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

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  Lecture 9: Rotating Imbalance

  > Download from iTunes U (MP4 - 258MB)

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  > Download English-US transcript (PDF)

  > Download English-US caption (SRT)

  • Video Chapters
    • Body on rollers with an internal rotating mass

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      Body on rollers with an internal rotating mass

      > Download from iTunes U (MP4 - 258MB)

      > Download from Internet Archive (MP4 - 258MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Mass moment of inertia definition as a summation

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      Mass moment of inertia definition as a summation

      > Download from iTunes U (MP4 - 258MB)

      > Download from Internet Archive (MP4 - 258MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Moments and Products of Inertia

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      Moments and Products of Inertia

      > Download from iTunes U (MP4 - 258MB)

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      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

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

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

  > Download from iTunes U (MP4 - 219MB)

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  > Download English-US transcript (PDF)

  > Download English-US caption (SRT)

  • Video Chapters
    • Equations of motion (EOM) and degrees of freedom (DOF)

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      Equations of motion (EOM) and degrees of freedom (DOF)

      > Download from iTunes U (MP4 - 219MB)

      > Download from Internet Archive (MP4 - 219MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Example 1: Finding EOMs and DOFs

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      Example 1: Finding EOMs and DOFs

      > Download from iTunes U (MP4 - 219MB)

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      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Example 2: EOM for Atwoods machine

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      Example 2: EOM for Atwoods machine

      > Download from iTunes U (MP4 - 219MB)

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      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Example 3: Muddy card issue about dh/dt and torques

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      Example 3: Muddy card issue about dh/dt and torques

      > Download from iTunes U (MP4 - 219MB)

      > Download from Internet Archive (MP4 - 219MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Example 4: Rotating mass shaker and effect of gravity on torque

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      Example 4: Rotating mass shaker and effect of gravity on torque

      > Download from iTunes U (MP4 - 219MB)

      > Download from Internet Archive (MP4 - 219MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

    • Angular momentum for rigid bodies and the mass moment of inertia matrix, [I]

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      Angular momentum for rigid bodies and the mass moment of inertia matrix, [I]

      > Download from iTunes U (MP4 - 219MB)

      > Download from Internet Archive (MP4 - 219MB)

      > Download English-US transcript (PDF)

      > Download English-US caption (SRT)

Recitation Video and Notes

• Watch Recitation 5: Equations of Motion

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  Recitation 5: Equations of Motion

  > Download from iTunes U (MP4 - 139MB)

  > Download from Internet Archive (MP4 - 139MB)

  > Download English-US transcript (PDF)

  > Download English-US caption (SRT)

  • 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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