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  4. A round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I1 rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is

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Q. A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is

AIPMTAIPMT 2004System of Particles and Rotational Motion

Solution:

Applying conservation of angular momentum.
$I_1\omega=(I_1+I_2)\omega_1$
$\omega_1=\frac{I_1\omega}{(I_1+I_2)}$.