An engine flywheel initially rotates counterclockwise at 6.23 rotations/s. Then, during 22.1 s, its rotation rate changes to 3.33 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive. average angular acceleration: rad/s2
An engine flywheel initially rotates counterclockwise at 6.23 rotations/s. Then, during 22.1 s, its rotation rate changes to 3.33 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive. average angular acceleration: rad/s2
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Question
![**Problem Statement:**
An engine flywheel initially rotates counterclockwise at 6.23 rotations/s. Then, during 22.1 s, its rotation rate changes to 3.33 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.
**Solution:**
- **Initial Angular Velocity (\( \omega_i \))**: 6.23 rotations/s counterclockwise
- **Final Angular Velocity (\( \omega_f \))**: -3.33 rotations/s (since clockwise is negative)
- **Time Interval (\( \Delta t \))**: 22.1 s
**Steps to Solution:**
1. **Convert Rotations to Radians:**
\[
1 \text{ rotation} = 2\pi \text{ radians}
\]
- Initial Angular Velocity:
\[
\omega_i = 6.23 \times 2\pi \text{ rad/s}
\]
- Final Angular Velocity:
\[
\omega_f = -3.33 \times 2\pi \text{ rad/s}
\]
2. **Calculate the Average Angular Acceleration (\( \alpha \)):**
\[
\alpha = \frac{\omega_f - \omega_i}{\Delta t}
\]
3. **Substitute the Values:**
\[
\alpha = \frac{(-3.33 \times 2\pi) - (6.23 \times 2\pi)}{22.1}
\]
4. **Simplify:**
\[
\alpha = \frac{-2\pi(3.33 + 6.23)}{22.1} \, \text{rad/s}^2
\]
5. **Calculate Result:**
- Use a calculator to find the exact value.
**Box for Final Answer:**
average angular acceleration: \(\quad \underline{\quad \quad \quad \quad}\) rad/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f424ac-8f96-4172-b739-006cab2e5691%2F3d861ba2-471a-4045-9aec-b5c4e8eb1387%2F9kpvuc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
An engine flywheel initially rotates counterclockwise at 6.23 rotations/s. Then, during 22.1 s, its rotation rate changes to 3.33 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.
**Solution:**
- **Initial Angular Velocity (\( \omega_i \))**: 6.23 rotations/s counterclockwise
- **Final Angular Velocity (\( \omega_f \))**: -3.33 rotations/s (since clockwise is negative)
- **Time Interval (\( \Delta t \))**: 22.1 s
**Steps to Solution:**
1. **Convert Rotations to Radians:**
\[
1 \text{ rotation} = 2\pi \text{ radians}
\]
- Initial Angular Velocity:
\[
\omega_i = 6.23 \times 2\pi \text{ rad/s}
\]
- Final Angular Velocity:
\[
\omega_f = -3.33 \times 2\pi \text{ rad/s}
\]
2. **Calculate the Average Angular Acceleration (\( \alpha \)):**
\[
\alpha = \frac{\omega_f - \omega_i}{\Delta t}
\]
3. **Substitute the Values:**
\[
\alpha = \frac{(-3.33 \times 2\pi) - (6.23 \times 2\pi)}{22.1}
\]
4. **Simplify:**
\[
\alpha = \frac{-2\pi(3.33 + 6.23)}{22.1} \, \text{rad/s}^2
\]
5. **Calculate Result:**
- Use a calculator to find the exact value.
**Box for Final Answer:**
average angular acceleration: \(\quad \underline{\quad \quad \quad \quad}\) rad/s²
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