A) \[\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}\]
B) \[\omega \]
C) \[\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}\]
D) \[\frac{({{I}_{1}}+{{I}_{2}})\,\omega }{{{I}_{1}}}\]
Correct Answer: C
Solution :
Key Idea: When no external torque acts on a system of particles, then the total angular momentum of the system remains always a constant. The angular momentum of a disc of moment of inertia \[{{I}_{1}}\]and rotating about its axis with angular velocity \[\omega \]is \[{{L}_{1}}={{I}_{1}}\omega \] When a round disc of moment of inertia \[{{I}_{2}}\] is placed on first disc, then angular momentum of the combination is \[{{L}_{2}}=({{I}_{1}}+{{I}_{2}})\omega \] In the absence of any external torque, angular momentum remains conserved i.e., \[{{L}_{1}}={{L}_{2}}\] \[{{I}_{1}}\,\omega =({{I}_{1}}+{{I}_{2}})\omega \] \[\Rightarrow \] \[\omega '=\frac{{{I}_{2}}\omega }{I+{{I}_{2}}}\]
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