Planar lamina
Encyclopedia
In mathematics
, a planar lamina is a closed surface of mass
and surface density 
such that:
, over the closed surface.
The center of mass
of the lamina is at the point
where
moment of the entire lamin about the x-axis and 
moment of the entire lamin about the y-axis.
, over the closed surface.
, over the closed surface.
Example 1.
Find the center of mass of a lamina with edges given by the lines
, 
and 
, where the density is given as 
.
center of mass is at the point
Planar laminas can be used to determine moments of inertia, or center of mass.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a planar lamina is a closed surface of mass
and surface density such that:, over the closed surface.The center of mass
Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
of the lamina is at the point
where
moment of the entire lamin about the x-axis and moment of the entire lamin about the y-axis., over the closed surface., over the closed surface.Example 1.
Find the center of mass of a lamina with edges given by the lines
, and , where the density is given as .center of mass is at the point
Planar laminas can be used to determine moments of inertia, or center of mass.