Find the mass and the moments of inertia $I _ { x } , I _ { y }$, and $I _ { 0 }$ and the radii of gyration $\overline{\bar { x }}$ and $\overline {\bar { y }}$ for the lamina occupying the region $R$, where $R$ is the region bounded by the graphs of the equations $x = 2 \sqrt { y } , x = 0$, and $y = 2$, and having the mass density $\rho ( x , y ) = x y$.

Question

Quizplus · Accepted Answer

The Answer is

I _ { x } = \frac { 64 } { 5 } , I _ { y } = 16 , I _ { 0 } = \frac { 144 } { 5 } , \quad \overline {\bar { x } }= \sqrt { 3 } \quad \stackrel { = } { y } = \frac { 2 \sqrt { 15 } } { 5 }

Find the Mass and the Moments of Inertia Ix,IyI _ { x } , I _ { y }Ix​,Iy​

Find the Mass and the Moments of Inertia $I _ { x } , I _ { y }$