Center of Mass and Barycentric Coordinates - Wild Linear Algebra A

This lecture introduces applications of vectors to forces and motion, then develops center of mass, Archimedes' principle of the lever, affine combinations, and barycentric coordinates through graphical games and examples.

Syllabus

CONTENT SUMMARY: pg 1: @ Applications of vectors; force; breaking vectors into perpendicular components;
pg 2: @ velocity; Newton's 1st Law; acceleration; Newton's 2nd Law;
pg 3: @ Racetrack game;
pg 4: @ Trajectory game;
pg 5: @ Center of Mass; Archimedes' Principle of the lever; vector reformulation
pg 6: @ exercises ; center of mass;
pg 7: @ Connection between balance and affine combinations; remark on common notation points instead of vectors
pg 8: @ example; Barycentric coordinates;
pg 9: @ example: 3 coplanar masses;
pg 10: @ example continued from a vector point of view THANKS to EmptySpaceEnterprise
Introduction
Racetrack game
Trajectory game
Center of mass, Archimedes' Principle
Connection with affine combinations
Barycentric coordinates
Three co - planar masses