In the figure below, block $1$ has mass $\backslash (\backslash$mathrm$\{$m$\}\_\{1\}=440\backslash$mathrm$\{$~g$\}\backslash ),$ block $2$ has mass $\backslash (\backslash$mathrm$\{$m$\}\_\{2\}=512\backslash$mathrm$\{$~g$\}\backslash ),$ and the pulley, which is mounted on a horizontal axle with negligible friction, has radius $\backslash (\backslash$mathrm$\{$R$\}=5\mathrm{.}50\backslash )$ cm $.$ When released fromrest, block $2$ falls $70\mathrm{.}9$ cm in $5\mathrm{.}23$ s without the cord slipping on the pulley. What is its rotational inertia of the pulley?

Specify your answer in SI units up to $4$ decimal places. Do not include units.