21. Two-Dimensional Rotational 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

• Explain the rotational equivalent of Newton’s 2^nd law in component form: the relation between net torque on an object, its moment of inertia and its angular acceleration.
• Be able to explain that there are two possible models for describing rotational motion: conservation of energy and Newton’s 2^nd law (τ = Iα), but only the latter model can be used to determine information about the object’s motion as a function of time.
• Be able to apply and solve rotational equations to objects whose motion does not involve center-of-mass acceleration, such as a disk rotating about an axis through its center.

Preparation

Course Notes

Notes: Two-Dimensional Rotational Dynamics (PDF - 4.1MB)

Suggested Textbook Reading (Optional)

Chapter 10.1-10.2, 10.4. 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 Rotational Dynamics (PDF - 3.3MB)

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 - 2.1MB)

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/two-dimensional-rotational-motion/two-dimensional-rotational-dynamics/help-session-1/Ip83FGkiGRk.srt'}

Help Session 2

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/two-dimensional-rotational-motion/two-dimensional-rotational-dynamics/help-session-2/l-f7wkkL20k.srt'}

Help Session 3

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/two-dimensional-rotational-motion/two-dimensional-rotational-dynamics/help-session-3/BCMlz83W_5w.srt'}

Help Session 4

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/two-dimensional-rotational-motion/two-dimensional-rotational-dynamics/help-session-4/KMRb1VF65f0.srt'}

Help Session 5

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/two-dimensional-rotational-motion/two-dimensional-rotational-dynamics/help-session-5/yR3iWFus9qA.srt'}

Related Resources

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

• Try out the Torque interactive simulation from PhET.

 

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