For the mechanism shown on the right, the angular velocity and angular acceleration of the link OA are measured as ${}_2=2ra\frac{d}{s}$ counter$-$clockwise and ${}_2=1ra\frac{d}{s^2}$ clockwise. In addition, the angle is measured as ${}_2=30.$ Determine the following: $[30$pts$]$

$(1)$ Angular velocity and angular acceleration of link BC

$(2)$ Velocity and acceleration of the point B

$OA=AC=AB=0\mathrm{.}1m$