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An L-shaped bar ABC has known velocity v and acceleration a, at point A and known ang ular velocity WABC and angular acceleration a ABC- The dimensions and parameters you are to use are provided in the table below. Signs denote + for CCW,- for CW, + for right, and- for left. Determine the acceleration vector in terms of unit vectors for point C at this instant using vector math.

An L-shaped bar ABC has known velocity v and acceleration a, at point A and known ang ular velocity WABC and angular acceleration a ABC- The dimensions and parameters you are to use are provided in the table below. Signs denote + for CCW,- for CW, + for right, and- for left. Determine the acceleration vector in terms of unit vectors for point C at this instant using vector math.

Elements Of Electromagnetics
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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### Kinematics of an L-Shaped Bar **Problem Statement:** An L-shaped bar ABC has known velocity \( v_A \) and acceleration \( a_A \) at point A and known angular velocity \( \omega_{ABC} \) and angular acceleration \( \alpha_{ABC} \). The dimensions and parameters you are to use are provided in the table below. Signs denote + for counterclockwise (CCW), - for clockwise (CW), + for right, and - for left. **Objective:** Determine the acceleration vector in terms of unit vectors for point C at this instant using vector math. **Diagram:** The diagram represents the L-shaped bar ABC with the following components: - \( LAB \): the length from point A to point B. - \( LBC \): the length from point B to point C. - \( G \): the center of rotation. - \( v_A \): velocity at point A. - \( a_A \): acceleration at point A. - \( \omega_{ABC} \): angular velocity. - \( \alpha_{ABC} \): angular acceleration. The diagram also depicts points A, B, and C and the angles formed by the bar segments. **Table of Parameters:** | Units | \( L_{AB} \) (in) | \( L_{BC} \) (in) | \( \theta \) (deg) | \( \omega_{ABC} \) (rad/s) | \( \alpha_{ABC} \) (rad/s²) | \( v_A \) (in/s) | \( a_A \) (in/s²) | |-------|-------------------|-------------------|--------------------|---------------------------|-----------------------------|------------------|-------------------| | A - F | 7.5 | 5.0 | 33 | 3.5 | 21 | 13.0 | 24.0 | - \( L_{AB} \): length from point A to point B. - \( L_{BC} \): length from point B to point C. - \( \theta \): angle formed by the L-shaped bar. - \( \omega_{ABC} \): angular velocity. - \( \alpha_{ABC} \): angular acceleration. - \( v_A \): velocity at point A. - \( a_A \): acceleration at point A. **Solution Steps:** 1
Transcribed Image Text:### Kinematics of an L-Shaped Bar **Problem Statement:** An L-shaped bar ABC has known velocity \( v_A \) and acceleration \( a_A \) at point A and known angular velocity \( \omega_{ABC} \) and angular acceleration \( \alpha_{ABC} \). The dimensions and parameters you are to use are provided in the table below. Signs denote + for counterclockwise (CCW), - for clockwise (CW), + for right, and - for left. **Objective:** Determine the acceleration vector in terms of unit vectors for point C at this instant using vector math. **Diagram:** The diagram represents the L-shaped bar ABC with the following components: - \( LAB \): the length from point A to point B. - \( LBC \): the length from point B to point C. - \( G \): the center of rotation. - \( v_A \): velocity at point A. - \( a_A \): acceleration at point A. - \( \omega_{ABC} \): angular velocity. - \( \alpha_{ABC} \): angular acceleration. The diagram also depicts points A, B, and C and the angles formed by the bar segments. **Table of Parameters:** | Units | \( L_{AB} \) (in) | \( L_{BC} \) (in) | \( \theta \) (deg) | \( \omega_{ABC} \) (rad/s) | \( \alpha_{ABC} \) (rad/s²) | \( v_A \) (in/s) | \( a_A \) (in/s²) | |-------|-------------------|-------------------|--------------------|---------------------------|-----------------------------|------------------|-------------------| | A - F | 7.5 | 5.0 | 33 | 3.5 | 21 | 13.0 | 24.0 | - \( L_{AB} \): length from point A to point B. - \( L_{BC} \): length from point B to point C. - \( \theta \): angle formed by the L-shaped bar. - \( \omega_{ABC} \): angular velocity. - \( \alpha_{ABC} \): angular acceleration. - \( v_A \): velocity at point A. - \( a_A \): acceleration at point A. **Solution Steps:** 1
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