$A$ swimmer curls their body before entering the water so that...

Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds $\omega_1$ and $\omega_2$ are rotating along collinear axes passing through their centers of mass and perpendicular to their planes. If the two discs are made to rotate together along the same axis,what will be the rotational kinetic energy of the system?

$A$ small disk is attached to the end of a light inextensible string,which passes through a hole in a frictionless horizontal tabletop. Initially,the disk moves on a circle of radius $R$ with kinetic energy $K_0$. The string is then slowly pulled so that the disk finally rotates on a circle of radius $\frac{R}{\eta}$. What is the work $W$ done in pulling the string?

$A$ man standing on a turn-table is rotating at a certain angular frequency with his arms outstretched. He suddenly folds his arms. If his moment of inertia with folded arms is $75 \%$ of that with outstretched arms,then his rotational kinetic energy will

Two small beads are initially at $A$ on an equilateral triangle made of uniform wires. The triangle is rotated about the vertical axis $AO$. The beads are released from rest simultaneously and slide down along $AB$ and $AC$ respectively (as shown in the figure). Which quantities are conserved as the beads slide down? (Friction is negligible)

$A$ thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$. If two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring,the ring will then rotate with an angular velocity: