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# Summary - Centroid Mechanical Engineering Notes | EduRev

## Mechanical Engineering : Summary - Centroid Mechanical Engineering Notes | EduRev

The document Summary - Centroid Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Engineering Mechanics - Notes, Videos, MCQs & PPTs.
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Centroid

The point at which the total area of a plane figure or lamina is assumed to be concentrated is called centroid

Centroid of a Line

Centroid of an Area

Characteristics of Centroid

• The centroid represents the geometric center of a body
• The centroid may be located at a point that does not lie on the line/area.
• The coordinates of centroid is calculated with reference to the chosen axis
• An area can have only one centroid for all positions of the figure.
• In case of symmetric figures, centroid is located along the axes of symmetry

Centroid Of Regular Figures

 Centre of Gravity Centre of gravity is the point about which the resultant of the whole weight of the body may be considered to act. It is denoted by G

A. CENTROID OF COMPOSITE FIGURES

Note : If the area has a hole or cut out portion, the first moment of inertia and area must be subtracted to yield the centroid

B. PAPPUS GULDINUS THEOREMS

Pappus Guldinus Theorems are two theorems describing a simple way to calculate volumes (solids) and surface areas (shells) of revolution.

First Theorem

The surface area A of a surface of revolution generated by rotating a plane curve about an axis external to it and on the same plane is equal to the product of the arc length of the curve and the distance y traveled by its geometric centroid.

Examples

Second Theorem

The second theorem states that the volume V of a solid of revolution generated by rotating a plane area about an external axis is equal to the product of the area A and the distance y traveled by its geometric centroid

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## Engineering Mechanics - Notes, Videos, MCQs & PPTs

30 videos|72 docs|65 tests

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