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

Given: A disk, having an outer radius of $R,$ rotates with a rate of $$ about a shaft passing through

its center $O,$ with $$ increasing at a rate of ${}^{}.$ The shaft is supported by a pair of bearings on cart

A$.$ Cart A is moving to the right with a speed of $v_A$ and an acceleration of $a_A.$ At the instant of

interest, point B on the perimeter of the disk is at the same height as O $.$

Find: For this problem:

$($a$)$ Determine the velocity of point B$.$ Write your answer as a vector in terms of its $xyz$ components.

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

components.