Answer
$\omega_B=180rad/s$
$\omega_C=360rad/s$
Work Step by Step
The required angular velocity can be determined as follows:
$v_P=\omega_A r_A=60(0.075)=4.5m/s$
Now $\omega_B=\frac{v_P}{r_D}$
We plug in the known values to obtain:
$\omega_B=\frac{4.5}{0.025}=180rad/s$
Similarly, $v_{P^{\prime}}=\omega_Br_B$
$v_{P^{\prime}}=(180)(0.1)=18m/s$
and $\omega_C=\frac{v_{P^{\prime}}}{r_C}$
We plug in the known values to obtain:
$\omega_C=\frac{18}{0.05}$
$\implies \omega_C=360rad/s$
