$A$ uniform rod of length $l$, hinged at the lower end is free to rotate in the vertical plane . If the rod is held vertically in the beginning and then released, the angular acceleration of the rod when it makes an angle of $45^o$ with the horizontal ($I = ml^2/3$)

A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$ If another stationary disc having radius $\frac{ R }{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega_{2}$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is

If the angular momentum of a rotating body is increased by $200\ \%$, then its kinetic energy of rotation will be increased by .......... $\%$

A particle performs uniform circular motion with an angular momentum $L.$  If the angular frequency of the particle is doubled and kinetic energy is halved, its angular momentum becomes

$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)

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