In mathematics, a planar lamina (or plane lamina) is a figure representing a thin, usually uniform, flat layer of the solid. It serves also as an idealized model of a planar cross section of a solid body in integration. Planar laminas can be used to determine moments of inertia, or center of mass of flat figures, as well as an aid in corresponding calculations for 3D bodies. (Wikipedia).
Planar graphs, What are planar graphs? In this video we take a look at what a planar graph is and how Mathematica can check to see if a graph is planar. In short, a planar graph is one that can be drawn in the plane such that no edges cross. If you want to learn more about Mathematica,
From playlist Introducing graph theory
Calculus II - 7.6.2 Center of Mass of a Planar Lamina
This video takes you through using calculus techniques (rather than geometric formulas) to find the center of mass of a planar lamina. Calculus I playlist corresponds to chapters 1-5 of Calculus 11e, Larson, Edwards: https://www.youtube.com/playlist?list=PLl-gb0E4MII1ml6mys-RXoQ0O3GfwBPVM
From playlist Calculus II (Entire Course)
Theorem of Pappus to find Volume of Revolution Calculus 2
If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profrobbob I introduce the Theorem of Pappus and then work through 2 examples. The first example is finding the volume of a Tarus at 2:40 and the second ex
From playlist Calculus 2
Moments and Center of Mass 3 - Planar Lamina of Uniform Density
Calculus: We present formulas for the moments and center of mass of a planar lamina of uniform density rho. Examples considered are (a) a rectangle of height h and base b, (b) the upper half of the unit disk, and (c) the region between y=x and y=x^2-x from x=0 to x=1. For part (c), we
From playlist Calculus Pt 4: Applied Integration
Moments and Center of Mass 4 - Integral Formula for Planar Lamina
Calculus: We derive the integral formula for the moments of a planar lamina using the limit process for integration.
From playlist Calculus Pt 4: Applied Integration
From playlist M. Graph Theory
A tool to measure the area of any shape
A polar planimeter, which measures the area of a region when you trace around it. This is episode 9 of my video series about calculating devices. My video about doing calculus with a planimeter: http://youtu.be/KrAnfwCPbks End song inspired by "Hotter than a molotov" by The Coup. Chri
From playlist Calculating Devices Review / HowTos
The Matching Problem in General Graphs is in Quasi-NC - Ola Svensson
Computer Science/Discrete Mathematics Seminar I Topic: The Matching Problem in General Graphs is in Quasi-NC Speaker: Ola Svensson Affiliation: École polytechnique fédérale de Lausanne Date: January 22, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction to Planar Graphs and Euler's Formula
This video introduces planar graphs and Euler's formula. http://mathispower4u.com
From playlist Graph Theory (Discrete Math)
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Year 13/A2 Mechanics Chapter 4.1, 4.2 (Moments)
Welcome to the first lesson on the topic of moments, which are essentially the turning effects of forces acting around a fixed point. This lesson introduces the concept of a moment and its definition, providing practice in how to calculate a moment. We then move on and take a look at the
From playlist Year 13/A2 Mechanics
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Center of Mass in a Planar Lamina Centroid Calculus 2 (3 Examples)
If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profrobbob Example with functions y in terms of x at 6:56 Example with functions x in terms of y at 19:22 Example with Common Geometric Regions at 33:46 Fin
From playlist Calculus 2
Planar Graphs - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Worldwide Calculus: Integration in R²
Lecture on 'Integration in R²' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Integrals
Center of Mass & Centroid Problems - Calculus
This calculus video tutorial provides a basic introduction into the center of mass of a system also known as the centroid. It explains how to find the x and y coordinates of the centroid of a planar lamina which is a 2d region. The center of mass occurs where an object or a region can be
From playlist New Calculus Video Playlist
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Using the slope formula to determine if points make up a rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Find the Centroid of a Bounded Region Involving Two Quadratic Functions
This video explains how to determine the centroid of a triangular region bounded by two quadratic functions with uniform density. Site: http://mathispower4u.com
From playlist Applications of Integration: Arc Length, Surface Area, Work, Force, Center of Mass