Chapter_09_1 - Chapter9 Centroidsand CenterofGravity...

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03/16/10 Chapter 9 - Centroids 1 Chapter 9 Centroids and  Center of Gravity
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03/16/10 Chapter 9 - Centroids 2
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03/16/10 Chapter 9 - Centroids 3 Objectives To discuss the concept of the center of  gravity, center of mass, and centroids  (centers of area). To show how to determine the location of the  center of gravity and centroid for a system of  particles and a body of arbitrary shape. To use the theorem of Pappus and Guldinus  for finding the area and volume for a surface  of revolution. 
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03/16/10 Chapter 9 - Centroids 4 Center of Gravity The center of gravity G is a point which locates the resultant weight of a system of particles. The weights of the particles is considered to be a parallel force system. The system of weights can be replaced by a single weight acting at the Center of Gravity.
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03/16/10 Chapter 9 - Centroids 5
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03/16/10 Chapter 9 - Centroids 6
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03/16/10 Chapter 9 - Centroids 7 = = n 1 i i R W W Total Weight n n 3 3 2 2 1 1 R R W x ~ W x ~ W x ~ W x ~ W x + + + = x location: n n 3 3 2 2 1 1 R R W y ~ W y ~ W y ~ W y ~ W y + + + = y location: n n 3 3 2 2 1 1 R R W z ~ W z ~ W z ~ W z ~ W z + + + = z location:
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03/16/10 Chapter 9 - Centroids 8 = = = = = = = = = n 1 i i i n 1 i i n 1 i i i n 1 i i n 1 i i i n 1 i i W W z ~ z W W y ~ y W W x ~ x particle i the of weight W particle i the of s coordinate z ~ , y ~ , x ~ gravity of center the of s coordinate z , y , x th i th i i i
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Chapter 9 - Centroids 9 = = = = = = = = = n 1 i i i n 1 i i n 1 i i i n 1 i i n 1 i i i n 1 i i m m z ~ z m m y ~ y m m x ~ x particle
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Chapter_09_1 - Chapter9 Centroidsand CenterofGravity...

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