Answer
The new angular speed of the disk is $16.9~Hz$
Work Step by Step
We can find the initial rotational inertia of the disk:
$I_0 = \frac{1}{2}MR^2$
$I_0 = \frac{1}{2}(0.80~kg)(0.170~m)^2$
$I_0 = 0.01156~kg~m^2$
We can find the final rotational inertia of the disk and clay:
$I_f = \frac{1}{2}MR^2+mr^2$
$I_f = \frac{1}{2}(0.80~kg)(0.170~m)^2+(0.120~kg)(0.080~m)^2$
$I_f = 0.01233~kg~m^2$
We can use conservation of angular momentum to find the new angular speed:
$L_f = L_0$
$I_f~\omega_f = I_0~\omega_0$
$\omega_f = \frac{I_0~\omega_0}{I_f}$
$\omega_f = \frac{(0.01156~kg~m^2)(18.0~Hz)}{0.01233~kg~m^2}$
$\omega_f = 16.9~Hz$
The new angular speed of the disk is $16.9~Hz$.
