24. Angular Momentum

• 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

• Be able to calculate the vector product of two vectors using unit vectors associated with both a Cartesian coordinate system and a cylindrical coordinate system.
• Describe the meaning of the terms that appear in the definition of angular momentum about a point.
• Be able to calculate the angular momentum about a point for a particle undergoing linear motion or circular motion using vectors and the relation between change in angular momentum and torque for 2-dimensional rotation.
• Recognize why the angular momentum of a symmetric body rotating about the symmetry axis points along the axis of rotation.
• Explain why the component of the angular momentum of a rigid body rotating about a fixed axis (z-axis) is L_z = Iω_z.
• Explain why τ_s = dL_s / dt is a consequence of Newton’s 2^nd Law.

Preparation

Course Notes

Notes: Angular Momentum of a Point Particle (PDF - 2.1MB)

Suggested Textbook Reading (Optional)

Chapter 10.5. 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: Angular Momentum (PDF - 1.3MB)

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)

Problem Solving Help

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

Help Session

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Related Resources

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

• Read the Physics material on Connexions:
  • Angular Momentum
  • Second Law of Motion in Angular Form
  • Angular Momentum (Check your understanding)
• Read through the materials on HyperPhysics:
  • Newton's 2nd Law: Rotation
  • Angular Momentum of a Particle
• Try out the Torque interactive simulation from PhET.

 

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