To find the angular acceleration, we use the formula:

$\alpha = \frac{\omega_f - \omega_i}{t}$

where:

• $\alpha$ is the angular acceleration (rad/s²),
• $\omega_f = 138 \, \text{rad/s}$ is the final angular velocity,
• $\omega_i = 0 \, \text{rad/s}$ is the initial angular velocity,
• $t = 6.1 \, \text{s}$ is the time.

Substituting the given values:

$\alpha = \frac{138 - 0}{6.1}$

$\alpha = \frac{138}{6.1} \approx 22.62 \, \text{rad/s}^2$

Final Answer:

The angular acceleration is approximately 22.62 rad/s².

---

Do you want me to explain this calculation in more detail or explore further? Here are some related questions to expand on this topic:

1. What is the total angular displacement during this period?
2. How many revolutions does the saw blade complete in this time?
3. What is the linear acceleration of a point on the edge of the blade?
4. How do you convert angular acceleration to linear acceleration?
5. How would the angular acceleration change if the time to reach 138 rad/s was doubled?

Tip: Always ensure you have consistent units (e.g., seconds for time, radians for angular measurements) when solving rotational motion problems.