Statics/Geometric Properties of Lines and Areas

Centroids Of Common Shapes Of Areas And Lines

Trianglular Area

$Area=\frac{bh}{2}$

Quarter Circular Area

$Area=\frac{\pi r^2}{4}$

Semicircular Area

$Area=\frac{\pi r^2}{2}$

Semiparabolic Area

$Area=\frac{2a}{3}$

Parabolic Area

$Area=\frac{4ah}{3}$

Parabolic Spandrel

$Area=\frac{ah}{3}$

Circular Sector

$Area=\alpha r^2$

Quarter Circular Arc

$Area=\frac{\pi }{2}$

Semi Circular Arc

$Area=\pi r$

Arc Of Circle

$Area=2\alpha r$

Moments Of Inertia of Common Geometric Shapes

Rectangle

$I=\frac{b{h}^3}{12}$

Circle

$I=\frac{\pi r^4}{4}$

Hollow circle

This is used for hollow cylinders where there is solid material between the outer and inner radius, but no material between the inner radius and the center, like a pipe's cross-section.

$I=\frac{\pi (r_o-r_i{)}^4}{4}$

$r_o$ is the outer radius $r_i$ is the inner radius