A flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400\, kgm^2$, its rotational kinetic energy is
$2 \times 10^6\, J$
$3 \times 10^3\, J$
$500\,\pi^2 \,J$
$12 \times 10^3\, J$
A solid cylinder of mass $3\, kg$ is rolling on a horizontal surface with velocity $4\, m s^{- 1}$. It collides with a horizontal spring of force constant $200 \,N m^{-1}$. The maximum compression produced in the spring will be ............... $\mathrm{m}$
If the angular momentum of a rotating body is increased by $200\ \%$, then its kinetic energy of rotation will be increased by .......... $\%$
A disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/\sec .$ Its rotational kinetic energy is
Write the formula for rotational kinetic energy.