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The rod is attached with ball-and-socket joints to smooth collars A and B at its end points. A is moving upward at a constant speed of vA = 6.4 ft/s . The angular velocity of the rod is directed perpendicular to the axis of the rod. Determine the magnitude of the velocity of B at the instant shown Determine the x, y, and z components of the angular velocity of the rod using scalar notation.

The rod is attached with ball-and-socket joints to smooth collars A and B at its end points. A is moving upward at a constant speed of vA = 6.4 ft/s . The angular velocity of the rod is directed perpendicular to the axis of the rod. Determine the magnitude of the velocity of B at the instant shown Determine the x, y, and z components of the angular velocity of the rod using scalar notation.

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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The rod is attached with ball-and-socket joints to smooth collars A and B at its end points. A is moving upward at a constant speed of vA = 6.4 ft/s . The angular velocity of the rod is directed perpendicular to the axis of the rod.

Determine the magnitude of the velocity of B at the instant shown

Determine the x, y, and z components of the angular velocity of the rod using scalar notation.

### Problem Overview **Description:** The rod is attached with ball-and-socket joints to smooth collars \( A \) and \( B \) at its end points. \( A \) is moving upward at a constant speed of \( v_A = 6.4 \, \text{ft/s} \). The angular velocity of the rod is directed perpendicular to the axis of the rod. #### Figure 1: - The rod forms a 3D shape with: - Point \( A \) moving upward along the \( z \)-axis. - Point \( B \) located 2 ft along the \( x \)-axis and 6 ft along the \( y \)-axis from the z-axis origin. - The rod length from \( A \) to \( B \) is 3 ft. ### Part A **Task:** Determine the magnitude of the velocity of \( B \) at the instant shown. **Input Box:** - Enter the value and units for \( v_B \). **Guidance:** - Express your answer to three significant figures and include the appropriate units. ### Part B **Task:** Determine the \( x \), \( y \), and \( z \) components of the angular velocity of the rod using scalar notation. **Input Box:** - Format the answer using three significant figures separated by commas. **Units:** - \( \omega_{AB} \) are in rad/s. --- This setup allows students to practice dynamic systems' calculations by exploring translational and rotational motion relationships.
Transcribed Image Text:### Problem Overview **Description:** The rod is attached with ball-and-socket joints to smooth collars \( A \) and \( B \) at its end points. \( A \) is moving upward at a constant speed of \( v_A = 6.4 \, \text{ft/s} \). The angular velocity of the rod is directed perpendicular to the axis of the rod. #### Figure 1: - The rod forms a 3D shape with: - Point \( A \) moving upward along the \( z \)-axis. - Point \( B \) located 2 ft along the \( x \)-axis and 6 ft along the \( y \)-axis from the z-axis origin. - The rod length from \( A \) to \( B \) is 3 ft. ### Part A **Task:** Determine the magnitude of the velocity of \( B \) at the instant shown. **Input Box:** - Enter the value and units for \( v_B \). **Guidance:** - Express your answer to three significant figures and include the appropriate units. ### Part B **Task:** Determine the \( x \), \( y \), and \( z \) components of the angular velocity of the rod using scalar notation. **Input Box:** - Format the answer using three significant figures separated by commas. **Units:** - \( \omega_{AB} \) are in rad/s. --- This setup allows students to practice dynamic systems' calculations by exploring translational and rotational motion relationships.
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