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Two discs of moments of inertia `I_1` and `I_2` about their respective axes, rotating with angular frequencies, `omega_1` and `omega_2` respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be `A`.A. `(I_1 omega_1 + I_2 omega_2)/(I_1 + I_2)`B. `(I_2 omega_1 + I_1 omega_2)/(I_1 + I_2)`C. `(I_1 omega_1 + I_2 omega_2)/(I_1 - I_2)`D. `(I_2 omega_1 + I_1 omega_2)/(I_1 - I_2)` |
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Answer» Correct Answer - A (a) Total initial angular momentum of the two discs is `L_i = I_1 omega_1 + I_2 omega_2` When two discs are brought into contact face to face (one on top of the other) and their axes of rotation coincide, the moment of inertia `I` of the system is equal to the sum of their individual moments of inertia. i.e., `I = I_1 + I_2` Let `omega` be the final angular speed of the system. The final angular momentum of the system is. `L_f = I omega = (I_1 + I_2) omega` As no external torque acts on the system, therefore according to law of conservation of angular momentum, we get `L_i = L_f` `I_i omega_1 + I_2 omega_2 = (I_1 + I_2) omega` `omega = (I_1 omega_1 + I_2 omega_2)/(I_1 + I_2)`. |
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