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WildLinAlg3: Center of mass and barycentric coordinates

Here we discuss applications of vectors, first of all to forces, velocity and acceleration, and discuss two of Newton's important laws. We look at motion in the grid plane, and discuss two interesting games: the racetrack game and the trajectory game.This is the third lecture in a first course on Linear Algebra given by N J Wildberger at UNSW.We introduce some graphical games (Racetrack Game, Trajectory Game) with velocities and accelerations in a grid plane, and then discuss center of mass, Archimedes principle of the lever, and barycentric coordinates. Lots of interesting topics! CONTENT SUMMARY: pg 1: @00:08 Applications? of vectors; force; breaking vectors into perpendicular components;pg 2: @05:58 velocity; Newton's 1st Law; acceleration; Newton's 2nd Law;pg 3: @08:56 Racetrack game;pg 4: @15:10 Trajectory game;pg 5: @18:51 Center of Mass; Archimedes' Principle of the lever; vector reformulationpg 6: @21:59 exercises ; center of mass;pg 7: @24:58 Connection between balance and affine combinations; remark on? common notation (points instead of vectors)pg 8: @29:36 example; Barycentric coordinates;pg 9: @31:28 example: 3 coplanar masses;pg 10: @35:23 example continued from a vector point of view (THANKS to EmptySpaceEnterprise)
Length: 48:11

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