2224-Sec13_6-HWT

2224-Sec13_6-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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Math 2224 Multivariable Calculus–Sec.13.6: Moments and Centers of Mass I. Review: Center of Mass in 2-D A. Definitions 1. Moment, Mo =( mass)(directed distance) 2. Moment about the y -axis, M y =(mass)(directed distance from the y -axis) 3. Moment about the x -axis, M x =(mass)(directed distance from the x -axis) B. Formulas for Moment, Mass & Center of Mass of a Lamina with Density Function, ! . Mass : M = dm a b ! = " dA a b ! Moment about the y # axis : M y = ! x dm a b ! = ! x dA a b ! Moment about the x # axis : M x = ! y dm a b ! = ! y dA a b ! Center of Mass : X = M y M , Y = M x M C. When integrating wrt x : ! x = x , ! y = t x ( ) + b x ( ) 2 and dA = t x ( ) ! b x ( ) " # \$ % dx , where t x ( ) =top curve, b x ( ) =bottom curve and ( x ) = density function constant. The formulas above can be rewritten as Mass : M = dm a b ! = ( x ) t x ( ) # b x ( ) ( ) dx a b ! Moment about the y # axis : M y = [ ( x )] x t x ( ) # b x ( ) ( ) dx a b ! Moment

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This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224-Sec13_6-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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