Centroids and Centers of Gravity

Center of Gravity of Bodies and Centroids of Volumes

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

$W \, \bar = \Sigma wy$

$W \, \bar = \Sigma wz$

Centroids of volumes

$V \, \bar = \Sigma vx$

$V \, \bar = \Sigma vy$

$V \, \bar = \Sigma vz$

Centroids Determined by Integration

Centroid of area $\displaystyle A \, \bar = \int_a^b x_c \, dA$

$\displaystyle A \, \bar = \int_a^b y_c \, dA$

Centroid of lines

$\displaystyle L \, \bar = \int_a^b x_c \, dL$

$\displaystyle L \, \bar = \int_a^b y_c \, dL$

Center of gravity of bodies

$\displaystyle W \, \bar = \int_a^b x_c \, dW$

$\displaystyle W \, \bar = \int_a^b y_c \, dW$

$\displaystyle W \, \bar = \int_a^b z_c \, dW$

Centroids of volumes

$\displaystyle V \, \bar = \int_a^b x_c \, dV$

$\displaystyle V \, \bar = \int_a^b y_c \, dV$

$\displaystyle V \, \bar = \int_a^b z_c \, dV$

Centroids of Common Geometric Shapes