Given: The yoke shown below rotates about a fixed axis with a constant rate of ${}_0.$ A disk,

of radius $r,$ rotates about its center C at a constant rate of ${}_{\text{d}\text{i}\text{s}\text{k}}$ relative to yoke. The $xYZ$

coordinate system is fixed with the $x-$axis aligned with the fixed rotation axis of the yoke. The

$xyz$ coordinate system is attached to the disk with the $z-$axis aligned with the rotation axis of the

disk for all time. For the position shown below, the $xyz$ axes are aligned with the $xYZ$ axes.

Find: For the position shown:

$($a$)$ Determine the angular velocity and angular acceleration of the disk. Write your answers as

vectors in terms of their $xyz$ components.

$($b$)$ Determine the acceleration of point B of the disk. Write your answer as a vector in terms of

its $xyz$ components.

Use the following parameters in your analysis: ${}_0=3ra\frac{d}{s},{}_{\text{d}\text{i}\text{s}\text{k}}=2ra\frac{d}{s},d=0\mathrm{.}5m,b=1\mathrm{.}5$

m and $r=0\mathrm{.}25m.$