Answer
The angular speed after coupling is $~~750~rev/min$
Work Step by Step
We can use conservation of angular momentum to find the angular speed after coupling:
$L_f = L_i$
$(I_1+I_2)~\omega_f = I_1~\omega_1+I_2~\omega_2$
$\omega_f =\frac{ I_1~\omega_1+I_2~\omega_2}{I_1+I_2}$
$\omega_f =\frac{(3.30~kg~m^2)(450~rev/min)+(6.60~kg~m^2)(900~rev/min)}{3.30~kg~m^2+6.60~kg~m^2}$
$\omega_f = 750~rev/min$
The angular speed after coupling is $~~750~rev/min$
