Engineering Dynamics

Angular Momentum and Torque

« Previous | Next »

Session Overview

Covered this week: Week 3 continues with more difficult examples of the computation of velocity and acceleration in translating and rotating frames. Angular momentum is introduced and the general formulation of the relation between torque and the time rate of change of angular momentum is introduced, including cases where the angular momentum is computed with respect to moving parts. Two very important cases are discussed: torque and angular momentum with respect to fixed axes of rotation and with respect to the center of mass. The principles presented this week explain why the passengers on this swing ride feel an upward lift as the central structure whirls. Image courtesy of Hillbraith 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 3: Problems and Concept Questions (PDF)

Videos

Lecture Videos

• Watch Lecture 5: Impulse, Torque, and Angular Momentum for a System of Particles

  • Video Chapters

    • Lecture outline and Use of tangential and normal coordinates with an example
    • A review of the principle of linear momentum and impulse
    • The definition of the angular momentum of a particle with respect to a moving reference point
    • Example of the torque/angular momentum relationship to a carnival ride

  • Watch Lecture 6: Torque and the Time Rate of Change of Angular Momentum

    • Video Chapters
      • Intro to the time rate of change of linear and angular momentum for a particlecoordinates
      • Example 1: Rotating mass on a string; dP/dt = tension
      • Example 2a-Pulling the string from a rotating mass through a hole at the axis of rotation. Conservation of angular momentum, h
      • Example 2b-work done equals the change in kinetic energy
      • Example 3b: Computing external and internal structural torques using dh / dt; angular momentum vector not aligned with the axis of rotation
      • Question and answer session

  Recitation Video and Notes

  • Watch Recitation 3: Motion in Moving Reference Frames
    • This recitation includes a concept review for the week and covers a problem on velocity and acceleration of a point in a plane using polar coordinates.
  • Recitation 3 Notes: V and A of a Point in a Moving Frame (PDF - 1.6MB)
    • 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 3: Concept Question Answer Key (PDF)
• Problem Set 3: Problem Solutions and Explanations (PDF - 1.1MB)

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

« Previous | Next »