Calculus: Center of Mass and Centroids Explained

Learn how to find the Center of Mass (Centroid) of a planar region using Calculus! 🧮⚖️

In this video, we break down the concepts of moments and centers of mass for 2D laminas. We move from discrete masses on a seesaw to continuous regions defined by functions.

Key topics covered:
🔹 The intuition behind Center of Mass (Balance Point)
🔹 Understanding Moments (Mass × Distance)
🔹 Formulas for Discrete Masses
🔹 Integral formulas for Moments about the X and Y axes
🔹 How to calculate the Centroid coordinates (x̄, ȳ)
🔹 Using Symmetry to simplify problems

Perfect for Calculus 2 students or anyone interested in physics and engineering applications of integration! 🚀

#Calculus #Math #Education #Engineering #Physics #Integration #Centroid

Chapters:
00:00 - Introduction
00:13 - What is it?
00:34 - Moments
00:57 - Discrete Masses
01:16 - Planar Laminas
01:36 - Moment about Y
01:57 - Moment about X
02:18 - Formulas
02:39 - Symmetry
02:59 - Summary
03:20 - Outro

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