An round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its…
An 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 $\mathrm{I}_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:
$\frac{I_2 \omega}{I_2+I_2}$
$\omega$
$\frac{I_1 \omega}{I_1+I_2}$
$\frac{\left(I_1+I_2\right) \omega}{I_1}$
Solution
From law of conservation of angular momentum we have:
$\begin{aligned}
& I_1 \omega_1=\left(I_1+I_2\right) \omega_2 \\
& \therefore \quad \omega_2=\frac{I_1 \omega_1}{\left(I_1+I_2\right)}=\frac{I_1 \omega}{I_1+I_2} \\
&
\end{aligned}$
.