A thin uniform disc welded (rigidly fixed) horizontally at its rim to a mass less stick, as shown in the figure. When the disc and stick system is rotated about the origin on a horizontal frictionless plane with angular speed $\omega$, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed $\omega$ in this case.

 

Now consider two similar systems as shown in the figure. Case (a) the disc with its face vertical and parallel to x-z plane; Case (b) the disc with its face making an angle of 45⁰ with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed $\omega$ about the z-axis.

Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?