A rigid cube is in motion. At the time depicted in the figure the face $ABCD$ is vertical, the velocity of vertex $A$ is vertical down with value $v$, the velocity of vertex $C$ is vertical up with value $v$. The velocity of vertex $H$ has a vertical component up with magnitude $v$ and an horizontal component pointing towards vertex $D$ with magnitude $v$ and the resulting velocity points from $H$ to $C$ (the velocity from $H$ to $C$ makes a 45 degree angle with $DH$). The cube has side $s$.
What are the points with minimum and maximum velocity in the cube at this time?
If the velocity of $H$ were purely vertical up, then the cube would do a planar rotation counterclockwise around $A$. The horizontal component of the velocity of $H$ makes it so that in addition to the vertical counterclockwise rotation there is a rotation of $AEHD$ around $A$. The resulting rotation is a 3D rotation. The velocity of a given point $\textbf{r}=(x,y,z)$ on the cube can be written as the velocity of a given vertex say $A$ + a rotation about that point through $$\textbf{v}=\textbf{v}_{A}+\vec{\omega}\times\textbf{r}$$
How do I find out $\vec{\omega}$, the angular velocity of the cube about $A$? I suppose I cant just add the $\vec{\omega}$ for the two rotations.