Question $3(10$ points$)$

A drum of $4-$in$.$ radius is attached to a disk of $8-in.$ radius. The disk and drum have a combined weight of $15$ lb and a combined radius of gyration of $6$ in $.$ A cord is attached as shown and pulled with a force $P$ of magnitude $5$ lb $.$ Knowing that the coefficients of static and kinetic friction are $0\mathrm{.}25$ and $0\mathrm{.}20$ respectively,

determine

$($a$)$ whether or not the disk slides, $[5$ marks$]$

$($b$)$ the angular acceleration of the disk $[5$ marks$]$

$($hint: start with a free body diagram and kinetic diagram$)$