27. Two-Dimensional Rotation and Translation Dynamics

• Course Home
• Syllabus
• Introduction to Mechanics

  • 1. Units and Dimensional Analysis
  • 2. Problem Solving and Estimation
• Mathematics: The Language of Science

  • 3. Cartesian Coordinates and Vectors
• Translational Kinematics

  • 4. One-Dimensional Kinematics and Free Fall
  • 5. One-Dimensional Kinematics: Non-Constant Acceleration
  • 6. Two-Dimensional Kinematics
• Force and Newton's Laws of Motion

  • 7. Concept of Force
  • 8. Applications of Newton's Second Law
• Circular Motion

  • 9. Circular Motion Kinematics
  • 10. Circular Motion Dynamics
• Conservation of Energy

  • 11. Work and Energy
  • 12. Work and the Dot Product
  • 13. Potential Energy
  • 14. Application of Energy Conservation
  • 15. Mechanical Energy and the Simple Harmonic Oscillator
• Momentum

  • 16. Momentum and Impulse
  • 17. Systems, Center of Mass, and Conservation of Momentum
  • 18. Collision Theory
  • 19. Continuous Mass Flow
• Two-Dimensional Rotational Motion

  • 20. Two-Dimensional Rotational Kinematics
  • 21. Two-Dimensional Rotational Dynamics
  • 22. Torque and the Simple Harmonic Oscillator
  • 23. Static Equilibrium
• Angular Momentum

  • 24. Angular Momentum
  • 25. Conservation of Angular Momentum
• Rotation and Translation

  • 26. Two-Dimensional Rotation and Translation Kinematics
  • 27. Two-Dimensional Rotation and Translation Dynamics
• Central Force Motion

  • 28. Central Force Motion and the Kepler Problem
• Download Course Materials

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Learning Objectives

• Analyze the motion of a rigid body using a systematic methodology involving torque and rate of change of angular momentum. Recognize the analogy to the methodology of solving problems involving force and acceleration.
• Be able to apply and solve rotational equations of motion to objects whose motion involves acceleration of center of mass, such as a yo-yo rolling on a table, or a rigid cylinder rolling down an inclined plane.
• Be able to apply the conservation of angular momentum to solve problems involving rotation and translation of rigid objects.

Preparation

Course Notes

Notes: Rotation and Translation (PDF - 4.5MB)

Suggested Textbook Reading (Optional)

Chapter 10.3. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: with Modern Physics. 12th ed. San Francisco, CA: Addison-Wesley, 2007. ISBN: 9780805321876.

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

Read through the class slides carefully. They explain all of the concepts from the module.

Slides: Two-Dimensional Rotation and Translation Dynamics (PDF - 1.1MB)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems. If you are struggling with the Challenge Problems, watch the Homework Help Session videos, which will give you tips on how to tackle problems of this type.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF - 2.7MB)

Problem Solving Help

In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.

Help Session 1

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-1/W6dBTiQXO44.srt'}

Help Session 2

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-2/bE67z8cuqXk.srt'}

Help Session 3

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-3/JQCU0fFgC4k.srt'}

Help Session 4

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-4/v3OkjgTSObo.srt'}

Help Session 5

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-5/cKN-HOOQrhE.srt'}

Help Session 6

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/rotation-and-translation/two-dimensional-rotation-and-translation-dynamics/help-session-6/8oaRJ8buOLA.srt'}

Related Resources

There are countless resources available online to help you learn physics. Try these:

• Read the Physics material on Connexions:
  • Role of Friction in Rolling
  • Rolling Along an Incline
  • Pulley in Rolling
• Read through the materials on HyperPhysics:
  • Rotational-Linear Parallels
  • Rotational Kinetic Energy
  • Rolling Objects
• Learn about rolling without slipping from Dr. Richard Vawter at Western Washington University.

 

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