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Mechanics II - Dynamics

Purpose of Course  showclose

Dynamics is a sub-branch of the general field of study known as Mechanics.  It is very closely related to—and often combined with—the study of Statics, which you encountered in ME102: Mechanics I.

In both Statics and Dynamics, we use Newton’s 2nd Law: F = ma.  In Statics, the sum of the applied forces is always zero, thus making the acceleration zero.  This was very important to the structures studied in Statics.  Catastrophe generally results when structures (like bridges and buildings) accelerate.  Very likely you are quite pleased—even if you do not realize it every time—when you cross a bridge that does not accelerate while you are on it, and we have Newton’s First Law to thank for it.  Newton’s First Law states that objects will continue to do what they are doing unless unbalanced forces make them do otherwise.  This law includes the law equilibrium condition that the moments will also sum to zero, and that there will thus be no rotational acceleration.  In Dynamics, the sum of the forces will not necessarily be zero (if it is zero, then the sum of the moments is not).  We will thus study accelerated motion.

As with PHYS101: Introduction to Mechanics, we will begin this course by studying the accelerated motion of particles (also known as the Kinematics of Particles).  We will only look at what an object is doing (the position, velocity, acceleration)—not why it might be doing that.

In Unit 2, we will take a look at the Kinetics of Particles, or the study of the why of Kinematics.  We will want to know how to change the velocity of a particle in order to learn what causes accelerations.

We will then take a step towards the more realistic by considering the size, shape, and orientation of objects as they accelerate.  We term this type of motion “Rigid Body Motion.”  We begin, in Unit 3, with the Kinematics of Rigid Bodies, looking first at the rotational motion of objects.  We will then introduce the possibility that objects can move (and accelerate) translationally and rotationally at the same time.  In Unit 4, we will look at sample problems that will help you understand the concepts learned in Unit 1, Unit 2, and Unit 3. Next, in Unit 5, we study the Kinematics of such motion.

In Unit 6, we will look at many of the principles we learned in the first few units-this time, in three-dimensions.  We will begin with the three-dimensional Kinematics of a Rigid Body and then finish with three-dimensional Kinetics.

We will complete our study of Dynamics with Unit 7, a look at Vibrational Motion, or what happens when objects oscillate about a neutral state. In Unit 4, we will look at sample problems that will help you understand the concepts learned in Unit 5, Unit 6, and Unit 7.

Course Information  showclose

Welcome to ME202: Mechanics II - Dynamics. General information about the course and its requirements can be found below.
 
Course Designer: Ron Agarwala and Dr. Kenneth S. Manning, Ph.D. 

Primary Resources: This course is comprised of a range of different free, online materials.  However, the course makes primary use of the following:
Requirements for Completion: The course requires that you read all assigned lecture materials and watch all related web media.  Pay attention to example problems and how the theory is applied to real-world problems.
 
You need to obtain 70% or above in the final exam to “pass” the course.  You will be notified of your grade immediately upon taking and submitting the final exam.  If you do not pass the exam, you may take it again.
 
Time Commitment: This course should take you a total of 95 1/2 hours to complete.  The course also contains unit and subunit time advisories.  Please plan your time effectively.
 
Tips/Suggestions: This course is a very important one in the ME discipline.  Take your time, go through the course material, and take notes as you go along.

Learning Outcomes  showclose

Upon successful completion of this course, the student will be able to:

  • Formulate rectilinear and curvilinear motion in one-dimension.
  • Solve projectile motion problems.
  • Identify and solve problems with normal, tangential, and cylindrical components for curvilinear motion in one-dimension.
  • Formulate relative motion of two particles and relative motion using translating axes for particles in one-dimension.
  • Identify Newton’s second law.
  • Identify equations of motion for a system of particles in one-dimension.
  • Identify equations of motion in rectangular, normal, tangential, and cylindrical components in one-dimension.
  • Identify orbital motion and space mechanics.
  • Solve work, energy, power, and efficiency for particles and systems of particles in one-dimension. 
  • Identify energy, potential energy, and conservation of energy for particles and systems of particles in one-dimension.
  • Identify impulse, momentum, and conservation of momentum for particles and systems of particles in one-dimension.
  • Identify angular momentum, angular impulse, and impact for particles and systems of particles in one-dimension.
  • Identify translation and rotation of rigid bodies in two-dimensions. 
  • Identify absolute and relative motion analysis in two-dimensions. 
  • Identify Instantaneous Center of Zero Velocity. 
  • Identify acceleration and rotating axes in two-dimensions.
  • Formulate Moment of Inertia for Rigid bodies.
  • Identify planar kinetic equations of motion, translation, rotation, and general plane motion for rigid bodies. 
  • Identify work, 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 principles 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.
  • Identify kinematics of rigid bodies in three-dimensions.
  • Identify general motion and relative motion in three-dimension. 
  • Identify angular motion and kinetic energy in three-dimension. 
  • Identify undamped free and force vibrations.
  • Identify viscous damped free and forced vibrations.  

Course Requirements  showclose

In order to take this course, you must:

√    Have access to a computer.

√    Have continuous broadband Internet access.

√    Have the ability/permission to install plug-ins or software (e.g.  Adobe Reader or Flash).

√    Have Internet explorer.

√    Have the ability to download and save files and documents to a computer.

√    Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).

√    Be competent in the English language.

√    Have read the Saylor Student Handbook.

√    Have completed all the required mathematics courses for the mechanical engineering discipline, including: ME001/MA101, ME002/MA102ME003/MA221

√    Have completed the following required science course for the mechanical engineering discipline: ME005/PHYS101

√    Have completed the following mechanical engineering courses as prerequisites listed in “The Core Program” of the mechanical engineering discipline, including: ME101 and ME102

Unit Outline show close


Expand All Resources Collapse All Resources
  • Unit 1: Kinematics of Particles  

    In this first unit, we will look at the motion of particles.  We are specifically concerned with the position, velocity, and acceleration of objects.  To keep things from getting cloudy, as we consider each object (whether a car, a space shuttle, or a molecule), we will only pay attention to where that object is, not how it is orientated or where it is pointing.           

    Initially, we will consider one-dimensional motion alone.  Consider an everyday example: as you drive along the highway, you have the option of going in only one direction.  You can come back by the same highway, but you are still on one single straight-line path. We will also formulate and solve problems to understand the practical implications of theory learned.

    Unit 1 Time Advisory   show close
    Unit 1 Learning Outcomes   show close
  • 1.1 Rectilinear Kinematics: Continuous Motion  
    • Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Rectilinear Motion”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Rectilinear Motion” (PDF)
       
      Instructions: Rectilinear kinematics involves the motion of particles in a straight line.  Please read the entire webpage linked above, which will introduce you to rectilinear motion.  This reading will give you a general understanding of motion of particles in one-dimension along a straight line.  Make sure to go over Examples 1 through 6 to understand the practical applications of rectilinear motion; you may access these examples by clicking on the hyperlinks for each.  It may also help to take notes while read this section.
       
      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 “Rectilinear Motion” and “Rectilinear Motion-Application”

      Links: Connexions: Sunil Kumar Singh’s “Rectilinear Motion” (PDF) and “Rectilinear Motion-Application” (PDF)
       
      Also Available In:
      iBooks
       
      Instructions: Rectilinear kinematics involves the motion of particles in a straight line.  Please click on both links above, and read each of these articles, which will introduce you to rectilinear motion, in their entirety.  These readings will provide you with a general understanding of motion of particles in one-dimension along a straight line.  Pay particular attention to Example 1 for the “Rectilinear Motion” and Examples 1 through 4 of the “Rectilinear Motion-Application” reading to understand the practical applications of rectilinear motion.  It may also help to take notes while reading these sections.
       
      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)

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rectilinear Coordinates”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rectilinear Coordinates” (YouTube)

      Also Available in: iTunes U

      Instructions: Rectilinear kinematics involves the motion of particles in a straight line.  Please click on link above, and watch the video, which will introduce you to rectilinear motion.  The video will provide you with a general understanding of motion of particles in one-dimension along a straight line.  Pay particular attention to Example problems solved on the board by the professor.  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.  The video will take around 1 hour and 20 minutes to watch.

      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.

  • 1.2 General Curvilinear Motion  
  • 1.2.1 Curvilinear Motion-Rectangular Components  
    • Reading: Utah State University: Dr. Urroz’s “Lecture 3A- Curvilinear Motion in Cartesian Coordinates”

      Link: Utah State University: Dr. Urroz’s “Lecture 3A- Curvilinear Motion in Cartesian Coordinates” (PDF)
       
      Instructions: Curvilinear motion involves the motion of particles along a curved path. In this section we will examine curvilinear motion and its components along x, y, and z direction.  Please click on the link above, and select the link for Lecture 3A, titled “Curvilinear motion in Cartesian Coordinates,” to open the PDF file.  Read the sections of the lecture titled “General Curvilinear Motion” and “Curvilinear Motion: General and Rectangular Components.”  Please take notes as you read this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Curvilinear Motion”

      Link: Real-world-physics-problems.com: “Curvilinear Motion” (HTML)
       
      Instructions: Curvilinear motion involves the motion of particles along a curved path.  In this section, we will examine curvilinear motion and its components along x, y, and z direction.  Please click on the link above, and read the entire webpage.  Please read the example problem at the bottom of the webpage.  Please make sure to take notes while you read.
       
      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 “Curvilinear Motion -Rectangular Coordinates”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Curvilinear Motion-Rectangular Coordinates” (PDF)
       
      Instructions: Curvilinear motion involves the motion of particles along a curved path.  The examples here will help you understand practical applications of curvilinear motion.  Please click on the links for “Example 1,” “Example 2,” and “Example 3,” and attempt the example problems; you may review the solutions after you try each problem.
       
      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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Curvilinear Motion”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Curvilinear Motion” (YouTube)

      Also Available in: iTunes U
       
      Instructions: Curvilinear motion involves the motion of particles along a curved path.  Please click on link above, and watch the video, which will introduce you to curvilinear 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.  The first 18 minutes of the video explains curvilinear motion.

      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.

  • 1.2.2 Motion of a Projectile  
    • Reading: Utah State University: Dr. Urroz’s “Lecture 3B - Projectile Motion”

      Link: Utah State University: Dr. Urroz’s “Lecture 3B - Projectile Motion” (PDF)
       
      Instructions: Motion of a projectile deals with curvilinear motion acted upon by gravity.  For instance, motion of rockets or missiles is considered as projectiles.  Please click on the link above, and then select the hyperlink for Lecture 3B, titled “Projectile Motion,” to open the PDF file.  Read the section titled “Motion of a Projectile.”  It may be beneficial to take notes as you read this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Projectile Motion”

      Link: Real-world-physics-problems.com: Projectile Motion” (HTML)
       
      Instructions: Motion of a projectile deals with curvilinear motion acted upon by gravity.  For instance, motion of rockets or missiles is considered as projectiles.  Please click on the link above. and read the entire webpage.  Please take notes while reviewing this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Projectile Motion Example-The Physics of Volleyball”

      Link: Real-world-physics-problems.com: “Projectile Motion Example-The Physics of Volleyball” (HTML)
       
      Instructions: Motion of a projectile deals with curvilinear motion acted upon by gravity.  Physics of Volleyball is a great example of projectile motion.  Please go through the example to see how projectile motion and its equations can be applied to the real world.  Please click on the link above, and read the entire webpage.  Please take notes while reading this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Lecture: YouTube: The Saylor Foundation: Ken Mannings’s “Projectile Motion”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Projectile Motion” (YouTube)
       
      Instructions: Please continue watching the video titled “Dynamics Curvilinear Motion” after 18 minutes. Motion of a projectile deals with curvilinear motion acted upon by gravity.  For instance, motion of rockets or missiles is considered as projectiles. Please click on link above, and watch the video, which will introduce you to projectile 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 pay attention to the problems solved by the professor on the board.  Watch the video from 18 minutes to the end of the video.

      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.

  • 1.2.3 Normal and Tangential Components  
    • Reading: Utah State University: Dr. Urroz’s “Curvilinear Motion: Normal and Tangential Components”

      Link: Utah State University: Dr. Urroz’s “Curvilinear Motion: Normal and Tangential Components” (PDF)
       
      Instructions: Curvilinear motion can be further broken down into normal (acting towards the center of the curve) or tangential components (perpendicular to normal).  Click on the link above, and then select the hyperlink for Lecture 4, titled “Curvilinear Motion: Normal and Tangential Components,” to open the PDF file.  Read the section titled “Curvilinear Motion: Normal and Tangential Components.”  It may be beneficial to take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Wikipedia: “Normal and Tangential Components”

      Link: Wikipedia: “Normal and Tangential Components” (PDF)
       
      Instructions: Curvilinear motion can be further broken down into normal (acting towards the center of the curve) or tangential components (perpendicular to normal).  Please click on the link above to go to the Wikipedia article, and then read the entire webpage.  Please take notes on this topic as you read this article.
       
      Terms of Use: The article above is released under a Creative Commons Attribution-Share-Alike License 3.0 (HTML).  You can find the original Wikipedia version of this article here (HTML).

    • Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Normal and Tangential Coordinates”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Normal and Tangential Coordinates” (PDF)
       
      Instructions: Curvilinear motion can be further broken down into normal (acting towards the center of the curve) or tangential components (perpendicular to normal).  The problems here will help you understand curvilinear motion problems broken down into normal and tangential components from a practical viewpoint.  Please click on the hyperlinks for “Example 1,” “Example 2,” and “Example 3,” and read the example problems.  You may want to attempt solving the problems, and then check your answers against the 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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Normal Coordinates”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Normal Coordinates” (YouTube)
       
      Also Available in: iTunes U
       
      Instructions:  Although the video is titled “Dynamics Normal Coordinates”, the theme of the lecture is “Normal and Tangential components”.  Curvilinear motion can be further broken down into normal (acting towards the center of the curve) or tangential components (perpendicular to normal). Please click on link above, and watch the video, which will introduce you to normal and tangential components.  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 pay attention to the problems solved by the professor on the board. The video is about 1 hour 15 minutes long.

      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.

  • 1.2.4 Cylindrical Components  
    • Reading: Utah State University: Dr. Urroz’s “Curvilinear Motion: Cylindrical Components”

      Link: Utah State University: Dr. Urroz’s “Curvilinear Motion: Cylindrical Components” (PDF)
       
      Instructions: Cylindrical coordinates are another alternative to express curvilinear motion in addition to normal and tangential component.  Please click on the link above, and then select the hyperlink for Lecture 5, titled “Curvilinear Motion: Cylindrical Components,” to open the PDF file.  Read the section titled and “Curvilinear Motion: Cylindrical Components.”
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamic Polar Coordinates”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamic Polar Coordinates” (YouTube)
       
      Also Available in: iTunes U
       
      Instructions: Cylindrical coordinates are another alternative to express curvilinear motion in addition to normal and tangential component. Polar coordinates are subclass of cylindrical coordinates without the “z” direction. Please click on link above, and watch the video, which will introduce you to cylindrical/polar coordinates.  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 pay attention to the problems solved by the professor on the board. The video is about 1 hour 16 minutes long.

      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.

  • 1.3 Relative Motion  
  • 1.3.1 Relative Motion-Dependent Motion of Two Particles  
    • Reading: Utah State University: Dr. Urroz’s “Absolute Dependent Motion"

      Link: Utah State University: Dr. Urroz’s “Absolute Dependent Motion” (PDF)
       
      Instructions: Please click on the link above, and then select the hyperlink for Lecture 6A, titled “Absolute Dependent Motion,” to open the PDF file.  Read the through the entire lecture.  

      Note: When there are two particles in a problem, and we are concerned with how they move in relation to each other, we call it “relative motion.”  Their individual motions might be dependent on one another, as when they are connected somehow, or their motions might be completely independent of one another.  It may help to take notes as you read this material.

      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Connexions: Sunil Kumar Singh’s “Relative Velocity in One Dimension” and “Relative Velocity in One Dimension (Application)”

      Links: Connexions: Sunil Kumar Singh’s “Relative Velocity in One Dimension” (PDF) and “Relative Velocity in One Dimension (Application)” (PDF)
       
      Instructions: When there are two particles in a problem, and we are concerned with how they move in relation to each other, we call it “relative motion.”  Their individual motions might be dependent on one another, as when they are connected somehow, or their motions might be completely independent of one another.  Please click on the above links, and read each PDF in its entirety.  For the “Relative Velocity in One Dimension Application” reading, pay particular attention to Examples 1 through 6.  It may help to take notes as you read these webpages.
       
      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 and here (HTML). 

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Relative Motion”

      Link: YouTube: Saylor Foundation: Ken Manning’s “Dynamics Relative Motion” (YouTube)
       
      Also Available in: iTunes U
       
      Instructions:  When there are two particles in a problem, and we are concerned with how they move in relation to each other, we call it “relative motion.”  Their individual motions might be dependent on one another, as when they are connected somehow, or their motions might be completely independent of one another.  Please click on the link above, and watch the video, which will introduce you to relative 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 pay attention to the problems solved by the professor on the board.  The video is about 1 hour 8 minutes long.

      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.

  • 1.3.2 Relative-Motion Using Translating Axes  
    • Reading: Utah State University: Dr. Urroz’s “Relative Motion With Translating Axes"

      Link: Utah State University: Dr. Urroz’s “Relative Motion With Translating Axes” (PDF)
       
      Instructions: The reading in this subunit deals with relative motion of two particles, where the frame of reference of the particle’s motion moves relative fixed frame of reference.  Please click on the link above, and then select the hyperlink for Lecture 6B, titled “Relative Motion With Translating Axes,” to open the PDF file.  Read through the entire lecture.  Please take notes as you read this material
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Unit 2: Kinetics of a Particle  

    So far, we have only been concerned with what a particle is doing, i.e. what is the particle’s position?  What is its velocity? What is its acceleration?  We have not yet asked “How do particles get that acceleration?  How do we make particles accelerate in certain ways?”
               
    In this unit, we will use three methods to answer those questions (and others).  These three methods are really three ways of looking at Newton’s 2nd Law  [ ∑F = ma ] but each will allow us to solve certain types of problems in very efficient ways.  One of the methods can in fact save your life. We will also formulate and solve problems to understand the practical implications of theory learned.

    Unit 2 Time Advisory   show close
    Unit 2 Learning Outcomes   show close
  • 2.1 Force and Acceleration  
  • 2.1.1 Newton’s Second Law of Motion  
    • Reading: Utah State University: Dr. Urroz’s “Newton’s Equations of Motion”

      Link: Utah State University: Dr. Urroz’s “Newton’s Equations of Motion” (PDF)
       
      Instructions: Please click on the link above, and then select the hyperlink for Lecture 7A, titled “Newton’s Equations of Motion” to open the PDF file.  Read the section titled “Newton’s Laws of Motion.”
                 
      Newton’s Second Law is the first of three methods we will use to solve the very reasonable question: “How do we get a particle to accelerate in a particular way?”  This method works for very general problems.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Newton’s Law of Motion”

      Link: Real-world-physics-problems.com: “Newton’s Law of Motion” (HTML)
       
      Instructions: Please click on the link above, and read the entire webpage.  This lecture will introduce you to Newton’s Equation of Motion.  Please take notes as you read this section.
       
      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 Particle Linear Kinetics”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Particle Linear Kinetics” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video is titled “Dynamics Particle Linear Kinetics” but the theme here is Newton’s Second Law which is the first of three methods we will use to solve the very reasonable question: “How do we get a particle to accelerate in a particular way?”  This method works for very general problems.  Please click on link above, and watch the video, which will introduce you to Newton’s Second Law.  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 pay attention to the problems solved by the professor on the board.  Please watch the entire video (1 hour 20 minutes).  This video will also help you understand sections 2.12 through 2.14.

      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.

  • 2.1.2 Newton’s Second Law-The Equation of Motion  
  • 2.1.3 Equation of Motion for a System of Particles  
  • 2.1.4 Rectangular Coordinates  
    • Reading: Utah State University: Dr. Urroz’s “Equations of Motion in Rectangular Coordinates”

      Link: Utah State University: Dr. Urroz’s “Equations of Motion in Rectangular Coordinates” (PDF)
       
      Instructions: In this subunit, the motion of the particle will be expressed in Cartesian coordinate system.  Cartesian coordinate systems are also commonly referred to as coordinates along “X” and “Y” directions in two-dimensions and “X”, “Y”, and “Z” directions in three-dimensions.  Please click on the link above, and select the hyperlink for Lecture 7B, titled “Equations of Motion in Rectangular Coordinates,” to open the PDF file.  Read the section titled “Equation of Motion: Rectangular Coordinates.”  It may also help to take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 2.1.5 Normal and Tangential Coordinates  
    • Reading: Utah State University: Dr. Urroz’s “Normal and Tangential Coordinates”

      Link: Utah State University: Dr. Urroz’s “Normal and Tangential Coordinates” (PDF)
       
      Instructions: This subunit deals with equation of motion in normal and tangential components like curvilinear motion.  This will help you analyze accelerations and forces in normal and tangential direction.  Please click on the link above, and then select the link to Lecture 8, titled “Equations of Motion in Normal- Tangential Coordinates,” to open the PDF file.   Read the section titled “Equations of Motion: Normal and Tangential Coordinates.”  It may help to take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 2.1.6 Cylindrical Coordinates  
    • Reading: Utah State University: Dr. Urroz’s “Cylindrical Coordinates”

      Link: Utah State University: Dr. Urroz’s “Cylindrical Coordinates” (PDF)
       
      Instructions: In addition to analyzing forces in normal and tangential direction, this subunit will help you analyze equations of motion in the radial, traverse, and z direction.  Please click on the link above, and then select the hyperlink for Lecture 9, titled “Equations of Motion in Cylindrical Coordinates,” to open the PDF file.  Read the section titled “Equations of Motion: Cylindrical Coordinates.”  It may help to take notes as you read.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 2.1.7 Orbital Motion and Space Mechanics  
  • 2.2 Work and Energy  
  • 2.2.1 Work Done by a Force  
    • Reading: Utah State University: Dr. Urroz’s “Work Done by a Force”

      Link: Utah State University: Dr. Urroz’s “Work Done by a Force” (PDF)
       
      Instructions: Please click on the link above, and then select the hyperlink for Lecture 10, titled “Work of a Force / Principles of Work and Energy,” to open the PDF file.  Read the section titled “Work of a Force.”
          
      Note: This is our second method for solving kinetics problems.  This works quite well when either the forces or the problem itself are position-dependent.  Make sure to take notes while reading this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Connexions: Sunil Kumar Singh’s “Work”

      Link: Connexions: Sunil Kumar Singh’s “Work” (PDF)
       
      Also Available In:
      iBooks
       
      Instructions: This section deals with work and work done by a constant and variable force.  Click on the link above, and read the entire article.  Please pay particular attention to working through problems 1 through 3 to understand the practical application.  Make sure to take notes as you read.
       
      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 version can be found here (HTML).

    • Reading: Real-world-physics-problems.com: “Work”

      Link: Real-world-physics-problems.com: “Work” (HTML)
       
      Instructions: This section deals with work and work done by a constant and variable force.  Click on the link above, and read the section titled “Work Done on a Particle.”  Please take notes as you read this section.
       
      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 Work and Energy 1””

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Work and Energy 1” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video is titled “Dynamics Work and Energy 1” and covers material related to Work and Energy and specifically work done by a Force.  This is our second method for solving kinetics problems.  This works quite well when either the forces or the problem itself are position-dependent.  Please click on the link above, and watch the video, which will introduce you to the work and energy approach and the work done by a force.  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 17 minutes).  This video will also help you understand sections 2.2.2 through 2.2.3.

      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.

  • 2.2.2 Work and Energy Principle  
    • Reading: Utah State University: Dr. Urroz’s “Work and Energy Principle”

      Link: Utah State University: Dr. Urroz’s “Work and Energy Principle” (PDF)
       
      Instructions: This subunit will help you understand the work and energy balance of a particle.  Please click on the link above, and then select the hyperlink for Lecture 10 Notes Summary, titled “Work / Principle of Work and Energy,” to open the PDF file.  Read the section titled “Principle of Work and Energy.”  Please take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Connexions: Sunil Kumar Singh’s “Work and Energy”

      Link: Connexions: Sunil Kumar Singh’s “Work and Energy” (PDF)
       
      Also Available In:
      iBooks

      Instructions: This reading will help you to understand the work and energy balance of a particle.  Click on the link above, and read the sections titled “Energy” and “Work and Kinetic Energy.”  Please take notes as you read through 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 “Work-Energy Relation”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Work-Energy Relation” (PDF)
       
      Instructions: The problems here will help you understand work, energy, and interactions between them.  Please click on the links for “Example 1,” “Example 2,” “Example 3,” “Example 4,” and “Example 5,” and read through the example problems.  Try to attempt the problems, 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.

  • 2.2.3 Work and Energy Principle for a System of Particles  
    • Reading: Utah State University: Dr. Urroz’s “Work and Energy Principle for a System of Particles”

      Link: Utah State University: Dr. Urroz’s “Work and Energy Principle for a System of Particles” (PDF)
       
      Instructions: This reading will help you to understand the work and energy balance of a system of particles.  Please click on the link above, and select the link for Lecture 10 Notes Summary, titled “Work / Principle of Work and Energy,” to open the PDF file.  Read the section titled “Principle of Work and Energy for a System of Particles.”
       
      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 Work Energy 2”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Work Energy 2"  (YouTube)
       
      Also Available in: iTunes U
       
      Instructions:  The title of the video is “Dynamics Work Energy 2” and it covers Work and Energy related to particles and System of Particles.  This is our second method for solving kinetics problems.  This works quite well when either the forces or the problem itself are position-dependent.  Please click on link above, and watch the video, which will introduce you to the work and energy approach and the work donefor a system of particles.  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 16 minutes), which is based on problem solving on its entirety.

      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.

  • 2.2.4 Power and Efficiency  
    • Reading: Utah State University: Dr. Urroz’s “Power and Efficiency”

      Link: Utah State University: Dr. Urroz’s “Power and Efficiency” (PDF)
       
      Instructions: Power deals with capacity of machine or device while efficiency deals with how the machine or devices executes this capacity. Please click on the link above, and then select the hyperlink under Slide Lecture Notes titled “Power and Efficiency,” to open the PDF file.  Read the section entire lecture.  Make sure you take notes as you read.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 2.2.5 Conservative Forces and Potential Energies  
    • Reading: Utah State University: Dr. Urroz’s “Conservative Forces and Potential Energies”

      Link: Utah State University: Dr. Urroz’s “Conservative Forces and Potential Energies” (PDF)
       
      Instructions: This subunit deals with how energy is stored in device and system along certain paths.  Energy stored in an extended or compressed spring is considered potential energy.  Please click on the link above, and then select the link under Slide Lecture Notes titled “Conservative Forces & Potential Energy,” to open the PDF file.  Read the entire lecture.  Make sure 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 “Conservative Force” and “Potential Energy”

      Links: Connexions: Sunil Kumar Singh’s “Conservative Force” (PDF) and “Potential Energy” (PDF)
       
      Also Available In:
      iBooks (First Reading)
      iBooks (Second Reading)
       
      Instructions:  This subunit deals with how energy is stored in device and system along certain paths.  Click on the links above, and read each of these articles in their entirety.  Pay particular attention to Example 1 for the “Conservative Force” reading.  Make sure to take notes as you read.

      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 and here (HTML)

    • Reading: University of Nebraska-Lincoln: Dr. M. Negahban’s “Potential Energy”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Potential Energy” (PDF)
       
      Instructions: The problems here will help you understand how potential energy is computed and conserved.  Please read the entire webpage, and also click on the links for “Example 1,” “Example 2,” and “Example 3.”  You may want to attempt these examples before reviewing the 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.

  • 2.2.6 The Conservation of Energy  
    • Reading: Utah State University: Dr. Urroz’s “The Conservation of Energy ”

      Link: Utah State University: Dr. Urroz’s “The Conservation of Energy” (PDF)
       
      Instructions: This subunit deals with how energy balance is maintained when it is converted from one form to another.  Please click on the link above, and then select the hyperlink for Lecture 12, titled “Conservation Forces/ Potential Energy/Conservation of Energy,” to open the PDF file.  Read the section titled “Conservation of Energy.”  It may also help 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 “Conservation of Energy”

      Link: Connexions: Sunil Kumar Singh’s “Conservation of Energy” (PDF)
       
      Instructions: This subunit deals with how energy balance is maintained when it is converted from one form to another.  Click on the link above, and read the entire article.  Please 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)

  • 2.3 Impulse and Momentum  
  • 2.3.1 Linear Impulse and Momentum Principle  
    • Reading: Utah State University: Dr. Urroz’s “Linear Impulse and Momentum Principle”

      Link: Utah State University: Dr. Urroz’s “Linear Impulse and Momentum Principle” (PDF)
       
      Instructions: Impulse is the action of a force for a short period of time, while momentum deals with the product of mass and velocity of a particle (how much energy is there).  Please click on the link above, and then select the hyperlink for Lecture 13, titled “Linear Impulse and Momentum / Conservation of Momentum,” to open the PDF file.  Read the section titled “Principle of Linear Impulse and Momentum.”

      Note: This is our third method for solving these kinetics problems.  This one works best when the forces and/or the problem are time-dependent.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Impulse and Momentum”

      Link: Real-world-physics-problems.com: “Impulse and Momentum” (HTML)
       
      Instructions: Impulse is the action of a force for a short period of time, while momentum deals with the product of mass and velocity of a particle (how much energy is there).  Please click on the link above, and read entire webpage.  Take notes while reading this section.
       
      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 Linear Momentum”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Linear Momentum” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  Impulse is the action of a force for a short period of time, while momentum deals with the product of mass and velocity of a particle (how much energy is there).  Please click on the link above, and watch the video, which will introduce you to linear momentum.  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 4 minutes).  This video will also help you understand sections 2.32 through 2.33.

      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.

  • 2.3.2 Impulse and Momentum for a System of Particles  
  • 2.3.3 Conservation of Momentum for a System of Particles  
  • 2.3.4 Impact/Collision  
    • Reading: Utah State University: Dr. Urroz’s “Impact”

      Link: Utah State University: Dr. Urroz’s “Impact” (PDF)
       
      Instructions: This subunit will help you understand the mechanics of motion when two bodies collide for a short period of time.  Please click on the link above, and then select the hyperlink for Lecture 14, titled “Impact (collisions),” to open the PDF file.  Read the entire file (2 pages).
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Elastic Collision”

      Link: Real-world-physics-problems.com: “Elastic Collision” (HTML)
       
      Instructions: This reading will help you to understand the mechanics of motion when two bodies collide for a short period of time.  Please click on the link above, and read entire webpage.  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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Impact”

      Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Impact” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video will help you understand the mechanics of motion when two bodies collide for a short period of time.  Please click on link above, and watch the video, which will introduce you to impact.  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 19 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.

  • 2.3.5 Angular Momentum  
    • Reading: Utah State University: Dr. Urroz’s “Angular Momentum”

      Link: Utah State University: Dr. Urroz’s “Angular Momentum” (PDF)
       
      Instructions: This reading will help you to understand the moment of a particle’s linear momentum.  Please click on the link above, and select the hyperlink for Lecture 15, titled “Angular Momentum/Moment & Angular Momentum/Conservation,” to open the PDF file.  Read the section titled “Angular Momentum.”  Take notes as you read this material.
       
      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 Angular Momentum”

      Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Angular Momentum” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video will help you understand the moment of a particle’s linear momentum.  Please click on the link above, and watch the video, which will introduce you to angular momentum.  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 13 minutes).  This section will also help you understand section 2.36.

      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.

  • 2.3.6 Principle of Angular Impulse and Momentum  
    • Reading: Utah State University: Dr. Urroz’s “Angular Impulse and Momentum Principle”

      Link: Utah State University: Dr. Urroz’s “Angular Impulse and Momentum Principle” (PDF)
       
      Instructions: This subunit discusses how angular impulse and momentum are related and conserved.  Please click on the link above, and select the link for Lecture 15, titled “Angular Momentum/Moment & Angular Momentum/Conservation,” to open the PDF file.  Read the section titled “Angular Impulse and Momentum Principles.” Take notes while reading this section.
       
      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 “Impulse-Momentum Relation”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Impulse-Momentum Relation” (PDF)
       
      Instructions: The problems here will help you to understand how impulse and momentum are computed and how they are related.  Please click on the links for “Example 1,” “Example 2,” “Example 3,” and “Example 4.”  Review these problems; you may consider attempting these exercises and then checking your answers against the 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.

  • Unit 3: Two-Dimensional Kinematics of a Rigid Body  

    In the first two units, we studied objects as single points, without any particular orientation.  We will now abandon this simplified view and study full objects.  As with particle dynamics, we will begin with a look at the kinematics of rigid bodies, but will not consider 1-D motion since these objects (and the points on them) exist in at least 2-D (in a plane). We will also formulate and solve problems to understand the practical implications of theory learned. 

    Unit 3 Time Advisory   show close
    Unit 3 Learning Outcomes   show close
  • 3.1 Rigid Body Kinematics  
  • 3.1.1 Planar Rigid-Body Motion  
    • Reading: Utah State University: Dr. Urroz’s “Planar Rigid-Body Motion”

      Link: Utah State University: Dr. Urroz’s “Planar Rigid-Body Motion” (PDF)
       
      Instructions: This subunit will deal with planar rigid body’s motion, such as translation, rotation, and general plane motion.  Please click on the link above, and select the hyperlink for Lecture 16, titled “Rotation,” to open the PDF file.   Read the section titled “Planar Rigid-Body Motion.”  Please take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Rigid Body Dynamics”

      Link: Real-world-physics-problems.com: “Rigid Body Dynamics” (HTML)
       
      Instructions: This subunit will deal with planar rigid body’s motion, such as translation, rotation, and general plane motion.  Please click on the link and read entire webpage.  Make your notes while perusing this section.
       
      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 “Motion of Rigid Bodies”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Motion of Rigid Bodies” (PDF)
       
      Instructions: The problems here will help you understand rigid body motion.  Please click on the links for “Example 1,” “Example 2,” “Example 3,” and “Example 4,” and review each example problem.  You may want to attempt these problems before reviewing the solutions on each of these webpages.
       
      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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body Kinematics”

      Link:  YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Rigid Body Kinematics” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  The title of the video is “Dynamics Rigid Body Kinematics “and his video deals with planar rigid body’s motion, such as translation, rotation, and general plane motion.  Please click on the link above, and watch the video, which will introduce you to rigid body 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 18 minutes).  This section will also help you understand sections 3.1.2 and 3.1.3.
       
      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.

  • 3.1.2 Translation  
    • Reading: Utah State University: Dr. Urroz’s “Translation”

      Link: Utah State University: Dr. Urroz’s “Translation” (PDF)
       
      Instructions: This subunit deals with translating rigid bodies, where all points on the body move with the same velocity and acceleration.  Please click on the link above, and select the hyperlink for Lecture 22 Slide Lecture Notes, titled “Planar Kinetic Equations of Motion / Translation,” to open the PDF file.  Read the sections about “Translation.”  This reading will introduce you the fundamental principles of translation as applied to planar rigid-body motion.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 3.1.3 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” (PDF)
                 
      Instructions: Please click on the link above, and select the hyperlink for Lecture 16, titled “Rotation,” to open the PDF file.  Read the section titled “Rotation about a Fixed Axis.”  This reading will introduce you to the fundamental principles of rotation about a fixed axis as applied to planar rigid-body motion.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Connexions: Sunil Kumar Singh’s “Rotation”

      Link: Connexions: Sunil Kumar Singh’s “Rotation” (HTML or PDF)
       
      You can access the PDF version from the download tab in the top right corner of the page.
       
      Instructions: This reading will introduce you to the fundamental principles of rotation about a fixed axis as applied to planar rigid-body motion.  Click on the link above, and read the entire webpage.  Make sure to go through the application at the bottom of the webpage.  Take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 3.1.4 Absolute Motion Analysis  
    • Reading: Utah State University: Dr. Urroz’s “Absolute Motion Analysis”

      Link: Utah State University: Dr. Urroz’s “Absolute Motion Analysis” (PDF)
       
      Instructions: This subunit will help you to understand the motion of a rigid body with respect to a fixed point.  Please click on the link above, and select the hyperlink for Lecture 16, titled “Absolute motion,” to open the PDF file.  Read the entire lecture.  Take notes as you read this material.
       
      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 Absolute Motion”

      Link:  YouTube: The Saylor Foundation: Ken Manning’s “Dyanmics Absolute Motion” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video will help you understand the motion of a rigid body with respect to a fixed point.  Please click on the link above, and watch the video, which will introduce you to absolute 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 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.

  • 3.2 Relative-Motion Analysis  
  • 3.2.1 Instantaneous Center of Zero Velocity  
    • Reading: Utah State University: Dr. Urroz’s “Instantaneous Center of Zero Velocity”

      Link: Utah State University: Dr. Urroz’s “Instantaneous Center of Zero Velocity” (PDF)
       
      Instructions: This subunit will help you to understand point of zero velocity on a rigid body.  Please click on the link above, and then select the hyperlink for Lecture 18 Summary, titled “Rigid body: instantaneous center of zero velocity,” to open the PDF file.  Read the entire file (3 pages).
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Instant Center”

      Link: Real-world-physics-problems.com: “Instant Center” (HTML)
       
      Instructions: This subunit will help you understand point of zero velocity on a rigid body.  Please click on the link above, and read entire webpage.  Make sure to go over the example at the bottom of the webpage.  Take notes as you read this material.
       
      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 “Instantaneous Center of Velocity”

      Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Instantaneous Center of Velocity” (PDF)
       
      Instructions: These problems will help you to apply the concept of instantaneous center of velocity.  Please read the text on the webpage, and click on the links for “Example 1,” “Example 2,” “Example 3,” and “Example 4,” and review these example problems.  Try to work through each problem before reviewing the solutions on each webpage.
       
      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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Relative Velocity”

      Link:  YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Relative Velocity” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video will help you understand the motion of a rigid body with respect to another.  Please click on the link above, and watch the video, which will introduce you to relative velocity.  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 22 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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Instantaneous Center”

      Link: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Instantaneous Center” (YouTube)
       
      Also Available in: iTunes U
       
      Instructions:  This video will help you understand point of zero velocity on a rigid body.  Please click on the link above, and watch the video, which will introduce you to instantaneous center.  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 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.

  • 3.2.2 Acceleration  
    • Reading: Utah State University: Dr. Urroz’s “Acceleration”

      Link: Utah State University: Dr. Urroz’s “Acceleration” (PDF)
       
      Instructions: This subunit will help you understand acceleration of a rigid body undergoing general plane motion.  Please click on the link above, and select the hyperlink for Lecture 19 Summary, titled “Rigid-body motion: acceleration,” to open the PDF file.  Read the entire file (2 pages).
       
      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 Relative Acceleration”

      Link:  YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Relative Acceleration” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video will help you understand acceleration of a rigid body.  Please click on the link above, and watch the video, which will introduce you to acceleration and relative acceleration.  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 23 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.

  • 3.2.3 Rotating Axes  
    • Reading: Utah State University: Dr. Urroz’s “Rotating Axes”

      Link: Utah State University: Dr. Urroz’s “Rotating Axes” (PDF)
       
      Instructions: This subunit will help you understand motion of particles when the axis is rotating.  Please click on the link above, and select the hyperlink for Lecture 20, titled “Rigid Body: Rotating Axes,” to open the PDF file.  Read the entire file.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 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   show close
    Unit 4 Learning Outcomes   show close
  • 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” (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” (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” (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” (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.

    • Lecture: YouTube: The Saylor Foundation: Ken Manning’s “Dynamics Work Energy 3”

      Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Work Energy 3” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This Video is titled “Dynamics Work Energy 3” and 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 watch the video, which will introduce you to work and energy.  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 20 minutes).  This video will also help you understand sections 4.2.2 through 4.2.6.

      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.

    • Reading: Real-world-physics-problems.com: “Work”

      Link: Real-world-physics-problems.com: “Work” (HTML)
       
      Instructions: This section deals with work and work done by a constant and variable force.  You may notice you have read the first part of this webpage earlier in subunit 2.2.1.  For this subunit, please read the section titled “Work Done on a Rigid Body.”  Please take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.2.2 Kinetic Energy  
    • Reading: Utah State University: Dr. Urroz’s “Kinetic Energy”

      Link: Utah State University: Dr. Urroz’s “Kinetic Energy” (PDF)
       
      Instructions: This subunit deals with the computation of energy when rigid bodies are in motion.  The lecture will introduce you to Kinetic Energy for Rigid Bodies.  Please click on the link above, and select the hyperlink for Lecture 25, titled “Kinetic Energy,” to open the PDF file.  Read the section titled “Kinetic Energy.” 
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Kinetic Energy”

      Link: Real-world-physics-problems.com: “Kinetic Energy” (HTML)
       
      Instructions: This subunit deals with the computation of energy when rigid bodies are in motion.  The lecture will introduce you to Kinetic Energy for Rigid Bodies.  Click on the link above, and read the section titled “Kinetic Energy for a Rigid Body.”  Take notes as you read this section.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.2.3 Work Done by a Force  
    • Reading: Utah State University: Dr. Urroz’s “Work Done by a Force”

      Link: Utah State University: Dr. Urroz’s “Work Done by a Force”(PDF)
       
      Instructions: This subunit helps you understand how work done by a force is computed when it displaces the rigid body.  Please click on the link above, and select the hyperlink for Lecture 25, titled “Kinetic Energy,” to open the PDF file.  Read the section titled “The Work of a Force.”  It may be beneficial to take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.2.4 Work Done by a Couple  
    • Reading: Utah State University: Dr. Urroz’s “Work Done by a Couple”

      Link: Utah State University: Dr. Urroz’s “Work Done by a Couple” (PDF)
       
      Instructions: This subunit deals with the work done by equal and opposite moments.  Please click on the link above, and select the hyperlink for Lecture 25, titled “Kinetic Energy,” to open the PDF file.  Read the section titled “The Work of a Couple.”  Make you take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Work of a Force Couple”

      Link: Real-world-physics-problems.com: “Work of a Force Couple” (HTML)
       
      Instructions: This subunit deals with the work done by equal and opposite moments.  You may notice that you have read parts of this webpage in earlier subunits.  For this subunit, please read the section titled “Work of a Force Couple.”  Take notes on this reading.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.2.5 Work and Energy Principle  
    • Reading: Utah State University: Dr. Urroz’s “Work and Energy Principle”

      Link: Utah State University: Dr. Urroz’s “Work and Energy Principle”(PDF)
       
      Instructions: This subunit deals with how work and energy are interrelated for a rigid body.  Please click on the link above, and select the hyperlink for Lecture 25, titled “Kinetic Energy,” to open the PDF file.  Read the section titled “Principle of Work and Energy.”  It may help to take notes as you read this material.
       
      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 “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: The problems in this subunit will help you to understand how work and energy are computed for rigid bodies and how are they interrelated.  Please read the text on this webpage, and click on the links for “Example 1,” “Example 2,” “Example 3,” “Example 4,” and “Example 5.”  Work through these examples, and then check their solutions on each webpage.
       
      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.

  • 4.2.6 The Conservation of Energy  
    • Reading: Utah State University: Dr. Urroz’s “The Conservation of Energy”

      Link: Utah State University: Dr. Urroz’s “The Conservation of Energy”(PDF)
       
      Instructions: This subunit deals with how work and energy are conserved in energy balance.  Please click on the link above, and select the hyperlink for Lecture 26, titled “Conservation of Energy-Planar Kinetics,” to open the PDF file.  Read the entire 1-page file, and take notes as you read.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

    • Reading: Real-world-physics-problems.com: “Conservation of Energy”

      Link: Real-world-physics-problems.com: “Conservation of Energy” (HTML)
       
      Instructions: This subunit deals with how work and energy are conserved in energy balance.  Click on the link above, and read the section titled “Conservation of Energy for a Rigid Body.”  It may be beneficial to take notes as you read this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.3 Impulse and Momentum  
  • 4.3.1 Linear and Angular Momentum  
    • Reading: Utah State University: Dr. Urroz’s “Linear and Angular Momentum”

      Link: Utah State University: Dr. Urroz’s “Linear and Angular Momentum” (PDF)
       
      Instructions: This subunit deals with linear momentum when rigid bodies are translating and with angular momentum when the rigid bodies are subjected to moment (rotated about a fixed axis).  Please click on the link above, and then select the hyperlink for Lecture 27, titled “Linear and Angular Momentum,” to open the PDF file.  Read the section titled “Linear and Angular Momentum,” and take notes on this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.3.2 Principle of Impulse and Momentum  
    • Reading: Utah State University: Dr. Urroz’s “Principle of Impulse and Momentum”

      Link: Utah State University: Dr. Urroz’s “Principle of Impulse and Momentum” (PDF)
       
      Instructions: This subunit deals with the interrelation of impulse and moment for rigid bodies.  Please click on the link above, and select the hyperlink for Lecture 27, titled “Linear and Angular Momentum,” to open the PDF file.  Read the section titled “Principle of Impulse and Momentum,” and take notes on this material.
       
      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 Impulse Momentum”

      Link: YouTube:  The Saylor Foundation: Ken Manning’s “Dynamics Impulse Momentum” (YouTube)
       
      Also Available in:  iTunes U
       
      Instructions:  This video deals with the interrelation of impulse and momentum for rigid bodies.  Please click on the link above, and watch the video, which will introduce you to impulse and momentum and the relation between them.  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 9 minutes).  This video will also help you understand section 4.3.3.

      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.

  • 4.3.3 Conservation of Momentum  
    • Reading: Utah State University: Dr. Urroz’s “Conservation of Momentum”

      Link: Utah State University: Dr. Urroz’s “Conservation of Momentum”(PDF)
       
      Instructions: This subunit deals with the momentum balance of systems that collide.  Please click on the link above, and then select the hyperlink for Lecture 28, titled “Conservation of Momentum” to open the PDF file.  Read the entire 1-page file, and take notes on this topic.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 4.3.4 Eccentric Impact  
    • Reading: Oakland University: Dr. Latcha’s “Eccentric Impact”

      Link: Oakland University: Dr. Latcha’s “Eccentric Impact” (PowerPoint)
       
      Instructions: Eccentric impact takes place when two bodies do not collide along a straight line but rather at an angle.  The equations of impulse and momentum have to take into account the angles of impact for rigid bodies undergoing eccentric impact.  Please click on the link above, and select the hyperlink for Lecture 18, titled “Notes” after the title “Impulse and Momentum for Planar Rigid Bodies, Eccentric Impact,” to open the PowerPoint file.  Read the section titled “Eccentric Impact,” and take notes on this material.
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Unit 5: Three-Dimensional Dynamics  

    So far we have dealt equations of motion and mechanics in two dimensions.  Two dimensional analyses are essential to understanding how particles and rigid bodies behave when acted upon by forces and moments.  As most of the objects are three dimensional, projecting the theories learned in two dimensional mechanics to three dimensional is important to capture realistic and real world scenarios.  We will now take all that we have learned so far and extend it into full three-dimensions.We will also formulate and solve problems to understand the practical implications of theory learned.

    Unit 5 Time Advisory   show close
    Unit 5 Learning Outcomes   show close
  • 5.1 Kinematics in Three Dimensions  
  • 5.1.1 Kinematics of a Rigid Body  
  • 5.1.2 Rotational Motion about a Fixed Point  
  • 5.1.3 General Motion in Three-Dimensions  
  • 5.2 Kinetics of a Rigid Body in Three Dimensions  
  • 5.2.1 Angular Momentum  
  • 5.2.2 Kinetic Energy  
    • Reading: MIT OpenCourseWare: Dr. Widnall’s “Kinetic Energy”

      Link: MIT OpenCourseWare: Dr. Widnall’s “Kinetic Energy” (PDF)
       
      Instructions: This subunit deals with the energy experienced by three dimensional bodies when they are subjected to motion.  Please click on the link above, and then scroll down to Lecture 27.  Then, click on the “PDF” hyperlink after the title “3D Rigid Body Dynamics: Kinetic Energy, Instability, Equations of Motion”to open the PDF file.  Read the section titled “Kinetic Energy for Systems of Particles” and “Kinetic Energy for 3D Rigid Bodies.”  Take notes as you read this material.

      Terms of Use: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License.  It is attributed to Bill Widnall and can be found in its original form here

  • Unit 6: Vibrations  

    Objects subject to a restoring force will vibrate about a neutral position.  In this unit, we will look at the four basic modes of vibration and then derive ways in which we can model them. We will also formulate and solve problems to understand the practical implications of theory learned.

    Unit 6 Time Advisory   show close
    Unit 6 Learning Outcomes   show close
  • 6.1 Vibrational Motion  
  • 6.1.1 Undamped Free Vibration  
    • Reading: Utah State University: Dr. Urroz’s “Undamped Free Vibration”

      Link: Utah State University: Dr. Urroz’s “Undamped Free Vibration” (PDF)
       
      Instructions: This subunit deals with bodies that will undergo vibrations under the application of gravity or when a spring acts on a body.  There is no external force acting on this body, and the bodies are not subjected to any opposing frictional forces.  Please click on the link above, and then scroll down to Lecture 29.  Then, click on the hyperlink titled “Undamped Free Vibration” to open the PDF file.  Read the entire file (3 pages).
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

      The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

      Submit Materials

  • 6.1.2 Undamped Forced Vibration  
    • Reading: Utah State University: Dr. Urroz’s “Undamped Forced Vibration”

      Link: Utah State University: Dr. Urroz’s “Undamped Forced Vibration” (PDF)
       
      Instructions: This subunit deals with bodies that will undergo vibrations under the application of external forces.  The bodies are not subjected to any opposing frictional forces.  Please click on the link above, and scroll down to Lecture 30.  Then, click on the hyperlink titled “Undamped Forced Vibration” to open the PDF file.  Read the entire file (3 pages).
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

      The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

      Submit Materials

  • 6.1.3 Viscous Damped Free Vibration  
    • Reading: Utah State University: Dr. Urroz’s “Viscous Damped Free Vibration”

      Link: Utah State University: Dr. Urroz’s “Viscous Damped Free Vibration” (PDF)
       
      Instructions: This subunit deals with bodies that will undergo vibrations under the application of gravity or when a spring acts on a body.  There is no external force acting on this body, but the bodies are subjected to opposing frictional forces.  Please click on the link above, and then scroll down to Lecture 31.  Then, click on the hyperlink titled “Solving ODEs” to open the PDF file.  Read the section titled “Viscous Damped Free Vibration.”
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

      The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

      Submit Materials

  • 6.1.4 Viscous Damped Forced Vibration  
    • Reading: Utah State University: Dr. Urroz’s “Viscous Damped Forced Vibration”

      Link: Utah State University: Dr. Urroz’s “Viscous Damped Forced Vibration”(PDF)
       
      Instructions: This subunit deals with bodies that will undergo vibrations under the application of external force acting on this body and the bodies are subjected to opposing frictional forces.  Please click on the link above, and scroll down to Lecture 31.  Then, click on the hyperlink titled “Solving ODEs” to open the PDF file.  Read the section titled  “Viscous Damped Forced Vibration.”
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

      The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

      Submit Materials

  • 6.2 Example Problems of Vibrational Motion  
  • 6.2.1 Example Problems of Free Vibration  
    • Reading: Brown University: Dr. A. F. Bower’s “Free Vibration”

      Link: Brown University: Dr. A. F. Bower’s “Free Vibration” (HTML)
       
      Instructions: The problems in this subunit will help you apply principles learned in free vibration of rigid bodies under the application of frictional or non-frictional forces (viscous and non-viscous frictional forces).  Scroll down about 2/3 of the webpage until you reach Example 1.  Please read through “Example 1,” “Example 2,” and “Example 3.”
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • 6.2.2 Example Problems of Forced Vibration  
    • Reading: Brown University: Dr. A. F. Bower’s “Forced Vibration”

      Link: Brown University: Dr. A. F. Bower’s “Forced Vibration” (HTML)
       
      Instructions: The problems in this subunit will help you apply principles learned in forced vibration of rigid bodies under the application of frictional or non-frictional forces (viscous and non-viscous frictional forces).  Please scroll down almost to the bottom of the webpage until you reach the heading “5.4.7 Example Problems in Forced Vibrations,” and read “Example 1,” “Example 2,” and “Example 3.”
       
      Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Final Exam  

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