Section 13.4 Notes - If is a continuous density function on the lamina corresponding to a plane region R then the mass m of the lamina is given by

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Summary of Section 6.6 Mass is a measure of a body’s resistance to changes in motion. The center of mass is the point at which a fulcrum could be located to attain equilibrium. The moment about the origin is a measure of the tendency of a system to rotate about the origin. Similarly, the moment about the x-axis is a measure of the tendency of a system to rotate about the x-axis. A planar lamina is a thin, flat plate of material of constant density. Density is a measure of mass per unit of volume. For a planar lamina density is considered to be a measure of mass per unit of area. If the density is constant , Mass = ∫ ∫ ∫ ∫ = = R R dA dA A ρ In section 13.4 we will extend the formulas from section 6.6 to the case where the density is variable . Definition of Mass of a Planar Lamina of Variable Density
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: If is a continuous density function on the lamina corresponding to a plane region R, then the mass m of the lamina is given by ∫ ∫ = R dA y x m ) , ( . Moments and Center of Mass of a Variable Density Planar Lamina Let be a continuous density function on the planar lamina R. The moments of mass with respect to the x- and y- axes are ∫ ∫ = R x dA y x y M ) , ( and ∫ ∫ = R y dA y x x M ) , ( . If m is the mass of the lamina, then the center of mass is ( 29 . , , = m M m M y x x y If R represents a simple plane region rather than a lamina, the point ( 29 y x , is called the centroid of the region....
View Full Document

This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

Ask a homework question - tutors are online