Homework H$\mathrm{.}3.$F

Given: A shaft is rotating at a constant rate of $$ about a fixed axis. A disk of radius $R$ is able to

roll without slipping in a slot that is cut longitudinally into the shaft. The position of the disk's

center A is controlled by an hydraulic cylinder that is extending at a constant rate of $d^{}.$ Consider

a set of coordinate axes $xyz$ that are attached to the disk, and a set of coordinate axes $xYZ$ that

are fixed in space.

Find: For this problem,

$($a$)$ determine the angular velocity and angular acceleration of the disk.