Answer
$\omega_B=300rad/s$
$\omega_C=600rad/s$
Work Step by Step
We can determine the required angular velocity as follows:
We know that
$\omega_A=20t+40$
at $t=3s$
$\omega_A=20(3)+40=100rad/s$
The speed at point P is given as
$v_P=\omega_Ar_A$
$\implies v_P=100\times 0.075=7.5m/s$
Now, $\omega_B=\frac{v_P}{r_B}$
$\implies \omega_B=\frac{7.5}{0.025}=300rad/s$
Similarly, $v_P^{\prime}=\omega_Br_B$
$\implies v_P^{\prime}=300\times 0.1=30m/s$
Now, $\omega_C=\frac{v_P^{\prime}}{r_C}$
We plug in the known values to obtain:
$\omega_C=\frac{30}{0.05}=600rad/s$
