**Problem 16–109**The ends of bar \( AB \) are confined to move along the paths shown. At a given instant, \( A \) has a velocity of \( 8 \, \text{ft/s} \) and an acceleration of \( 3 \, \text{ft/s}^2 \). Determine the angular velocity and angular acceleration of \( AB \) at this instant.**Diagram Explanation:**The diagram depicts a mechanical system where bar \( AB \) is constrained to move such that point \( A \) slides vertically, and point \( B \) follows a curved path. - **Velocity and Acceleration at Point A:** - \( v_A = 8 \, \text{ft/s} \) (downward) - \( a_A = 3 \, \text{ft/s}^2 \) (downward)- **Bar AB Configuration:** - The length of the bar \( AB \) is \( 4 \, \text{ft} \). - Both \( A \) and \( B \) form a \( 30^\circ \) angle with the horizontal and vertical axis, respectively.The main task is to calculate the angular velocity and angular acceleration of the bar \( AB \) at the given instant.

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16–109. The ends of bar AB are confined to move along the paths shown. At a given instant, A has a velocity of 8 ft/s and an acceleration of 3 ft /s². Determine the angular velocity and angular acceleration of AB at this instant.

16–109. The ends of bar AB are confined to move along the paths shown. At a given instant, A has a velocity of 8 ft/s and an acceleration of 3 ft /s². Determine the angular velocity and angular acceleration of AB at this instant.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**Problem 16–109**

The ends of bar \( AB \) are confined to move along the paths shown. At a given instant, \( A \) has a velocity of \( 8 \, \text{ft/s} \) and an acceleration of \( 3 \, \text{ft/s}^2 \). Determine the angular velocity and angular acceleration of \( AB \) at this instant.

**Diagram Explanation:**

The diagram depicts a mechanical system where bar \( AB \) is constrained to move such that point \( A \) slides vertically, and point \( B \) follows a curved path.

- **Velocity and Acceleration at Point A:**
- \( v_A = 8 \, \text{ft/s} \) (downward)
- \( a_A = 3 \, \text{ft/s}^2 \) (downward)

- **Bar AB Configuration:**
- The length of the bar \( AB \) is \( 4 \, \text{ft} \).
- Both \( A \) and \( B \) form a \( 30^\circ \) angle with the horizontal and vertical axis, respectively.

The main task is to calculate the angular velocity and angular acceleration of the bar \( AB \) at the given instant.

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