Answer
The new angular velocity is $15.6~rad/s$
Work Step by Step
We can use conservation of angular momentum to find the final angular velocity:
$L_f = L_0$
$I_f~\omega_f = I_0~\omega_0$
$\omega_f = \frac{I_0~\omega_0}{I_f}$
$\omega_f = \frac{(2.50~kg~m^2)(10.0~rad/s)}{1.60~kg~m^2}$
$\omega_f = 15.6~rad/s$
The new angular velocity is $15.6~rad/s$.
