Question

in the gear train shown in the illustration, if the driver gear rotates at 120 revolutions per minute (rpm), at what rpm does the driven gear rotate? a 40 b 60 c 120 d 360 click the button or type the letter next to your answer.

Explanation:

Step1: Recall gear ratio formula

The formula for gear ratio is \( \text{Gear Ratio} = \frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driver gear}} \), and the relationship between rpm of driver (\( N_d \)) and driven (\( N_D \)) is \( \frac{N_D}{N_d} = \frac{\text{Teeth on driver}}{\text{Teeth on driven}} \) (since speed is inversely proportional to number of teeth for meshed gears).

Step2: Identify teeth counts

Driver gear teeth (\( T_d \)) = 12, Driven gear teeth (\( T_D \)) = 36, Driver rpm (\( N_d \)) = 120.

Step3: Apply the formula

\( N_D = N_d \times \frac{T_d}{T_D} \)
Substitute values: \( N_D = 120 \times \frac{12}{36} \)

Step4: Simplify the calculation

\( \frac{12}{36} = \frac{1}{3} \), so \( N_D = 120 \times \frac{1}{3} = 40 \)

Answer:

A. 40