centroid of line

719 Closed Straight Lines | Centroid of Composite Lines

Problem 719
Determine the centroid of the lines that form the boundary of the shaded area in Fig. P-718.

Trapezoidal area with isosceles triangle subtracted from the bottom


717 Symmetrical Arcs and a Line | Centroid of Composite Line

Problem 717
Locate the centroid of the bent wire shown in Fig. P-717. The wire is homogeneous and of uniform cross-section.

A line and two arcs in vertical symmety


716 Semicircular Arc and Lines | Centroid of Composite Figure

Problem 716
A slender homogeneous wire of uniform cross section is bent into the shape shown in Fig. P-716. Determine the coordinates of the centroid.

Vertical line, semicircular arc, and 30 deg line


Centroids and Centers of Gravity

Centroids of Composite Figures

Center of gravity of a homogeneous flat plate
$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$


Centroids of areas
$A \, \bar{x} = \Sigma ax$

$A \, \bar{y} = \Sigma ay$


Centroids of lines
$L \, \bar{x} = \Sigma lx$

$L \, \bar{y} = \Sigma ly$


Center of Gravity of Bodies and Centroids of Volumes

Center of gravity of bodies
$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$

$W \, \bar{z} = \Sigma wz$


Centroids of volumes
$V \, \bar{x} = \Sigma vx$

$V \, \bar{y} = \Sigma vy$

$V \, \bar{z} = \Sigma vz$


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