# ME202: Mechanics II - Dynamics

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.

This unit will take you approximately 15 hours to complete.

☐    Subunit 3.1: 8 hours

☐    Subunit 3.1.1: 4 hours

☐    Subunit 3.1.2: 0.5 hour

☐    Subunit 3.1.3: 1.5 hours

☐    Subunit 3.1.4: 2  hours

☐    Subunit 3.2:  7 hours

☐    Subunit 3.2.1: 3.5 hours

☐    Subunit 3.2.2: 2.0 hours

☐    Subunit 3.2.3: 1.5 hours

Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• 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.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture16_ENGR2030.htm)”
(PDF)

Instructions: This subunit will deal with planar rigid body’s
motion, such as translation, rotation, and general plane motion.
Lecture 16, titled “Rotation,” to open the PDF file.   Read the
section titled “Planar Rigid-Body Motion.”  Please take notes as you

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.

• 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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture22_ENGR2030.htm)”
(PDF)

Instructions: This subunit deals with translating rigid bodies,
where all points on the body move with the same velocity and
hyperlink for Lecture 22 Slide Lecture Notes, titled “Planar Kinetic
Equations of Motion / Translation,” to open the PDF file.  Read the
fundamental principles of translation as applied to planar
rigid-body motion.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture16_ENGR2030.htm)”
(PDF)

hyperlink for Lecture 16, titled “Rotation,” to open the PDF file.
reading will introduce you to the fundamental principles of rotation
about a fixed axis as applied to planar rigid-body motion.

displayed on the webpage above.
``````
• Reading: Connexions: Sunil Kumar Singh’s “Rotation” Link: Connexions: Sunil Kumar Singh’s “Rotation” (HTML or PDF)

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.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture16_ENGR2030.htm)”
(PDF)

of a rigid body with respect to a fixed point.  Please click on the
“Absolute motion,” to open the PDF file.  Read the entire lecture.
Take notes as you read this material.

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

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture18_ENGR2030.htm)”
(PDF)

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).

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

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.

• 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.

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.

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture19_ENGR2030.htm)”
(PDF)

a rigid body undergoing general plane motion.  Please click on the
“Rigid-body motion: acceleration,” to open the PDF file.  Read the
entire file (2 pages).

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

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](http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE2030/Lectures/Lecture20_ENGR2030.htm)”
(PDF)