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CENTROIDS & CENTERS OF GRAVITY
CENTROIDS & CENTERS OF GRAVITY
CENTROIDS & CENTERS OF GRAVITY
For Area
For Line
For Volume
CENTROIDS & CENTERS OF GRAVITY: COMMON SHAPES - AREAS
CENTROIDS & CENTERS OF GRAVITY: COMMON SHAPES - LINES
CENTROIDS & CENTERS OF GRAVITY: COMMON SHAPES - VOLUMES
CENTROIDS & CENTERS OF GRAVITY Example 1:
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3 4
CENTROIDS & CENTERS OF GRAVITY Example 2:
Determine the location of the centroid.
CENTROIDS & CENTERS OF GRAVITY Example 4:
Determine centroid of the composite line shown in the diagram.
Source: STATICS made simple, 4th Edition, 2018
CENTROIDS & CENTERS OF GRAVITY Example 3:
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3 4
O
THEOREMS OF PAPPUS-GULDINUS
• Surface of revolution is generated by rotating a
plane curve about a fixed axis.
• Area of a surface of revolution is
equal to the length of the generating
curve times the distance traveled by
the centroid through the rotation.
LyA 2
THEOREMS OF PAPPUS-GULDINUS
• Body of revolution is generated by rotating a plane
area about a fixed axis.
• Volume of a body of revolution is
equal to the generating area times
the distance traveled by the centroid
through the rotation.
AyV 2
THEOREMS OF PAPPUS-GULDINUS EXAMPLE :
Determine the volume of the composite body using theorem of Pappus.
THEOREMS OF PAPPUS-GULDINUS EXAMPLE :
Source: STATICS made simple, 4th Edition, 2018
Contents in the slides are mostly taken from the following sources/references: 1. J. Walt Oler, Statics: Lecture Notes, Texas Tech University, USA, 2007. 2. Yunan Prawoto & Abd Rahman Musa, Statics, UTM Open Courseware, 2010. 3. R. C. Hibbeler, Engineering Mechanics-Statics, Pearson Education, NJ, USA, 2007.
EQUILIBRIUM 2D
ANY QUESTIONS ? ASK NOW OR REGRET LATER
REMINDER: PASSING MARK = 50%