# 17. Systems, Center of Mass, and Conservation of Momentum

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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 2nd Law and 3rd 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 3rd law.

## Preparation

### Course Notes

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

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

Watch the following excerpts from the Physics I lecture videos:

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## 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)

## 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'}

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### 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'}

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### 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'}

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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:
• Read through the materials on HyperPhysics:
• Read about the Law of Momentum Conservation from the Physics Classroom.

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