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.