Engineering Dynamics

Angular Momentum and Rotating Masses

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Session Overview

Covered this week: In week 5, we introduce the concept of mass moment of inertia as the summation of the contributions of individual mass particles to the total angular momentum of the system. We find the mass moment of inertia matrix and explain the meaning of the diagonal and off-diagonal terms. We introduce the relationship between torque and time rate of change of angular momentum. There is no problem set this week. A street performer in Quebec City juggles torches by repeatedly throwing and rotating the burning rods. Image courtesy of Reza Vaziri on Flickr.

Videos

Lecture Videos

• Watch Lecture 9: Rotating Imbalance

  • Video Chapters
    • Body on rollers with an internal rotating mass
    • Mass moment of inertia definition as a summation
    • Moments and Products of Inertia

• Watch Lecture 10: Equations of Motion, Torque, Angular Momentum of Rigid Bodies

  • Video Chapters
    • Equations of motion (EOM) and degrees of freedom (DOF)
    • Example 1: Finding EOMs and DOFs
    • Example 2: EOM for Atwoods machine
    • Example 3: Muddy card issue about dh/dt and torques
    • Example 4: Rotating mass shaker and effect of gravity on torque
    • Angular momentum for rigid bodies and the mass moment of inertia matrix, [I]

Recitation Video and Notes

• Watch Recitation 5: Equations of Motion
  • This recitation reviews free body diagram strategies, covers equations of motion for multiple degree-of-freedom systems, and addresses a dynamically balanced system.
• Recitation 5 Notes: Torque and Angular Momentum, Equations of Motion for Multiple Degree-of-Freedom Systems (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.

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