**Problem Statement:**At the instant shown, the shaft and plate rotate with an angular velocity of \( \omega = 14 \, \text{rad/s} \) and an angular acceleration of \( \alpha = 7 \, \text{rad/s}^2 \). Determine the velocity and acceleration of point \( D \) located on the corner of the plate at this instant. Express the result in Cartesian vector form.**Diagram Explanation:**The diagram illustrates a 3D coordinate system with a rotating shaft and rectangular plate. The important points and distances are labeled as follows:- **Points and Distances:** - \( O \): Center of rotation on the plate. - \( A \): Point on the shaft, 0.6 m from \( O \). - \( B \): Located on the x-axis, showing a part of the plate. - \( C \): A point on the plate where \( C = (0, 0.3, 0) \). - \( D \): Corner of the plate, located 0.4 m from \( O \) along both x and y directions.- **Axes:** - \( x \)-axis extends horizontally. - \( y \)-axis extends vertically on the plate plane. - \( z \)-axis is perpendicular to the plate.- **Rotational Characteristics:** - \( \omega \) and \( \alpha \) are shown as vectors along the axis of rotation (vertical). - Rotation occurs about the z-axis as indicated by arrows circling the shaft.**Objective:**The task is to compute the velocity and acceleration at point \( D \) due to the given angular velocity and acceleration conditions of the rotating system, using Cartesian vector communication.

Answered: Image /qna-images/answer/59da40e8-ad0c-44c1-a881-a06f54cd86c1.jpg

16-36. At the instant shown, the shaft and plate rotates with an angular velocity of w = 14 rad/s and angular acceleration of a = 7 rad/s². Determine the velocity and acceleration of point D located on the corner of the plate at his instant. Express the result in Cartesian vector form. X' D 0.4 m B 0.4 m a 0.6 m 0.2 m) C 0.3 m 0.3 m C=(-0.3

16-36. At the instant shown, the shaft and plate rotates with an angular velocity of w = 14 rad/s and angular acceleration of a = 7 rad/s². Determine the velocity and acceleration of point D located on the corner of the plate at his instant. Express the result in Cartesian vector form. X' D 0.4 m B 0.4 m a 0.6 m 0.2 m) C 0.3 m 0.3 m C=(-0.3

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

**Problem Statement:**

At the instant shown, the shaft and plate rotate with an angular velocity of \( \omega = 14 \, \text{rad/s} \) and an angular acceleration of \( \alpha = 7 \, \text{rad/s}^2 \). Determine the velocity and acceleration of point \( D \) located on the corner of the plate at this instant. Express the result in Cartesian vector form.

**Diagram Explanation:**

The diagram illustrates a 3D coordinate system with a rotating shaft and rectangular plate. The important points and distances are labeled as follows:

- **Points and Distances:**
- \( O \): Center of rotation on the plate.
- \( A \): Point on the shaft, 0.6 m from \( O \).
- \( B \): Located on the x-axis, showing a part of the plate.
- \( C \): A point on the plate where \( C = (0, 0.3, 0) \).
- \( D \): Corner of the plate, located 0.4 m from \( O \) along both x and y directions.

- **Axes:**
- \( x \)-axis extends horizontally.
- \( y \)-axis extends vertically on the plate plane.
- \( z \)-axis is perpendicular to the plate.

- **Rotational Characteristics:**
- \( \omega \) and \( \alpha \) are shown as vectors along the axis of rotation (vertical).
- Rotation occurs about the z-axis as indicated by arrows circling the shaft.

**Objective:**

The task is to compute the velocity and acceleration at point \( D \) due to the given angular velocity and acceleration conditions of the rotating system, using Cartesian vector communication.

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