A motorized telescope mount uses a compound gear system to adjust its viewing angle. The d… — Armed Services Vocational Aptitude Battery (ASVAB)

A motorized telescope mount uses a compound gear system to adjust its viewing angle. The driving gear, Gear W, has 24 teeth and rotates counter-clockwise at $400\text{ RPM}$ . Gear W meshes directly with Gear X, which has 96 teeth. Gear X and Gear Y are rigidly mounted on the same intermediate shaft. Gear Y has 30 teeth and meshes with the final output gear, Gear Z, which has 120 teeth. What is the rotational speed and direction of Gear Z?

$25\text{ RPM}$ , counter-clockwiseCevap
B
$25\text{ RPM}$ , clockwise
C
$400\text{ RPM}$ , counter-clockwise
D
$80\text{ RPM}$ , clockwise

Cevap

The final output gear, Gear Z, rotates at

25\text{ RPM}

in the counter-clockwise direction.

In a compound gear system, the overall speed ratio is determined by analyzing each meshing pair. The first pair (W to X) reduces the speed from

400\text{ RPM}

100\text{ RPM}

(

400 \times 24/96

) and reverses the direction from counter-clockwise to clockwise. Since Gear Y shares a shaft with Gear X, it also rotates at

100\text{ RPM}

clockwise. The second meshing pair (Y to Z) further reduces the speed from

100\text{ RPM}

25\text{ RPM}

(

100 \times 30/120

) and reverses the direction again, making the final output counter-clockwise.

Adım Adım Çözüm

Calculate the rotational speed and direction of Gear X.

Speed of Gear X is

100\text{ RPM}

, rotating clockwise.

Gear X is driven by Gear W. The speed ratio is

24/96 = 1/4

400\text{ RPM} \times (1/4) = 100\text{ RPM}

. Meshing gears rotate in opposite directions, so Gear X rotates clockwise.

Determine the speed and direction of Gear Y.

Speed of Gear Y is

100\text{ RPM}

, rotating clockwise.

Gear Y is rigidly mounted on the same shaft as Gear X, meaning they share the exact same rotational speed and direction.

Calculate the rotational speed and direction of Gear Z.

Speed of Gear Z is

25\text{ RPM}

, rotating counter-clockwise.

Gear Z is driven by Gear Y. The speed ratio is

30/120 = 1/4

100\text{ RPM} \times (1/4) = 25\text{ RPM}

. Meshing gears rotate in opposite directions, so Gear Z rotates counter-clockwise.

Anahtar Kavram

Compound Gear Trains and Rotational Direction

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