Homework H$\mathrm{.}2.$J

Given: A mechanism is made up of block B $,$ a circular disk having an outer radius of $R$ and link AD $.$ Block B is constrained to move along a horizontal surface with the disk being able to roll without slipping on block B $.$ Link AD is pinned to point A on the disk and to a slider at D $,$ with the slider being constrained to move along a horizontal guide. At the instant shown, A is directly to the right of the center C of the disk, and block B moves to the left with a constant speed of $v_B.$

Find: For the position shown:

$($a$)$ Determine the angular velocities of the disk and link AD $.$ Write your answers as vectors.

$($b$)$ Determine the angular accelerations of the disk and link AD$.$ Write your answers as vectors.