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Importan Centroi

The document discusses the center of gravity and centroid. The center of gravity (G) is a point that locates the resultant weight of a system of particles. It can be found using formulas that involve summing or integrating the weight (W) and position (x, y, z) of each particle. The centroid (C) defines the geometric center of an object. Formulas to find the centroid depend only on the object's geometry (volume V, area A, or length L) if the material is uniform. Centroids of symmetric shapes will lie along the axis of symmetry.

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48 views2 pages

Importan Centroi

The document discusses the center of gravity and centroid. The center of gravity (G) is a point that locates the resultant weight of a system of particles. It can be found using formulas that involve summing or integrating the weight (W) and position (x, y, z) of each particle. The centroid (C) defines the geometric center of an object. Formulas to find the centroid depend only on the object's geometry (volume V, area A, or length L) if the material is uniform. Centroids of symmetric shapes will lie along the axis of symmetry.

Uploaded by

mingdi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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Centre of gravity and centroid:

The center of gravity (G) is a point that locates the


resultant weight of a system of particles.

Particles with weights W1, W2, , Wn can be replaced


by a resultant force of weight W located at the center of
gravity G.

To find the location of the center of gravity G(x,y,z):

(We can obtain z by imagining the coordinate system, with the particles fixed in it, as being
rotated 90 degrees about the x (or the y) axis).

Knowing W=mg, if we assume that the acceleration due to gravity (g) for every particle is
constant (g will be cancelled out)

A rigid body is composed of an infinite number of particles, hence it is necessary to use


integration instead of summation.

But dm=dV, with being the density and dv the volume of each particle. Therefore, the centre
of mass has the coordinates of
Centroid:

The centroid (C) is a point which defines the geometric center of an object. If the material
composing a body is uniform or homogeneous, the density of material is constant ( = constant).
Hence, the resulting formulas that define the centroid of a body depend only on the geometry of
the body {Volume (V), Area (A), or Length (L)}.

Centroid (volume):

Centroid (area):

Centroid (line):

The centroids of some shapes may be partially or completely specified by using conditions of
symmetry. In cases where the shape has an axis of symmetry, the centroid of the shape will lie
along that axis.

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