Certainly! Let's express the linear speed of the sawteeth in terms of \(\pi\).

### Part (b): Linear Speed of the Sawteeth in ft/s (in terms of \(\pi\))

1. **We already derived the linear speed** in the previous response as:
   \[
   v = \frac{3500\pi}{36} \, \text{ft/s}
   \]

2. **Simplify the fraction**:
   \[
   v = \frac{350\pi}{3.6} \, \text{ft/s}
   \]

3. **Further simplification**:
   \[
   v = \frac{350}{3.6}\pi \, \text{ft/s}
   \]
   Simplifying the division:
   \[
   v = \frac{875}{9}\pi \, \text{ft/s}
   \]

Thus, the linear speed of the sawteeth is \(\frac{875}{9}\pi \, \text{ft/s}\) in exact terms.

If you want the final answer in a more simplified or decimal form, let me know!

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Would you like to ask anything else or need more details?

### Related Questions:
1. How does the blade's diameter affect the linear speed in terms of \(\pi\)?
2. What would the linear speed be in terms of \(\pi\) if the blade radius were 14 inches?
3. How does the linear speed vary if the blade speed changes to 6,000 rpm in terms of \(\pi\)?
4. What is the impact of reducing the rpm by half on the linear speed in terms of \(\pi\)?
5. How would you convert this linear speed in terms of \(\pi\) to inches per second?

**Tip:** Working with angular and linear speeds in terms of \(\pi\) helps maintain precision in mathematical expressions, especially when dealing with circular motion.

Learn how to calculate the linear speed of sawteeth in terms of π. Follow a step-by-step solution using the linear speed formula v = r * ω. This problem involves concepts of circular motion and angular speed, suitable for advanced high school students.

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