Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
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

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

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
See similar textbooks
icon
Related questions
Question

  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. 



     

    b) Is the following statement true?

                    Point A shown above is the instant center of zero velocity of the disk at the moment.

     True

     False

**Rotational Motion of a Rolling Disc** **Problem Statement:** A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity \( \omega \) is \( 3.0 \, \text{rad/s} \), and the angular acceleration \( \alpha \) is \( 2.0 \, \text{rad/s}^2 \). The radius of the disc is \( r = 1.0 \, \text{m} \). **Diagram Explanation:** The accompanying diagram shows a disc rolling on a horizontal surface. Key elements in the diagram include: - **G**: The center of the disc. - **A**: The point of contact of the disc with the floor at any given instant. - The radius of the disc with the labeled 'r'. - The angular velocity \( \omega \) and angular acceleration \( \alpha \) are indicated by arrows indicating their directions of action. The graphical representation indicates the rotational motion with angular velocity \( \omega \) and angular acceleration \( \alpha \) at the center of the disc (point G) while point A remains in contact with the floor. **Concept Check:** b) Is the following statement true? **Statement:** "Point A shown above is the instant center of zero velocity of the disk at the moment." Options: - True - False **Educational Explanation:** In the context of rotational motion, the instant center of zero velocity is a point on a rigid body undergoing planar motion, which has zero velocity at a particular moment in time. For a rolling disc without slipping, this point lies at the point of contact with the floor, i.e., point A in the diagram, because this is the point where the tangential speed due to rotation exactly cancels out any translational speed resulting in a net velocity of zero. **Conclusion:** Therefore, the correct answer to whether point A is the instant center of zero velocity of the disk at the moment, is: - **True**
Transcribed Image Text:**Rotational Motion of a Rolling Disc** **Problem Statement:** A disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity \( \omega \) is \( 3.0 \, \text{rad/s} \), and the angular acceleration \( \alpha \) is \( 2.0 \, \text{rad/s}^2 \). The radius of the disc is \( r = 1.0 \, \text{m} \). **Diagram Explanation:** The accompanying diagram shows a disc rolling on a horizontal surface. Key elements in the diagram include: - **G**: The center of the disc. - **A**: The point of contact of the disc with the floor at any given instant. - The radius of the disc with the labeled 'r'. - The angular velocity \( \omega \) and angular acceleration \( \alpha \) are indicated by arrows indicating their directions of action. The graphical representation indicates the rotational motion with angular velocity \( \omega \) and angular acceleration \( \alpha \) at the center of the disc (point G) while point A remains in contact with the floor. **Concept Check:** b) Is the following statement true? **Statement:** "Point A shown above is the instant center of zero velocity of the disk at the moment." Options: - True - False **Educational Explanation:** In the context of rotational motion, the instant center of zero velocity is a point on a rigid body undergoing planar motion, which has zero velocity at a particular moment in time. For a rolling disc without slipping, this point lies at the point of contact with the floor, i.e., point A in the diagram, because this is the point where the tangential speed due to rotation exactly cancels out any translational speed resulting in a net velocity of zero. **Conclusion:** Therefore, the correct answer to whether point A is the instant center of zero velocity of the disk at the moment, is: - **True**
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Dynamics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS