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
  1. $\frac{\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) \omega}{\mathrm{I}_{1}}$
  2. $\frac{\mathrm{I}_{2} \omega}{\mathrm{I}_{1}+\mathrm{I}_{2}}$
  3. $\omega$
  4. $\frac{\mathrm{I}_{1} \omega}{\mathrm{I}_{1}+\mathrm{I}_{2}}$

Solution

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. $L_{i}=L_{f}$ $\begin{aligned} &\Rightarrow I_{1} \omega=(I_{1}+I_{2}) \omega_{2} \\ &\Rightarrow \omega_{2}=\frac{I_{1} \omega}{I_{1}+I_{2}} \end{aligned}$

Asked in: BITSAT 2021

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