https://file.aiquickdraw.com/mathbot/file/1728232322207pvn9775c.jpg

It looks like the image you uploaded contains a table related to gear ratios and RPM (revolutions per minute). From what I can see, the problem involves two gears (a large gear and a small gear), with given numbers of teeth, and the task is to complete the table by determining the RPM of the small gear.

The relationship between the gears in mesh can be defined by the formula:

\[
\frac{T_1}{T_2} = \frac{N_2}{N_1}
\]

Where:
- \( T_1 \) is the number of teeth of the large gear,
- \( T_2 \) is the number of teeth of the small gear,
- \( N_1 \) is the RPM of the large gear, and
- \( N_2 \) is the RPM of the small gear.

From the table:
- Large gear (\( T_1 \)) has 70 teeth.
- Small gear (\( T_2 \)) has 50 teeth.
- The RPM of the large gear (\( N_1 \)) is 140.

Now, we need to find the RPM of the small gear (\( N_2 \)) using the formula:

\[
N_2 = N_1 \times \frac{T_1}{T_2}
\]

Substituting the known values:

\[
N_2 = 140 \times \frac{70}{50} = 140 \times 1.4 = 196 \, \text{RPM}
\]

Thus, the RPM of the small gear is 196 RPM.

Would you like further clarification or more details? Here are some related questions for further understanding:

1. What happens to the small gear's RPM if its number of teeth decreases?
2. How would the relationship change if both gears had the same number of teeth?
3. What is the effect on RPM if the large gear's speed increases?
4. How would you calculate the torque transferred between the gears?
5. What practical applications might use such gear ratios?

**Tip**: When dealing with gear ratios, always remember that the RPM is inversely proportional to the number of teeth. This helps simplify gear system calculations.

Complete the table for two gears in mesh using a constant variation. The large gear has 70 teeth and an RPM of 140, while the small gear has 50 teeth. Find the RPM of the small gear.

Learn how to calculate the RPM of a small gear when two gears are in mesh. The large gear has 70 teeth and an RPM of 140, and the small gear has 50 teeth. Use the formula for gear ratios to solve the problem. Suitable for high school students.

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