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
$2 \times 10^6\, J$
$3 \times 10^3\, J$
$500\,\pi^2 \,J$
$12 \times 10^3\, J$
$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to $a$ point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. the angular momentum of the system about $P$ when the rod becomes vertical is :
A rod of length $50\,cm$ is pivoted at one end. It is raised such that if makes an angle of $30^o$ fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$ ) will be $(g = 10\,ms^{-2})$
The rotational kinetic energy of a solid sphere of mass $3 \;kg$ and radius $0.2\; m$ rolling down an inclined plane of height $7\; m$ is
Two bodies have their moments of inertia $I$ and $2 I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio
For the pivoted slender rod of length $l$ as shown in figure, the angular velocity as the bar reaches the vertical position after being released in the horizontal position is