Planar lamina

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In mathematics, a planar lamina is a closed set in a plane of mass and surface density such that:

, over the closed set.

The center of mass of the lamina is at the point

where moment of the entire lamina about the x-axis and moment of the entire lamina about the y-axis.

, over the closed surface.
, over the closed surface.
Bound region.jpg

Example 1.

Find the center of mass of a lamina with edges given by the lines and where the density is given as .

Integrate 2x + 3y + 2 with respect to y and substitute the limits 4-x and x

center of mass is at the point

Planar laminas can be used to determine moments of inertia, or center of mass.