Summary - Centroid Mechanical Engineering Notes | EduRev

Engineering Mechanics - Notes, Videos, MCQs & PPTs

Mechanical Engineering : Summary - Centroid Mechanical Engineering Notes | EduRev

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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

Summary - Centroid Mechanical Engineering Notes | EduRevSummary - Centroid Mechanical Engineering Notes | EduRev

Centroid of an Area

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

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

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

 

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

Summary - Centroid Mechanical Engineering Notes | EduRev

 

A. CENTROID OF COMPOSITE FIGURES

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

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.

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

Examples

Summary - Centroid Mechanical Engineering Notes | EduRev

 

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

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

Summary - Centroid Mechanical Engineering Notes | EduRev

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