Two discs of moment of inertia I_1 and I_2 an | vedclass

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Question

(D) According to the principle of conservation of angular momentum,the total angular momentum of the system remains constant when the two discs are co

Vedclass · Accepted Answer

$\frac{(I_1 \omega_1+I_2 \omega_2)^2}{2(I_1+I_2)}$

Vedclass · Answer

(D) According to the principle of conservation of angular momentum,the total angular momentum of the system remains constant when the two discs are coupled.Initial angular momentum $L_i = I_1 \omega_1 + I_2 \omega_2$.When the discs rotate together,they form a single system with a combined moment of inertia $I = I_1 + I_2$ and a common angular velocity $\omega$.The final angular momentum is $L_f = (I_1 + I_2) \omega$.Equating $L_i = L_f$,we get $\omega = \frac{I_1 \omega_1 + I_2 \omega_2}{I_1 + I_2}$.The rotational kinetic energy $K$ of the system is given by $K = \frac{1}{2} I \omega^2$.Substituting the values of $I$ and $\omega$:$K = \frac{1}{2} (I_1 + I_2) \left( \frac{I_1 \omega_1 + I_2 \omega_2}{I_1 + I_2} \right)^2$.$K = \frac{(I_1 \omega_1 + I_2 \omega_2)^2}{2(I_1 + I_2)}$.

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