A body of moment of inertia of $3\ kg - {m^2}$ rotating with an angular speed of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a speed of ......... $m/s$.

Two identical circular loops are moving with same kinetic energy one rolls $\&$ other slides. The ratio of their speed is 

$A$ 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 :

Consider a Disc of mass $5 \mathrm{~kg}$, radius $2 \mathrm{~m}$, rotating with angular velocity of $10 \mathrm{rad} / \mathrm{s}$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ___________$J$.

The speed of rolling of a ring of mass $M$ changes from $V$to $3\ V$. What is the change in its kinetic energy

Write the formula for power and angular momentum in rotational motion.