An industrial dough mixer is driven by a three-gear system. The motor is connected to Gear… — Armed Services Vocational Aptitude Battery (ASVAB)

An industrial dough mixer is driven by a three-gear system. The motor is connected to Gear A (the driving gear), which has 15 teeth and rotates counter-clockwise at $300\text{ RPM}$ . Gear A meshes with an intermediate idler Gear B, which has 45 teeth. Gear B then meshes with Gear C (the final driven gear), which has 75 teeth and turns the mixer blade. What is the rotational speed and direction of Gear C?

$60\text{ RPM}$ , counter-clockwiseAnswer
B
$60\text{ RPM}$ , clockwise
C
$100\text{ RPM}$ , counter-clockwise
D
$1500\text{ RPM}$ , counter-clockwise

Answer

The driven gear will rotate at

60\text{ RPM}

in the counter-clockwise direction.

The correct answer accurately determines both speed and direction. In a simple gear train, the idler gear (Gear B) does not change the final speed ratio. The overall ratio is found by comparing the driving gear (15 teeth) to the final driven gear (75 teeth). The ratio is

15/75

, or

1/5

. Therefore, Gear C spins at

1/5

the speed of Gear A (

300 \times 1/5 = 60\text{ RPM}

). For direction, meshing gears alternate: Gear A (counter-clockwise) drives Gear B (clockwise), which in turn drives Gear C (counter-clockwise).

Step-by-Step Solution

Determine the effect of the intermediate Gear B.

Gear B acts as an idler gear. It changes the direction of rotation between Gear A and Gear C, but does not affect the overall speed ratio of the system.

In a simple gear train, intermediate gears only bridge the gap and alter direction; the final speed is dictated exclusively by the first and last gears.

Calculate the final rotational speed of Gear C.

Speed ratio = (Teeth on Driving Gear) / (Teeth on Driven Gear) =

15 / 75 = 1/5

. The speed of Gear C is

300\text{ RPM} \times (1/5) = 60\text{ RPM}

Rotational speed is inversely proportional to the number of gear teeth. A larger driven gear will rotate slower than a smaller driving gear.

Determine the final direction of rotation for Gear C.

Gear A rotates counter-clockwise (CCW). Meshing Gear B rotates clockwise (CW). Meshing Gear C rotates counter-clockwise (CCW).

Adjacent meshing gears always rotate in opposite directions.

Key Concept

Idler gears change rotation direction but not the overall speed ratio, and larger driven gears result in a slower rotational speed.

Estimated Time:1m 0s

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