Answer
$\omega_{AB}=1.24rad/s$
Work Step by Step
We can determine the required angular velocity as follows:
According to the law of sines
$\frac{4}{sin 45}=\frac{r_{IC/B}}{sin30}=\frac{r_{IC/C}}{sin 105}$
This simplifies to:
$r_{IC/B}=\frac{4sin30}{sin45}=2.828in$
and $r_{IC/C}=\frac{4sin105}{sin45}=5.464in$
We know that
$v_C=\omega_{BC}(r_{IC/C})$
We plug in the known values to obtain:
$12=5.464\omega_{BC}$
This simplifies to:
$\omega_{BC}=2.1962rad/s$
Similarly, $v_B=\omega_{BC}(r_{IC/B})$
We plug in the known values to obtain:
$v_B=(2.1962)(2.828)=6.211in/s$
Now $v_B=\omega_{AB}r_{AB}$
We plug in the known values to obtain:
$6.211=5\omega_{AB}$
This simplifies to:
$\omega_{AB}=1.24rad/s$
