A solid cylinder of mass $20 \;kg$ rotates about its axis with angular speed $100\; rad s ^{-1}$ The radius of the cylinder is $0.25 \;m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one  end. Its maximum angular speed is $\omega$. Its centre of mass will rise upto maximum  height :-

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 ___________$J$.

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3 \mathrm{v}^2}{4 \mathrm{~g}}$ with respect to the initial position. The object is

A uniform thin rod of length $l$ is suspended from one of its ends and is rotated at $f$ rotations per second. The rotational kinetic energy of the rod will be