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Trigonometry
Question

Inertia and center of mass of a shell Find \(I _ ...

Inertia and center of mass of a shell Find \(I _ { z }\) and the center of mass of a thin shell of density \(\delta ( x , y , z ) = z\) cut from the upper portion of the sphere \(x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25\) by the plane \(z = 3\) .

Answer

\(( \overline { x } , \overline { y } , \overline { z } ) = ( 0,0,49 / 12 ) , I _ { z } = 640 \pi\)

Solution
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