2. A wheel spins rather slowly at first, taking 8 seconds for every spin. It then accelerates at rad/s². How long does it take for the wheel to make 2 T 3 complete turns? Fill in the table with what is given and what is needed. All values in the table should be in terms of radians. Hint: the answer is not 8 or 16. ΔΘ @i @f α At

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Chapter1: Units, Trigonometry. And Vectors
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**Problem:**

2. A wheel spins rather slowly at first, taking 8 seconds for every spin. It then accelerates at \(\frac{\pi}{3} \, \text{rad/s}^2\). How long does it take for the wheel to make 2 complete turns?

Fill in the table with what is given and what is needed. All values in the table should be in terms of radians. Hint: the answer is not 8 or 16.

**Table:**

| \(\Delta \theta\) |           |
|-------------------|-----------|
| \(\omega_i\)      |           |
| \(\omega_f\)      |           |
| \(\alpha\)        |           |
| \(\Delta t\)      |           |

**Explanation:**

- \(\Delta \theta\) represents the angular displacement.
- \(\omega_i\) is the initial angular velocity.
- \(\omega_f\) is the final angular velocity.
- \(\alpha\) is the angular acceleration.
- \(\Delta t\) is the time taken.

The problem asks you to determine the time \(\Delta t\) for the wheel to complete 2 full turns with the given acceleration. Fill in the table with values in radians based on the information provided.
Transcribed Image Text:**Problem:** 2. A wheel spins rather slowly at first, taking 8 seconds for every spin. It then accelerates at \(\frac{\pi}{3} \, \text{rad/s}^2\). How long does it take for the wheel to make 2 complete turns? Fill in the table with what is given and what is needed. All values in the table should be in terms of radians. Hint: the answer is not 8 or 16. **Table:** | \(\Delta \theta\) | | |-------------------|-----------| | \(\omega_i\) | | | \(\omega_f\) | | | \(\alpha\) | | | \(\Delta t\) | | **Explanation:** - \(\Delta \theta\) represents the angular displacement. - \(\omega_i\) is the initial angular velocity. - \(\omega_f\) is the final angular velocity. - \(\alpha\) is the angular acceleration. - \(\Delta t\) is the time taken. The problem asks you to determine the time \(\Delta t\) for the wheel to complete 2 full turns with the given acceleration. Fill in the table with values in radians based on the information provided.
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