Answer
The new angular velocity of the system is $~~0.347~rad/s$
Work Step by Step
We can use conservation of angular momentum to find the new angular velocity of the system:
$L_f = L_i$
$I_f~\omega_f = I_i~\omega_i$
$[\frac{1}{2}(4.00m)(R^2)+m(\frac{R}{2})^2]~\omega_f = [\frac{1}{2}(4.00m)(R^2)+mR^2]~\omega_i$
$(2.00R^2+\frac{R^2}{4})~\omega_f = (2.00R^2+R^2)~\omega_i$
$\frac{9}{4}~\omega_f = 3.00~\omega_i$
$\omega_f = \frac{4~\omega_i}{3}$
$\omega_f = \frac{(4)~(0.260~rad/s)}{3}$
$\omega_f = 0.347~rad/s$
The new angular velocity of the system is $~~0.347~rad/s$.
