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The circular disk of radius r = 0.40 m rotates about a fixed axis through point O with the angular properties w = 2.2 rad/s and a = 3.3 rad/s² with directions as shown in the figure. Determine the instantaneous values of the velocity and acceleration of point A. L Answers: VA = (i i -0.30r i + i j) m/s i) m/s²

The circular disk of radius r = 0.40 m rotates about a fixed axis through point O with the angular properties w = 2.2 rad/s and a = 3.3 rad/s² with directions as shown in the figure. Determine the instantaneous values of the velocity and acceleration of point A. L Answers: VA = (i i -0.30r i + i j) m/s i) m/s²

Structural Analysis
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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The circular disk of radius r = 0.40m rotates about a fixed axis through point O with the angular properties omega w= 2.2 rad/s and alpha a= 3.3 rad/s 2 with directions as shown in the figure. Determine the instantaneous values of the velocity and acceleration of point A.

The problem involves a circular disk with a radius \( r = 0.40 \, \text{m} \) that rotates about a fixed axis through point \( O \). The angular velocity is given as \( \omega = 2.2 \, \text{rad/s} \) and the angular acceleration is \( \alpha = 3.3 \, \text{rad/s}^2 \). The task is to determine the instantaneous values of the velocity and acceleration of point \( A \). ### Diagram Explanation - The disk is depicted as a blue circle with a center at point \( O \). - The radius \( r \) extends from \( O \) to the perimeter of the circle. - Angular velocity \( \omega \) is directed counterclockwise, indicated by an arrow along the perimeter. - Angular acceleration \( \alpha \) also acts counterclockwise and is represented by another arrow. - Point \( A \) is located at a distance of \( 0.30r \) along the horizontal \( x \)-axis from the edge of the disk. ### Answers Section For calculating the velocity and acceleration at point \( A \), expressions in vector form are provided: - \( \mathbf{v}_A = ( \_ \_ \_ ) \, \mathbf{i} + ( \_ \_ \_ ) \, \mathbf{j} \, \text{m/s} \) - \( \mathbf{a}_A = ( \_ \_ \_ ) \, \mathbf{i} + ( \_ \_ \_ ) \, \mathbf{j} \, \text{m/s}^2 \) Boxes labeled with “i” and “j” denote component values in the respective directions. The students are expected to compute these components based on the given angular properties and geometry of the problem.
Transcribed Image Text:The problem involves a circular disk with a radius \( r = 0.40 \, \text{m} \) that rotates about a fixed axis through point \( O \). The angular velocity is given as \( \omega = 2.2 \, \text{rad/s} \) and the angular acceleration is \( \alpha = 3.3 \, \text{rad/s}^2 \). The task is to determine the instantaneous values of the velocity and acceleration of point \( A \). ### Diagram Explanation - The disk is depicted as a blue circle with a center at point \( O \). - The radius \( r \) extends from \( O \) to the perimeter of the circle. - Angular velocity \( \omega \) is directed counterclockwise, indicated by an arrow along the perimeter. - Angular acceleration \( \alpha \) also acts counterclockwise and is represented by another arrow. - Point \( A \) is located at a distance of \( 0.30r \) along the horizontal \( x \)-axis from the edge of the disk. ### Answers Section For calculating the velocity and acceleration at point \( A \), expressions in vector form are provided: - \( \mathbf{v}_A = ( \_ \_ \_ ) \, \mathbf{i} + ( \_ \_ \_ ) \, \mathbf{j} \, \text{m/s} \) - \( \mathbf{a}_A = ( \_ \_ \_ ) \, \mathbf{i} + ( \_ \_ \_ ) \, \mathbf{j} \, \text{m/s}^2 \) Boxes labeled with “i” and “j” denote component values in the respective directions. The students are expected to compute these components based on the given angular properties and geometry of the problem.
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