The constant $40$ N force is applied to the $36$ kg stepped cylinder as shown. The centroidal radius of gyration of the cylinder is $k=200mm,$ and it rolls on the incline without slipping.

If the cylinder is at rest when the force is first applied, determine its angular velocity $8$ seconds later.

Answer: $24\mathrm{.}2ra\frac{d}{s}($CW$)$

$2$