A round disc of moment of inertia $\mathrm{I}_{2}$ about its axis perpendicular to its plane and passing…
A round disc of moment of inertia $\mathrm{I}_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $\mathrm{I}_{1}$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is
The corrected text with proper LaTeX formatting is:
Total angular momentum of the system initially $L_{i}=I_{1} w+I_{2}(0)=I_{1} w$
Total angular momentum of the system finally $L_{f}=(I_{1}+I_{2}) w_{2}$
According to conservation of angular momentum i.e. $L_{i}=L_{f}$
$\begin{aligned}
&\Rightarrow I_{1} \omega=(I_{1}+I_{2}) \omega_{2} \\
&\Rightarrow \omega_{2}=\frac{I_{1} \omega}{I_{1}+I_{2}}
\end{aligned}$