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Which of the following statements is correct about the direction of (ab/A)t? α B A W O It is perpendicular to the AB line and to the right. O It is along the AB line and from B to A. O It is perpendicular to the AB line and to the left. O It is along the AB line and from A to B.

Which of the following statements is correct about the direction of (ab/A)t? α B A W O It is perpendicular to the AB line and to the right. O It is along the AB line and from B to A. O It is perpendicular to the AB line and to the left. O It is along the AB line and from A to B.

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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**Understanding Rotational Motion: Direction of Acceleration in a Rotating Body** When analyzing rotational motion, it's crucial to comprehend the direction of the relative acceleration vector \((\mathbf{a}_{B/A})_t\). The vector \((\mathbf{a}_{B/A})_t\) represents the tangential component of the relative acceleration of point B with respect to point A. Consider the diagram below to understand the concept better: ![Diagram of Rotating Body with Points A and B](#) ### Diagram Explanation - **Object Shape**: An irregular, closed shape is shown outlined in black, shaded green. - **Points A and B**: Two points, A (bottom) and B (top), are marked with red dots and connected by a straight line labeled \( \mathbf{AB} \). - **Rotational Indicators**: The object rotates counterclockwise with angular velocity \( \omega \) and angular acceleration \( \alpha \), both indicated with black curved arrows pointing from left to right. ### Multiple Choice Question: **Which of the following statements is correct about the direction of \((\mathbf{a}_{B/A})_t\)?** - **A)** It is perpendicular to the \( \mathbf{AB} \) line and to the right. - **B)** It is along the \( \mathbf{AB} \) line and from B to A. - **C)** It is perpendicular to the \( \mathbf{AB} \) line and to the left. - **D)** It is along the \( \mathbf{AB} \) line and from A to B. Consider the rotational motion of our irregular object. Given that the object rotates counterclockwise, tangential acceleration always points in the direction of the object's motion at any given point. Given this understanding, select the option which fits this description correctly.
Transcribed Image Text:**Understanding Rotational Motion: Direction of Acceleration in a Rotating Body** When analyzing rotational motion, it's crucial to comprehend the direction of the relative acceleration vector \((\mathbf{a}_{B/A})_t\). The vector \((\mathbf{a}_{B/A})_t\) represents the tangential component of the relative acceleration of point B with respect to point A. Consider the diagram below to understand the concept better: ![Diagram of Rotating Body with Points A and B](#) ### Diagram Explanation - **Object Shape**: An irregular, closed shape is shown outlined in black, shaded green. - **Points A and B**: Two points, A (bottom) and B (top), are marked with red dots and connected by a straight line labeled \( \mathbf{AB} \). - **Rotational Indicators**: The object rotates counterclockwise with angular velocity \( \omega \) and angular acceleration \( \alpha \), both indicated with black curved arrows pointing from left to right. ### Multiple Choice Question: **Which of the following statements is correct about the direction of \((\mathbf{a}_{B/A})_t\)?** - **A)** It is perpendicular to the \( \mathbf{AB} \) line and to the right. - **B)** It is along the \( \mathbf{AB} \) line and from B to A. - **C)** It is perpendicular to the \( \mathbf{AB} \) line and to the left. - **D)** It is along the \( \mathbf{AB} \) line and from A to B. Consider the rotational motion of our irregular object. Given that the object rotates counterclockwise, tangential acceleration always points in the direction of the object's motion at any given point. Given this understanding, select the option which fits this description correctly.
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