$3)$ The entire system rotates about the vertical axis at constant angular speed $\backslash (\backslash$omega$\_\{1\}\backslash ),$ and the rotation rate $\backslash (\backslash$omega$\_\{2\}\backslash )$ of the rotor relative to bar BC also is constant.

a$)$ Describe the angular velocity of the rotor in terms of a superposition of simple rotations.

b$)$ Solely from an examination of the description in item $($a$),$ predict the direction$($s$)$ in which the angular acceleration of the rotor will be situated relative to the $\backslash ($ x y z $\backslash )$ axes defined in the sketch. Briefly explain your answer.

c$)$ Describe the angular velocity and angular acceleration of the rotor in terms of components relative to $\backslash ($ x y z $\backslash ).$