mer212: chapter 9 center of gravity and...

MER212: Chapter 9MER212: Chapter 9Center of Gravity and Centroid

Center of Gravity center of Mass • Center of Gravity, center of Mass, and the Centriod of a Body (9.1)

• Composite Bodies (9 3)• Composite Bodies (9.3)• Fluid Pressure (9.5)

Union CollegeMechanical Engineering

ESC020: Rigid Body Mechanics 1

Center of Gravity and Centroids



Resultant Weight and Center of Gravity Resultant Weight Resultant Weight

R iW W W dV Resultant of Weight=>Center of

Gravity

d

dWxW

WxW

Wxx iiii

dW

dWyW

WyW

Wyy

dWWW

iiii

iR

dW

dWzW

WzW

Wzz

dWWW

iiii

iR



dWWW iR

Centers of Mass

dV

dVx

dV

dVx

dm

dmx

dmg

dmgxm

mxgm

gmxx

i

ii

i

ii

dV

dVy

dV

dVy

dm

dmy

dmg

dmgym

mygm

gmyy

i

ii

i

ii

dV

dVz

dV

dVz

dm

dmz

dmg

dmgzm

mzgm

gmzz

i

ii

i

ii

Weight Specific Weight: Weight per unit volume Density: Mass per unit volume

Vm g

W m g



y p

Centroid of a Volume

dV

dVxV

Vxx ii

dVyVy

y

dVV

ii

i

dVzVz

dVVy

ii

i

dVVz

i

ii



Centroid of an AreadA dA dAA A A i i i i i i

i i i

x dA y dA z dAx A y A z Ax y z

A A AdA dA dA



Centroid of Line

x dLx

xdL

y dLy

ydL



Example 1 Locate the centroid of the Locate the centroid of the

triangular area shown



Example 2 Locate the centroids of the area Locate the centroids of the area

bounded by the two curves shown



Composite Bodies



Example 3 Locate the centroid for the area Locate the centroid for the area

shown



Example 4



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