Gear Train Calculation: Driver and Follower Turns

This problem involves calculating the relationship between the rotation of two gears in a gear train. We are given the number of teeth on the driver gear and the follower gear, along with the number of turns the driver gear makes. We need to find out how many times the follower gear turns.

Understanding Gear Ratios

In a simple gear train, the ratio of the number of turns made by the follower gear to the number of turns made by the driver gear is equal to the ratio of the number of teeth on the driver gear to the number of teeth on the follower gear. This is a fundamental concept in understanding how gears transmit motion and torque.

The formula representing this relationship is:

\[\frac{\text{Turns of Follower}}{\text{Turns of Driver}} = \frac{\text{Teeth on Driver}}{\text{Teeth on Follower}}\]

Or, using notation:

\[\frac{T_F}{T_D} = \frac{N_D}{N_F}\]

Given Information

Let's list the details provided in the question:

• Number of teeth on the driver gear (\(N_D\)): 18
• Number of teeth on the follower gear (\(N_F\)): 8
• Number of turns made by the driver gear (\(T_D\)): 16

We need to find the number of turns made by the follower gear (\(T_F\)).

Step-by-Step Calculation

We can use the gear ratio formula to find the number of turns for the follower gear. Substitute the given values into the formula:

\[\frac{T_F}{16} = \frac{18}{8}\]

To solve for \(T_F\), we can rearrange the equation:

\[T_F = 16 \times \frac{18}{8}\]

Now, perform the calculation:

First, simplify the fraction \(\frac{18}{8}\) or divide 16 by 8:

\[T_F = (16 \div 8) \times 18\]

\[T_F = 2 \times 18\]

\[T_F = 36\]

Conclusion

For every 16 turns of the driver gear, the follower gear turns 36 times. This means the follower gear rotates faster than the driver gear because it has fewer teeth.

Comparing this result with the given options, the correct option is 36.