# ME202: Mechanics II - Dynamics

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.

This unit will take you approximately 4.5 hours to complete.

☐    Subunit 5.1: 2.5 hours

☐    Subunit 5.2: 2 hours

Unit5 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• Identify kinematics of rigid body in three-dimensions.
• Identify general motion and relative motion in three-dimension.
• Identify angular motion and kinetic energy in three-dimension.

5.1 Kinematics in Three Dimensions   5.1.1 Kinematics of a Rigid Body   - Reading: MIT OpenCourseWare: Dr. Widnall’s “Kinematics of a Rigid Body” Link: MIT OpenCourseWare: Dr. Widnall’s “Kinematics of a Rigid Body” (PDF)

Instructions: This subunit deals with translation, rotational, and general plane motion of three dimensional objects.  Please click on the link above, and scroll down to Lecture 25.  Then, click on the “PDF” hyperlink after the title “3D Rigid Body Kinematics” to open the PDF file.  Read the entire document (10 pages).  Please note that this resource also covers the topic outlined in sections 5.1.2 and 5.1.3 of this course.  Make your notes while reading this section.

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   - Reading: MIT OpenCourseWare: Dr. Widnall’s “Angular Momentum” Link: MIT OpenCourseWare: Dr. Widnall’s “Angular Momentum” (PDF)

Also available in:

``````[EPUB](https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2011/07/ME202-5.2.1-Bill-Widnall.epub)

Instructions: This subunit deals with momentum experienced by three
dimensional objects when they are rotated about a fixed point.
Please click on the link above, and scroll down to Lecture 26.
Then, click on the “PDF” hyperlink after the title “3D Rigid Body
Dynamics: The Inertia Tensor” to open the PDF file.  Read the
section titled “Angular Momentum.”  Take notes as you read this
material.

is attributed to Bill Widnall and can be found in its original
form [here](http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec26.pdf).
``````

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.

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