If no external torque acts on a system,which of the following remains constant in both magnitude and direction?

An equilateral triangle $ABC$ is made of a uniform wire. Two identical beads are initially at $A$. The triangle is set to rotate about a vertical axis $AO$. The beads are then released simultaneously from rest to slide down along $AB$ and $AC$. Neglecting friction,which quantities are conserved as the beads slide down?

$A$ disc is rotating with an angular speed of $\omega$. If a child sits on it,which of the following is conserved?

$A$ swimmer,while jumping into a river from a height,easily forms a loop in the air if:

$A$ circular plate is rotating in a horizontal plane about an axis passing through its center and perpendicular to the plate with an angular velocity $\omega$. $A$ person sits at the center holding two dumbbells. When he stretches out his hands,the moment of inertia of the system becomes triple. If $E$ is the initial kinetic energy of the system,then the final kinetic energy will be $\frac{E}{x}$. The value of $x$ is $....$

In a playground,there is a merry-go-round of mass $120\ kg$ and radius $4\ m$. The radius of gyration is $3\ m$. $A$ child of mass $30\ kg$ runs at a speed of $5\ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.