CENTROIDS & CENTERS OF GRAVITYarahim/SEMM 1203 centroid.pdf · the centroid through the...

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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2

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:

1

2

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

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