Problem $1(95$ points$)$: A uniform thin $3$ kg disk with $100-$mm$-$radius spins at the constant rate ${}_2=8ra\frac{d}{s}$ about an axis held by a housing attached to a horizontal rod that rotates at the constant rate ${}_1=4ra\frac{d}{s}.$ Neglect mass of the housing attached to a horizontal rod.

a$)(10$pts$)$ Determine the angular velocity of the disk.

b$)(10pts)$ Determine the angular acceleration of the disk.

c$)(10pts)$ Determine the velocity of Point P on the rim of the disk if if $=0.$

d$)(10$pts$)$ Determine the acceleration of Point $P$ on the rim of the disk if $=0.$

e$)(5$pts$)$ Determine the acceleration of Point $P$ on the rim of the disk if $=60$

f$)(10$pts$)$ Determine angular momentum of $0.$

g$)(20$pts$)$ Determine the couple which represents the dynamic reaction at the support A

h$)(20$pts$)$ Determine the couple which represents the reaction at the support A with downward gravity $(-$ j$).$