Engineering Dynamics

Finding Equations of Motion for Rigid Body Rotation

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Session Overview

Covered this week: Week 7 emphasizes finding the equations of motion of rotating and translating rigid bodies. We introduce more complex problems and consider systems with more than one degree of freedom. We discuss how to cleverly select the point about which one computes torques and angular momentum and present examples. We use an important alternative form of Euler’s torque equation. Diagram of a double pendulum, a classic and extremely complex example of a system with multiple degrees of freedom. Public domain image.

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 6: Problems and Concept Questions (PDF)

Suggested Reading

• [Hibbeler] chapters 17 and 19

Videos

Lecture Videos

• Watch Lecture 13: Four Classes of Problems With Rotational Motion

  • Video Chapters

    • Review of applicable physical laws
    • Example Class 4 problem with moving points of constraint
    • Tipping box problem-alternative form of Eulers equation
    • Question and answer period

• Watch Lecture 14: More Complex Rotational Problems and Their Equations of Motion

  • Video Chapters
    • Cart and pendulum 2 DOF equations of motion
    • Center of percussion problem
    • Static and dynamic imbalance definitions

Recitation Video and Notes

• Watch Recitation 7: Cart and Pendulum, Direct Method
  • This recitation covers a direct method of breaking down a problem involving a cart and pendulum.
• Recitation 7 Notes: Equations of Motion for Cart & Pendulum (Lagrange) (PDF - 1.2MB)
  • 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 6: Concept Question Answer Key (PDF)
• Problem Set 6: 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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