Answer
$0.054Kgm^2$
Work Step by Step
We can determine the required moment of inertia as follows:
$I=\frac{2K}{\omega^2}$
We plug in the known values to obtain:
$I=\frac{2(4.6J)}{(13rad/s)^2}$
$\implies I=0.054Kgm^2$
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