Answer
$\omega_B=6.67rad/s$
Work Step by Step
The required angular velocity can be determined as follows:
$\omega_B=\frac{v_D}{r_B}~~~$[eq(1)]
We know that
$\omega_{CD}=\frac{v_D}{r_{CD}}$
$\implies 5=\frac{v_D}{0.4}$
This simplifies to:
$v_D=2m/s$
We plug in the known values in eq(1) to obtain:
$\omega_B=\frac{2}{0.3}$
$\implies \omega_B=6.67rad/s$
