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Problem $16\mathrm{.}104-$ A drum attached to a disk and a cord

A drum of $\backslash (4-\backslash$mathrm$\{$in$\}\backslash ).$ radius is attached to a disk of $8-$in$.$ radius. The disk and drum have a total weight of $11\mathrm{.}00$ lb and a combined radius of gyration of $6$ in $.$ A cord is attached as shown and pulled with a force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ of magnitude $5$ lb $.$ Know that the disk rolls without sliding.

Problem $16\mathrm{.}104.$a $-$ Angular acceleration of the disk and acceleration of the center of mass

Determine the angular acceleration of the disk and the acceleration of $\backslash ($ G $\backslash ).($Round the final answer to three decimal places.$)$

The angular acceleration of the disk is $\backslash (\backslash$quad $\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash$circlearrowright $\backslash ).$

The acceleration of $\backslash ($ G $\backslash )$ is $\backslash (\backslash$quad $\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash$rightarrow $\backslash ).$