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: A
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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