• # question_answer ${{I}_{1}}$ and ${{I}_{2}}$ are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are ${{\omega }_{1}}$ and ${{\omega }_{2}}$ respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be A)  $\frac{{{I}_{1}}+{{I}_{2}}}{{{\omega }_{1}}+{{\omega }_{2}}}$ B)  $\frac{{{I}_{2}}{{\omega }_{1}}-{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}-{{I}_{2}}}$ C)  $\frac{{{I}_{2}}{{\omega }_{1}}+{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}$ D)  $\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}$

According to conservation of angular momentum ${{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}=({{I}_{1}}+{{I}_{2}})\omega$ $\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{({{I}_{1}}+{{I}_{2}})}=\omega$