Explore applications of vectors in physics and mathematics in this 48-minute lecture from the Wild Linear Algebra series. Delve into force, velocity, and acceleration concepts, examining Newton's laws and their implications. Engage with interactive games like the Racetrack and Trajectory games to visualize motion in a grid plane. Investigate the center of mass, Archimedes' principle of the lever, and barycentric coordinates. Learn how to break vectors into perpendicular components and solve practical exercises. Discover the connection between balance and affine combinations, and analyze examples involving coplanar masses from both geometric and vector perspectives.
Center of Mass and Barycentric Coordinates - Wild Linear Algebra A
Insights into Mathematics via YouTube
Overview
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
Taught by
Insights into Mathematics
