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## Derivation and Explanation of Center of Mass Lecture (15 minutes)

Central Forces Notes Section 3

- Derivation of the equation of motion for the center of mass for a system of particles. The definition of the center of mass arises from this derivation–do not define it first.
- Discuss that the concept of center of mass as it arises in the derivation corresponds to students' intuitive notion.
- Discuss that geometric meaning of $\Vec R$, the position vector from the origin to the center of mass. Many students are so quick to put the origin at the center of mass, that $\Vec R$ does not represent a concept that they have thought about.
- Discussion of the meaning of the center of mass equation of motion.
- Relating the center of mass equation found to the Survivor Outerspace Activity.
- It is particularly helpful to connect the idea of center of mass position to other weighted averages (esp. if they have just done Spins and Waves).