Answer
$\omega_R=4 rad/s$
Work Step by Step
The required angular velocity can be determined as follows:
We know that
$v_C=\omega_A r_A~~~$[eq(1)]
and $v_R=\omega_A r_B=\omega_R r_{IC/R}~~~$[eq(2)]
Dividing eq(1) by eq(2), we obtain:
$\frac{v_C}{v_R}=\frac{r_A}{r_B}$
We plug in the known values to obtain:
$\frac{0.9}{v_R}=\frac{0.075}{0.15}$
This simplifies to:
$v_R=1.8m/s$
Now $\omega_R=\frac{v_R}{r_{IC/R}}$
We plug in the known values to obtain:
$\omega_R=\frac{1.5}{0.45}$
This simplifies to:
$\omega_R=4 rad/s$
