Which of the following remains constant in a central force field?

$A$ disc with moment of inertia $I_1$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Another disc with moment of inertia $I_2$ is placed on it,rotating about the same axis. What will be the combined angular velocity of both discs?

$A$ circular platform rotates in a horizontal plane about a vertical axis passing through its center. $A$ tortoise sits on the edge of the platform. The platform is given an initial angular velocity $\omega_0$. The tortoise now moves along a chord of the platform with a constant velocity (relative to the platform). How does the angular velocity $\omega(t)$ of the platform change with time $t$?

Two discs with moments of inertia $I_1$ and $I_2$ and angular speeds $\omega_1$ and $\omega_2$ are rotating about collinear axes passing through their centers of mass and perpendicular to their planes. If they are joined together to rotate about the same axis,the rotational kinetic energy of the system will be:

$A$ thin and circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about its geometrical axis with an angular velocity $\omega$. If another disc of same dimensions but of mass $M/4$ is placed gently on the first disc coaxially,then the new angular velocity of the system is:

$A$ horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time, a viscous fluid of mass $m$ is dropped at the centre and is allowed to spread out and finally fall off. The angular velocity during this period