For an RLC circuit driven with voltage of amplitude V_ m and...

Total angular momentum of the system initially (\mathrm{L}_{\mathrm{i}}=$\mathrm{I}$_{1} \mathrm{w}+$\mathrm{I}$_{2}(0)=$\mathrm{I}$_{1} \mathrm{w}) Total angular momentum of the system finally (\mathrm{L}_{\mathrm{f}}=\left($\mathrm{I}$_{1}+$\mathrm{I}$_{2}\right) \mathrm{w}_{2}) According to conservation of angular momentum i.e. (\mathrm{L}_{\mathrm{i}}=\mathrm{L}_{\mathrm{f}}) ($$\begin{aligned} &\Rightarrow \mathrm{I}_{1} \omega=\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) \omega_{2} \\ &\Rightarrow \omega_{2}=\frac{\mathrm{I}_{1} \omega}{\mathrm{I}_{1}+\mathrm{I}_{2}} \end{aligned}$$)