# Spiral Moment

$x = \theta\cos(\theta)\hspace{1cm}y=\theta\sin(\theta)\hspace{1cm}0\leq\theta\leq4\sqrt{3}$

The spiral object described above exists in the $$xy$$ plane and has a linear mass density $$(\sigma =\Large{\frac{1}{\theta}})$$.

Determine the object's moment of inertia with respect to an axis perpendicular to the $$xy$$ plane and passing through the point $$(x,y) = (0,0)$$.

Details and Assumptions: All angles are in radians

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