the speed and direction of Gear B.

Gear B rotates at

80\text{ rpm}

counter-clockwise.

Gear B has three times as many teeth as Gear A (60 vs 20), so it spins at one-third the speed (

240 / 3 = 80

). Meshing gears turn in opposite directions.

Determine the speed and direction of Gear C.

Gear C rotates at

80\text{ rpm}

counter-clockwise.

Gears mounted on the same solid axle rotate at the exact same speed and in the same direction.

Calculate the speed and direction of Gear D.

Gear D rotates at

20\text{ rpm}

clockwise.

Gear D has four times as many teeth as Gear C (40 vs 10), so it spins at one-quarter the speed of Gear C (

80 / 4 = 20

). Meshing gears turn in opposite directions.

Key Concept

Compound Gear Trains and Speed Reduction

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