17. Systems, Center of Mass, and Conservation of 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 identify a system of particles.
• Be able to distinguish internal and external forces on a system of particles.
• Be able to explain how Newton’s 2^nd Law and 3^rd Law are used to determine the effects of internal and external forces on a system of particles.
• Explain how the rate of change of momentum of a system is related to the external forces exerted on the system.
• Explain what is meant by the center of mass of a system.
• Explain how the total momentum of a system of particles is related to the velocity of the center of mass of the system.
• Explain why the acceleration of the center of mass of a system depends only on the total external force.
• Be able to determine the position vector of the center of mass of a system (based on a co-ordinate choice)
• Explain how conservation of momentum in a closed system is related to Newton’s 3^rd law.

Preparation

Course Notes

Notes: Systems, Conservation of Momentum and Center of Mass (PDF - 2.6MB)

Suggested Textbook Reading (Optional)

Chapter 8.2, 8.5. 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: Systems, Center of Mass, and Conservation of Momentum (PDF - 1.2MB)

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 - 2.4MB)

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/momentum/systems-center-of-mass-and-conservation-of-momentum/help-session-1/szEDiE0G6wg.srt'}

Help Session 2

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/momentum/systems-center-of-mass-and-conservation-of-momentum/help-session-2/1MS8jXiqX8w.srt'}

Help Session 3

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/momentum/systems-center-of-mass-and-conservation-of-momentum/help-session-3/-caU12WLSuw.srt'}

Related Resources

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

• Read the Physics material on Connexions:
  • Center of Mass
  • Collision
  • Laws Governing Collision
  • Elastic and Plastic Collisions (Application)
• Read through the materials on HyperPhysics:
  • Inelastic Collisions
  • Elastic Collisions
  • Center of Mass
• Read about the Law of Momentum Conservation from the Physics Classroom.

 

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