$A$ circular disc of mass $20 \ kg$ and radius $1 \ m$ is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of $2 \ rad \ s^{-1}$. Then the rotational kinetic energy of the disc is (in $J$)

$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.

$A$ solid cylinder of mass $M$ and radius $R$ is rotating about its geometrical axis. $A$ solid sphere of the same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be

$A$ flywheel is in the form of a solid circular disc with a mass of $72 \ kg$ and a radius of $0.5 \ m$. If it rotates at $70 \ rpm$,its rotational kinetic energy is ........ $J$.

$A$ solid sphere of mass $m$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $E_{sphere}/E_{cylinder}$ will be

$A$ thin uniform rod of mass $m$ and length $l$ is suspended from one end,which can oscillate in a vertical plane about the point of suspension. It is pulled to one side and then released. It passes through the equilibrium position with angular speed $\omega$. The kinetic energy while passing through the mean position is