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Center of mass and moments of inertia for wire with variable density Find the center of mass and the moments of inertia about the coordinate axes of a thin wire lying along the curve

$$

\mathbf { r } ( t ) = t \mathbf { i } + \frac { 2 \sqrt { 2 } } { 3 } t ^ { 3 / 2 } \mathbf { j } + \frac { t ^ { 2 } } { 2 } \mathbf { k } , \quad 0 \leq t \leq 2

$$

if the density is $\delta = 1 / ( t + 1 )$

$=\frac{56}{9}$

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University of Illinois at Urbana-Champaign