Is my relative motion analysis correct for this engineering problem?

[Precursor]

Homework Statement

The attempt at a solution

I used the concept of relative motion analysis for velocity:

V_B = V_A + V_B/A
(4) = (-2) + ω(3)
ω = 2 rad/s (CCW)

Is this correct?

 

[Precursor]

I know this is actually an engineering problem but it uses fundamental physics concepts, so it shouldn't be beyond the scope of this forum.

So can anyone confirm my solution?