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ME202: Mechanics II - Dynamics

Unit 4: Two-Dimensional Kinetics of a Rigid Body   We will now look at how we cause the 2-D rigid body accelerations studied in Unit 3.  As with particles, there are three approaches to these problems: analyzing force and acceleration, analyzing work and energy, and analyzing impulse and momentum. We will also formulate and solve problems to understand the practical implications of theory learned.

Unit 4 Time Advisory
This unit will take you approximately 24 hours to complete.

☐    Subunit 4.1: 11 hours

☐    Subunit 4.1.1: 4 hours

☐    Subunit 4.1.2: 1 hours

☐    Subunit 4.1.3: 2 hours

☐    Subunit 4.1.4: 2 hours

☐    Subunit 4.1.5: 2 hours

☐    Subunit 4.2: 8 hours

☐    Subunit 4.2.1: 3 hours

☐    Subunit 4.2.2: 1 hour

☐    Subunit 4.2.3: 0.5 hour

☐    Subunit 4.2.4: 1 hours

☐    Subunit 4.2.5: 1.5 hours

☐    Subunit 4.2.6: 1 hour

☐    Subunit 4.3: 5 hours

Unit4 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

  • Formulate Moment of Inertia for Rigid bodies.
  • Identify planar kinetic equations of motion, translation, rotation, and general plane motion for rigid bodies. 
  • Identify work and energy and kinetic energy for rigid bodies.
  • Compute work done by a force and work done by a couple for rigid bodies.
  • Identify work and energy principle and conservation of energy for rigid bodies.
  • Identify impulse, momentum, and conservation of momentum for a system of particles.
  • Identify impact and eccentric impact for a system of particles.

4.1 Force and Acceleration   4.1.1 Moment of Inertia   - Reading: Utah State University: Dr. Urroz’s “Moment of Inertia”

Link: Utah State University: Dr. Urroz’s “[Moment of
Inertia](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture21_ENGR2030.htm)”
(PDF)  
    
 Instructions: In this subsection, you will learn how to compute the
moment of inertia needed to compute rotational moment, which is
analogous to mass for translating rigid bodies.  Please click on the
link above, and select the hyperlink for Lecture 21 Summary Lecture
Notes titled “Moment of Inertia,” to open the PDF file.  Read the
entire file (3 pages).  It may be beneficial to take notes as you
read.  
    
 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: Connexions: Sunil Kumar Singh’s “Moment of Inertia of Rigid Bodies” Link: Connexions: Sunil Kumar Singh’s “Moment of Inertia of Rigid Bodies” (PDF)
     
    Also Available In:

    iBooks
     
    Instructions: In this subunit, you will learn how to compute the moment of inertia needed to compute rotational moment, which is analogous to mass for translating rigid bodies.  Click on the link above, and read the entire article.  Take notes as you read this material.
     
    Terms of Use: The article above is released under a Creative Commons Attribution 2.0 License (HTML).  It is attributed to Sunil Kumar Singh and the original versions can be found here (HTML).

  • Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Mass Moment of Inertia” Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Mass Moment of Inertia” (PDF)
     
    Instructions: In this subunit, you will learn how to compute the moment of inertia needed to compute rotational moment, which is analogous to mass for translating rigid bodies.  Please read the entire webpage linked above, and then click on the links for “Example 1,” “Example 2,” and “Example 3.”  Try to work through each of these examples, and review their solutions.
     
    Terms of Use: The linked material above has been reposted by the kind permission of Mehrdad Negahban, and can be viewed in its original form here.  Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

  • Reading: Connexions: Sunil Kumar Singh’s “Moment of Inertia of Rigid Bodies-Applications” Link: Connexions: Sunil Kumar Singh’s “Moment of Inertia of Rigid Bodies-Applications” (PDF)
     
    Also Available In:

    iBooks
     
    Instructions: In this subunit, you will learn how to apply the moment of inertia needed to compute rotational moment, which is analogous to mass for translating rigid bodies.  Click on the above link, and read the entire webpage.  Take notes as you read this material.
     
    Terms of Use: The article above is released under a Creative Commons Attribution 2.0 License (HTML).  It is attributed to Sunil Kumar Singh and the original versions can be found here (HTML).

4.1.2 Planar Kinetic Equations of Motion   - Reading: Utah State University: Dr. Urroz’s “Planar Kinetic Equations of Motion” Link: Utah State University: Dr. Urroz’s “Planar Kinetic Equations of Motion” (PDF)
 
Instructions: This subunit deals with translation, rotational, and general plane motion of rigid bodies.  Please click on the link above, and select the link for Lecture 22, titled “Planar Kinetic of Motion,” to open the PDF file.  Read the section titled “Planar Kinetic of Motion.”

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Planar Kinetic Equations of Motion” Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Equations for Two Dimensional Motion” (PDF)
     
    Instructions: The problems in this subunit will help you to understand the equation of motion for rigid bodies.  Please read the text on the webpage, and click on the links for “Example 1,” “Example 2,” “Example 3,” and “Example 4.”  Try to work through these examples, and then review their solutions.
     
    Terms of Use: The linked material above has been reposted by the kind permission of Mehrdad Negahban, and can be viewed in its original form here. Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

4.1.3 Translation   - Reading: Utah State University: Dr. Urroz’s “Translation”

Link: Utah State University: Dr. Urroz’s
“[Translation](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture22_ENGR2030.htm)”
(PDF)  
    
 Instructions: This subunit deals with the motion of rigid bodies
along straight paths.  Please click on the link above, and then
select the hyperlink for Lecture 22, titled “Planar Kinetic
Equations of Motion / Translation,” to open the PDF file.  Read the
section titled “Equations of Motion: Translation.”  
    
 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body Translation” Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body ranslation” (YouTube)
     
    Also Available in:  iTunes U
     
    Instructions:  This video will help you understand motion of rigid bodies along straight paths.  Please click on the link above, and watch the video, which will introduce you to translation.  It may also help to take notes while watching the video.  The video may be a little choppy, but it will help you understand the material that you have studied in this section. Please watch the entire video (1 hour 18 minutes).

    Terms of Use: The linked material above has been reposted by the kind permission of Kenneth S. Manning, PhD, Professor of Engineering at SUNY Adirondack, and the original version can be found here. Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

4.1.4 Rotation about a Fixed Axis   - Reading: Utah State University: Dr. Urroz’s “Rotation about a Fixed Axis”

Link: Utah State University: Dr. Urroz’s “[Rotation about a Fixed
Axis](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture23_ENGR2030.htm)”
(PDF)  
    
 Instructions: This subunit deals with the motion of rigid bodies
around an axis.  Please click on the link above, and select the
hyperlink for Lecture 23, titled “Planar Kinetics – Rotation About a
Fixed Axis” to open the PDF file.  Read the entire 1-page file.  
    
 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body Rotation” Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body Rotation” (YouTube)
     
    Also Available in:  iTunes U
     
    Instructions:  This video will help you understand motion of rigid bodies around an axis.  Please click on the link above, and watch the video, which will introduce you to rotation.  It may also help to take notes while watching the video.  The video may be a little choppy, but it will help you understand the material that you have studied in this section.  Please watch the entire video (1 hour 10 minutes).

    Terms of Use: The linked material above has been reposted by the kind permission of Kenneth S. Manning, PhD, Professor of Engineering at SUNY Adirondack, and the original version can be found here. Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

4.1.5 General Plane Motion   - Reading: Utah State University: Dr. Urroz’s “General Plane Motion”

Link: Utah State University: Dr. Urroz’s “[General Plane
Motion](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture24_ENGR2030.htm)”
(PDF)  
    
 Instructions: This subunit summarizes the overall equations of
motion, including translation and rotation into one.  Please click
on the link above, and then select the hyperlink for Lecture 24
Notes, titled “Planar Kenetics Equations of Motion- General Plane
Motion,” to open the PDF file.  Read the entire 1-page file.  
    
 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics General Motion” Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics General Motion” (YouTube)
     
    Also Available in:  iTunes U
     
    Instructions:  This video summarizes the overall equations of motion, including translation and rotation into one.  Please click on the link above, and watch the video, which will introduce you to general motion.  It may also help to take notes while watching the video.  The video may be a little choppy, but it will help you understand the material that you have studied in this section.  Please watch the entire video (1 hour 21 minutes).

    Terms of Use:  The linked material above has been reposted by the kind permission of Dr. Kenneth Manning and can be viewed in its original form here.  Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

4.2 Work-Energy Principle for Rigid Bodies   4.2.1 Work and Energy   - Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Work Energy Relation for a Rigid Body” Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Work Energy Relation for a Rigid Body” (PDF)
 
Instructions: This subunit deals with how to compute work and energy for rigid bodies subjected to force and displacement.  This is a technique to analyze mechanics of rigid bodies in addition to Newton’s law of motion. Please click on the link above, and read the entire webpage.  Pay particular attention to Examples 1 through 5.  Take notes as your read this material.
 
Terms of Use: The linked material above has been reposted by the kind permission of Mehrdad Negahban, and can be viewed in its original form here.  Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.