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The disk rolls without slipping such that it has an angular acceleration of a = 6 rad/s² and angular velocity of w = 3.2 rad/s at the instant shown. Assume point A lies on the periphery of the disk, 150 mm from C. (Figure 1)

The disk rolls without slipping such that it has an angular acceleration of a = 6 rad/s² and angular velocity of w = 3.2 rad/s at the instant shown. Assume point A lies on the periphery of the disk, 150 mm from C. (Figure 1)

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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**Figure Explanation** The diagram illustrates a mechanical setup with a circular component. The circle has a radius of 150 mm and is positioned such that it is in contact with a horizontal surface. An inclined link extends from the edge of the circle to a point directly above the contact point on the surface, creating a triangular configuration. The distance along the horizontal from the base of the circle to the point directly below the link is 400 mm. Additionally, the circle has a total diameter of 500 mm. Axes are labeled with x and y, indicating the directions of measurement. **Part D** The task is to determine the angular acceleration of the link at this moment, measured clockwise. **Instructions:** - Express the answer using three significant figures. - Enter a positive value if the angular acceleration is clockwise and a negative value if it is counterclockwise. **Input Box for Answer** - α_link = [ _______ ] rad/s² **Options for Input** - There are buttons to input various mathematical symbols and vectors. - Submit your answer using the "Submit" button. - If needed, request assistance by clicking "Request Answer."
Transcribed Image Text:**Figure Explanation** The diagram illustrates a mechanical setup with a circular component. The circle has a radius of 150 mm and is positioned such that it is in contact with a horizontal surface. An inclined link extends from the edge of the circle to a point directly above the contact point on the surface, creating a triangular configuration. The distance along the horizontal from the base of the circle to the point directly below the link is 400 mm. Additionally, the circle has a total diameter of 500 mm. Axes are labeled with x and y, indicating the directions of measurement. **Part D** The task is to determine the angular acceleration of the link at this moment, measured clockwise. **Instructions:** - Express the answer using three significant figures. - Enter a positive value if the angular acceleration is clockwise and a negative value if it is counterclockwise. **Input Box for Answer** - α_link = [ _______ ] rad/s² **Options for Input** - There are buttons to input various mathematical symbols and vectors. - Submit your answer using the "Submit" button. - If needed, request assistance by clicking "Request Answer."
### Disk Kinematics Problem **Problem Statement:** The disk rolls without slipping such that it has an angular acceleration of \(\alpha = 6 \, \text{rad/s}^2\) and an angular velocity of \(\omega = 3.2 \, \text{rad/s}\) at the instant shown. Assume point \(A\) lies on the periphery of the disk, 150 mm from point \(C\). *(Refer to Figure 1)* #### Tasks: **Part A:** Determine the magnitude of the acceleration of point \(A\) on the link. - Express your answer to three significant figures and include the appropriate units. \[ a_A = \] --- **Part B:** Determine the direction of the acceleration of point \(A\) on the link. - Express your answer using three significant figures. \[ \theta_{a_A} = \hspace{2mm} ^\circ, \text{ measured clockwise from the positive } x\text{-axis} \] --- **Part C:** Determine the acceleration of point \(B\) on the link. - Express your answer to three significant figures and include the appropriate units. \[ (a_B)_x = \] --- ### Figure Explanation The figure is a diagram of a disk rolling on a surface. Key components of the diagram include: - Point \(C\): The center of the disk. - Point \(A\): A point on the periphery of the disk, 150 mm away from \(C\). - Point \(B\): A point on the surface, 400 mm horizontally from the vertical through \(C\). - The disk has a radius labeled as 500 mm. - Coordinate axes are shown with \(x\) being horizontal and \(y\) being vertical. - Arrows indicate directions of possible motion or forces, like acceleration \(a\). This setup is typically used to solve problems involving rotational motion and kinematics.
Transcribed Image Text:### Disk Kinematics Problem **Problem Statement:** The disk rolls without slipping such that it has an angular acceleration of \(\alpha = 6 \, \text{rad/s}^2\) and an angular velocity of \(\omega = 3.2 \, \text{rad/s}\) at the instant shown. Assume point \(A\) lies on the periphery of the disk, 150 mm from point \(C\). *(Refer to Figure 1)* #### Tasks: **Part A:** Determine the magnitude of the acceleration of point \(A\) on the link. - Express your answer to three significant figures and include the appropriate units. \[ a_A = \] --- **Part B:** Determine the direction of the acceleration of point \(A\) on the link. - Express your answer using three significant figures. \[ \theta_{a_A} = \hspace{2mm} ^\circ, \text{ measured clockwise from the positive } x\text{-axis} \] --- **Part C:** Determine the acceleration of point \(B\) on the link. - Express your answer to three significant figures and include the appropriate units. \[ (a_B)_x = \] --- ### Figure Explanation The figure is a diagram of a disk rolling on a surface. Key components of the diagram include: - Point \(C\): The center of the disk. - Point \(A\): A point on the periphery of the disk, 150 mm away from \(C\). - Point \(B\): A point on the surface, 400 mm horizontally from the vertical through \(C\). - The disk has a radius labeled as 500 mm. - Coordinate axes are shown with \(x\) being horizontal and \(y\) being vertical. - Arrows indicate directions of possible motion or forces, like acceleration \(a\). This setup is typically used to solve problems involving rotational motion and kinematics.
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