Engineering Dynamics

Angular Momentum and Motion of Rotating Rigid Bodies

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Session Overview

Covered this week: Week 6 addresses the angular momentum of rigid bodies. First we examine the moment of inertia of a rigid body and use it to express the angular momentum of rigid bodies. We then address finding the equations of motion for rotating rigid bodies and discuss problem solving strategies. We break down typical problems into four different classes and present example problems for each class of problems. Finally, we introduce a more powerful formulation of the torque equation for rigid bodies. Spinning tops are an example of a rotating rigid body often used as a children’s toy. Image courtesy of Sean Dreilinger on Flickr.

Assignments

Problems and Concept Questions

Each problem set has concept questions paired with most problems. Answers to the concept questions are handed in before the overall problem set is due. You should therefore answer the concept questions in each problem set while watching the video lectures for the week. Then, use the Concept Question Answer Key (below in the Check Yourself section) to check your work before continuing to work on the problem set.

Please note that if your answer to the concept question is incorrect, it is likely that you may start down an unproductive pathway to a solution. Try to fully understand the answer to the concept question before you begin the regular problem.

• Problem Set 5: Problems and Concept Questions (PDF)

Videos

Lecture Videos

• Watch Lecture 11: Mass Moment of Inertia of Rigid Bodies

  • Video Chapters
    • Definition of moment of inertia matrix
    • Principle axes and symmetry rules
    • Example computation of Izz for a disk
    • Parallel axis theorem

• Watch Lecture 12: Problem Solving Methods for Rotating Rigid Bodies

  • Video Chapters
    • Four classes of rotational problems
    • Class 1: Rotation about fixed axis through center of mass
    • Class 2: Fixed axis rotation not through center of mass-pendulum example
    • Class 3: Unconstrained motion about center of mass-hockey puck example
    • Equivalent forces and moments acting only upon the center of mass
    • Class 4: Rotation about moving points; H/A alternative formulation in terms of H/G
    • Class 4 example of the pipe rolling on a truck bed

Recitation Video and Notes

• Watch Recitation 6: Angular Momentum and Torque
  • This recitation includes a concept review for the week, problems with the axis of spin on and not on the principal axis, and a discussion on finding the derivative of a rotating vector. The class concludes with a review of Quiz 1.
• Recitation 6 Notes: Moment of Inertia and Imbalance, Rotating Slender Rod (PDF - 1.1MB)
  • These recitation notes were compiled by Prof. David Gossard, another instructor for the course. His notes go over concepts and problems covered during the recitation sections he taught, and may not precisely correspond to the content covered in the above recitation video.

Check Yourself

Concept Question Answer Key and Problem Set Solutions

The solutions are presented in two files, one with the answers to the concept questions, and one with solutions and in-depth explanations for the problems. Work the problems on your own and check your answers when you’re done.

• Problem Set 5: Concept Question Answer Key (PDF)
• Problem Set 5: Problem Solutions and Explanations (PDF)

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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