1. 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.
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2. 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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5. Total Weight x location: y location: z location:
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7. Center of Mass
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8. Center of Gravity and Centroid for a Body
Consider a body to be a system of an infinite number of particles
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12. Center of Gravity of a Body
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13. CENTROID
The centroid C is a point which defines the geometric center of an object. Its location can be determined by formulas similar to those used for center of gravity or center of mass.
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15. Centroid of a Volume
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17. Centroid of an Area
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19. Centroid of a Line
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24. PROBLEM
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28. PROBLEM
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30. y
y = (h/b) (b - x) h C x b
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31. Strip Method
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35. PROBLEM
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39. Composite Bodies
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40. Composite Bodies
If a body is made up of several simpler bodies then a special technique can be used.
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41. Procedure Divide body into several subparts.
If the body has a hole or cutout, treat that as negative area.
Centroid will lie on line of symmetry.
Create Table and calculate centroid.
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43. xc yc
xc A
yc A
Body
Area
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47. Locate Centroid of the Composite Area
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48. 1 ft
3 ft 2 1 3
1 ft
2 ft
3 ft
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49. Segment A (ft2) x y xA yA 1 4.5 1 1 4.5 4.5 2 6 -1 1.5 -6 9
 A =  xA =  xA = 14
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50. 3
3 ft 2 1
1 ft
1 ft
2 ft
3 ft
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51. Segement A (ft2) x y xA yA 1 4.5 1 1 4.5 4.5 2 9 -1.5 1.5 -13.5 13.5
 A =  xA =  xA = 14
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52. 9.55
1 in
1 in
1 in
1 in
3 in
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53. 9.55 1 in 1 in 2 3 1 5 4 1 in 1 in 3 in Break into sub-areas
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55. 9.55
1 in 3
1 in 1
1 in
1 in 2
3 in
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56. 9.55
1 in 3
1 in 1
1 in
1 in 2
3 in
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57. 9.55
1 in 3
1 in 1
1 in
1 in 2
3 in
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59. h y b
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