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A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity ω= 3.0 rad/s, the angular acceleration α=2.0 rad/s2. The radius of the disc is r=1.0 m. Determine d) the direction of the acceleration of the point G________         A. up   B. down   C. left   D. right

A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity ω= 3.0 rad/s, the angular acceleration α=2.0 rad/s2. The radius of the disc is r=1.0 m. Determine d) the direction of the acceleration of the point G________         A. up   B. down   C. left   D. right

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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  1. A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity ω= 3.0 rad/s, the angular acceleration α=2.0 rad/s2. The radius of the disc is r=1.0 m. Determine

    d) the direction of the acceleration of the point G________





     
     
     

      A.

    up
      B.

    down
      C.

    left
      D.

    right
### Problem Statement A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity \(\omega\) is 3.0 rad/s, the angular acceleration \(\alpha\) is 2.0 rad/s². The radius of the disc is \(r = 1.0\) m. Determine the direction of the acceleration of the point \(G\). #### Diagram Explanation The diagram illustrates a disc rolling on a flat surface. The disc has a radius \(r\). The center of the disc is labeled as point \(G\), and another point on the edge of the disc is labeled as point \(A\). Both the angular velocity (\(\omega\)) and the angular acceleration (\(\alpha\)) are marked on the disc. The angular velocity \(\omega\) is shown in a counterclockwise direction. #### Multiple Choice Question The direction of the acceleration of point \(G\) is: - A. up - B. down - C. left - D. right #### Detailed Diagram Description - **Angular Velocity (\(\omega\))**: Indicated by a curved arrow around the center \(G\). The direction of the arrow is counterclockwise. - **Angular Acceleration (\(\alpha\))**: Also indicated by a curved arrow around the center \(G\). The direction of the arrow is counterclockwise. - **Radius (r)**: Shown as the distance from the center \(G\) to the edge of the disc where point \(A\) is located. The diagram helps visualize the rotational movement of the disc and the vectors associated with this rotational motion. ### Solution Approach We need to determine the direction of the acceleration of the point \(G\). Consider both tangential and centripetal components of acceleration for rolling motion. Analyzing these vectors and applying the concept of rolling without slipping will help understand the resultant direction. To prepare for the problem, recall the vectors involved in rolling motion, the equations for kinematic relationships, and how components combine to form the resultant acceleration in this context. ### Correct Answer After analyzing the components, the direction of the acceleration of the point \(G\) is: **B. down**
Transcribed Image Text:### Problem Statement A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity \(\omega\) is 3.0 rad/s, the angular acceleration \(\alpha\) is 2.0 rad/s². The radius of the disc is \(r = 1.0\) m. Determine the direction of the acceleration of the point \(G\). #### Diagram Explanation The diagram illustrates a disc rolling on a flat surface. The disc has a radius \(r\). The center of the disc is labeled as point \(G\), and another point on the edge of the disc is labeled as point \(A\). Both the angular velocity (\(\omega\)) and the angular acceleration (\(\alpha\)) are marked on the disc. The angular velocity \(\omega\) is shown in a counterclockwise direction. #### Multiple Choice Question The direction of the acceleration of point \(G\) is: - A. up - B. down - C. left - D. right #### Detailed Diagram Description - **Angular Velocity (\(\omega\))**: Indicated by a curved arrow around the center \(G\). The direction of the arrow is counterclockwise. - **Angular Acceleration (\(\alpha\))**: Also indicated by a curved arrow around the center \(G\). The direction of the arrow is counterclockwise. - **Radius (r)**: Shown as the distance from the center \(G\) to the edge of the disc where point \(A\) is located. The diagram helps visualize the rotational movement of the disc and the vectors associated with this rotational motion. ### Solution Approach We need to determine the direction of the acceleration of the point \(G\). Consider both tangential and centripetal components of acceleration for rolling motion. Analyzing these vectors and applying the concept of rolling without slipping will help understand the resultant direction. To prepare for the problem, recall the vectors involved in rolling motion, the equations for kinematic relationships, and how components combine to form the resultant acceleration in this context. ### Correct Answer After analyzing the components, the direction of the acceleration of the point \(G\) is: **B. down**
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