$A$ disc of mass $M$ and radius $R$ is moving with an angular velocity $\omega$ as shown in the figure. Find the angular momentum of the disc about the reference point $O$.

(N/A) The center of mass of the disc moves with a linear velocity $v = R\omega$ and rotates about its center of mass with angular velocity $\omega$.
The total angular momentum $L$ about point $O$ is the sum of the angular momentum due to the motion of the center of mass and the angular momentum due to rotation about the center of mass.
$L = L_{cm} + L_{rot}$
$L = (Mv)R + I_{cm}\omega$
Since $v = R\omega$ and $I_{cm} = \frac{1}{2}MR^2$,we have:
$L = M(R\omega)R + (\frac{1}{2}MR^2)\omega$
$L = MR^2\omega + \frac{1}{2}MR^2\omega$
$L = \frac{3}{2}MR^2\omega$