Answer
$\omega_{BC}=8.66 rad/s \circlearrowleft$
$\omega_{AB}=4 rad/s \circlearrowright$
Work Step by Step
The required angular velocity can be determine as follows:
$v_C=\omega_{CD} r_{CD}=4(0.5)=2m/s$
$v_B=\omega_{AB} r_{AB}=\omega_{AB}(1)=\omega_{AB}$
Similarly $r_{IC/B}=\frac{4}{cos30}=0.4619m$
and $r_{IC/C}=0.4tan30=0.231m$
We know that
$v_C=\omega_{BC}r_{IC/C}=0.231\omega_{BC}$
This simplifies to:
$\omega_{BC}=8.66 rad/s \circlearrowleft$
Similarly
$v_B=\omega_{BC} r_{IC/B}$
We plug in the known values to obtain:
$\omega_{AB}=(8.66)(0.4619)=4 rad/s \circlearrowright$
