Q$4{?}^{[11]}.$ The assembly consists of two slender rods each of weight $40$ lb and length $L=4ft$ and a disk of weight $16$ lb and radius $r=1ft.$ The stiffness of the spring is $k=5l\frac{b}{f}t.$ The spring is unstretched when $=45$ and the assembly is released from rest at this position. At the instant $=0,$

Show that $C$ is the instantaneous center of zero velocity of the bar $BC.$

Determine the angular velocities of the disk, rods $AB$ and $BC.$

The disk rolls without slipping. Take $I_G=\frac{1}{12}m{L}^2$ for the uniform bar, $I_G=\frac{1}{2}m{r}^2$ for the uniform disk and $g=32\mathrm{.}2f\frac{t}{s^2}$