### Problem Statement:The angular acceleration of a body which is rotating about a fixed axis is given by \( \alpha = -k \omega^2 \), where the constant \( k = 0.30 \) (no units). Determine the angular displacement and time elapsed when the angular velocity has been reduced to \( \frac{1}{10} \) times its initial value \( \omega_0 = 11.4 \, \text{rad/s} \). The initial rotation angle is \( \theta_0 = 0 \).### Solution:#### Given Data:- \( k = 0.30 \)- \( \omega_0 = 11.4 \, \text{rad/s} \)- Final angular velocity \( \omega_f = \frac{1}{10} \omega_0 = 1.14 \, \text{rad/s} \)- Initial rotation angle \( \theta_0 = 0 \)#### Required:1. Angular Displacement \( \theta \)2. Time Elapsed \( t \)### Answers:1. Angular Displacement:\[ \theta = \boxed{165.048 \, \text{rad}} \]2. Time Elapsed:\[ t = \boxed{2.632 \, \text{s}} \]

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The angular acceleration of a body which is rotating about a fixed axis is given by a = -kw², where the constant k = 0.30 (no units). Determine the angular displacement and time elapsed when the angular velocity has been reduced to 1/10 times its initial value wo = 11.4 rad/s. The initial rotation angle is 0o = 0. Answers: 0= t= i 165.048 2.632 S rad

The angular acceleration of a body which is rotating about a fixed axis is given by a = -kw², where the constant k = 0.30 (no units). Determine the angular displacement and time elapsed when the angular velocity has been reduced to 1/10 times its initial value wo = 11.4 rad/s. The initial rotation angle is 0o = 0. Answers: 0= t= i 165.048 2.632 S rad

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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### Problem Statement:

The angular acceleration of a body which is rotating about a fixed axis is given by \( \alpha = -k \omega^2 \), where the constant \( k = 0.30 \) (no units). Determine the angular displacement and time elapsed when the angular velocity has been reduced to \( \frac{1}{10} \) times its initial value \( \omega_0 = 11.4 \, \text{rad/s} \). The initial rotation angle is \( \theta_0 = 0 \).

### Solution:

#### Given Data:

- \( k = 0.30 \)
- \( \omega_0 = 11.4 \, \text{rad/s} \)
- Final angular velocity \( \omega_f = \frac{1}{10} \omega_0 = 1.14 \, \text{rad/s} \)
- Initial rotation angle \( \theta_0 = 0 \)

#### Required:

1. Angular Displacement \( \theta \)
2. Time Elapsed \( t \)

### Answers:

1. Angular Displacement:
\[ \theta = \boxed{165.048 \, \text{rad}} \]

2. Time Elapsed:
\[ t = \boxed{2.632 \, \text{s}} \]

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