A small water pump uses a direct gear drive system. The driving gear, attached to an elect… — Armed Services Vocational Aptitude Battery (ASVAB)

A small water pump uses a direct gear drive system. The driving gear, attached to an electric motor, has $20$ teeth and spins at $300\text{ rpm}$ . It meshes directly with a driven gear on the pump shaft that has $60$ teeth. What is the rotational speed of the driven gear in rpm?

Answer: 100 rpm

Answer

100 rpm

Because the driven gear has three times as many teeth as the driving gear (

60

compared to

20

), it requires three times the effort to turn. Therefore, it will rotate at exactly one-third the speed of the driving gear. Dividing the driving speed of

300\text{ rpm}

3

yields

100\text{ rpm}

Step-by-Step Solution

Recall the fundamental gear relationship formula.

S_1 \times T_1 = S_2 \times T_2

The product of the speed and number of teeth of the driving gear equals the product of the speed and number of teeth of the driven gear.

Substitute the given values into the formula.

300 \times 20 = S_2 \times 60

We are given the driving gear speed (

300\text{ rpm}

) and teeth (

20

), along with the driven gear teeth (

60

Solve for the driven gear speed (

S_2

S_2 = \frac{6000}{60} = 100\text{ rpm}

Isolating

S_2

provides the final rotational speed of the driven gear.

Key Concept

The speed of a driven gear is inversely proportional to its number of teeth compared to the driving gear.

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