# ME202: Mechanics II - Dynamics

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
This unit will take you approximately 20.5 hours to complete.

☐    Subunit 1.1: 4.5 hours

☐    Subunit 1.2: 10.5 hours

☐    Subunit 1.2.1: 3 hours

☐    Subunit 1.2.2: 2.5 hours

☐    Subunit 1.2.3: 3 hours

☐    Subunit 1.2.4: 2 hour

☐    Subunit 1.3: 5.5 hours

Unit1 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• Formulate rectilinear and curvilinear motion in one-dimension.
• Solve projectile motion problems.
• Identify and solve problems in 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.

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)

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture3_ENGR2030.htm)”
(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

displayed on the webpage above.
``````

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.

• 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.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture3_ENGR2030.htm)”
(PDF)

Instructions: Motion of a projectile deals with curvilinear motion
acted upon by gravity.  For instance, motion of rockets or missiles
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.

displayed on the webpage above.
``````

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.

• 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.

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.

• 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.

• 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.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture5_ENGR2030.htm)”
(PDF)

Instructions: Cylindrical coordinates are another alternative to
express curvilinear motion in addition to normal and tangential
hyperlink for Lecture 5, titled “Curvilinear Motion: Cylindrical
Components,” to open the PDF file.  Read the section titled and
“Curvilinear Motion: Cylindrical Components.”

displayed on the webpage above.
``````

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture6_ENGR2030.htm)”
(PDF)

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.

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).