$A$ person is rotating on a rotating table with their arms held down. Suddenly,they spread their arms out. What happens to their angular momentum?

$A$ particle is moving in a uniform circular motion. At which point in the plane of the circle will the angular momentum of the particle be conserved?

$A$ man stands on a rotating platform with his arms stretched horizontally,holding a $5\; kg$ weight in each hand. The angular speed of the platform is $30$ revolutions per minute. The man then brings his arms close to his body,with the distance of each weight from the axis changing from $90\; cm$ to $20\; cm$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $7.6\; kg\; m^2$.
$(a)$ What is his new angular speed? (Neglect friction.)
$(b)$ Is kinetic energy conserved in the process? If not,from where does the change come about?

An ice block is placed at the center of a circular table. The system is rotated about the axis of the table with an angular velocity $\omega$. If the ice starts melting without evaporation,the rotational speed of the system will:

$A$ thin ring of mass $M$ and radius $R$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If $4$ point masses each of mass $m$ are placed gently at the opposite ends of two mutually perpendicular diameters,what will be the new angular velocity of the system?

$A$ 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?