A motorized mixer uses two meshing gears to adjust the mixing speed. The driving gear, whi… — Armed Services Vocational Aptitude Battery (ASVAB)

A motorized mixer uses two meshing gears to adjust the mixing speed. The driving gear, which is attached to the motor, has $12$ teeth and spins at $150$ RPM. It meshes directly with a driven gear that has $36$ teeth. What is the rotational speed of the driven gear in RPM?

Answer: 50 RPM

Answer

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

36

12

). Because gears have an inverse relationship between size and speed, the larger driven gear will rotate at one-third the speed of the driving gear (

150 \div 3 = 50

RPM).

Step-by-Step Solution

State the gear speed formula

T_1 \times S_1 = T_2 \times S_2

To establish the inverse relationship between the number of gear teeth and rotational speed

Substitute the given values into the formula

12 \times 150 = 36 \times S_2

To set up the equation with the known tooth counts and driving speed

Solve for the unknown driven speed (

S_2

)

S_2 = \frac{1800}{36} = 50

To find the final RPM of the driven gear

Key Concept

The rotational speed of meshing gears is inversely proportional to their number of teeth.

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