View stunning SlideShares in full-screen with the new iOS app!Introducing SlideShare for AndroidExplore all your favorite topics in the SlideShare appGet the SlideShare app to Save for Later — even offline
View stunning SlideShares in full-screen with the new Android app!View stunning SlideShares in full-screen with the new iOS app!
Centroids in a Planar Lamina Young Lee Brian Lau Alvin Lau Jonathan Javier
Introduction to Centroids Centroid (Center of gravity) The center of mass of an object of uniform density Characteristics of a centroid If a region has a line of symmetry, then its centroid is on that line of symmetry If a region has two lines of symmetry, then the centroid is the point where they intersect Moment A measure of tendency to cause a body to rotate about a specific point No movement at the center of gravity Planar Lamina A thin and flat plate of material of constant density Density: measure of mass per unit of area
Illustration Moment of mi about the x-axis Moment of mi about the y-axis
Centroidal Equations Mass of lamina: Moment of planar lamina about the x-axis: Moment of planar lamina about the y-axis: Center of Mass:
Example Find the centroid of the region bounded by the graphs f(x) = x and g(x) = x4 Centroid: (0.56, 0.37)
Centroids: Real Life Application Balance Balancing thin objects on a point (2-D) Balancing two people on a see-saw (1-D) Infrastructure Knowing the centroid of parts of buildings ensures buildings to be stable (3-D) Crimes Mapping the density of crimes in a certain area Locomotion Locating the centroid of a vehicle to increase stability