A Plane Lamina with Constant Density $\rho ( x , y ) = 6$

question 139

Short Answer

A plane lamina with constant density $\rho ( x , y ) = 6$ occupies a region in the $x y$ -plane bounded by a simple closed path $C$ . Its moments of inertia about the axes are
$$I _ { x } = - \frac { \rho } { 3 } \int _ { C } y ^ { 3 } d x \text { and } I _ { y } = \frac { \rho } { 3 } \int _ { C } x ^ { 3 } d y$$
Find the moments of inertia about the axes, if $C$ is a rectangle with vertices $( 0,0 ) , ( 4,0 )$ , $( 4,5 )$ and $( 0,5 )$

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Definitions:

Parallel

In biology, this might refer to the occurrence or development of similar traits or structures in organisms not closely related, often due to similar environmental pressures.

Proteins

Large biomolecules consisting of one or more long chains of amino acid residues, essential for the structure, function, and regulation of the body's tissues and organs.

Genetic Material

The molecules (DNA or RNA) that carry the genetic instructions used in the growth, development, functioning, and reproduction of organisms.

DNA Ligase

A biological catalyst that assists in the fusion of DNA strands through the facilitation of a phosphodiester bond formation.