The $M.I.$ of a body about the given axis is $1.2 \, kg \cdot m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500 \, J$,an angular acceleration of $25 \, rad/s^2$ must be applied about that axis for a duration of ........ $s$.

$A$ disc of mass $1\,kg$ and radius $R$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of the disc. $A$ body of the same mass as that of the disc is fixed at the highest point of the disc. Now the system is released. When the body comes to the lowest position,its angular speed will be $4 \sqrt{\frac{x}{3 R}} \text{ rad s}^{-1}$ where $x=$ (Given $g = 10 \text{ m s}^{-2}$)

$A$ cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of the wheel is $10 \ kg$ and the radius is $10 \ cm$. It can rotate freely without any friction. Initially,the wheel is at rest. If a steady pull of $20 \ N$ is applied on the cord,the angular velocity (in $rad/s$) of the wheel,after the cord is unwound by $1 \ m$,would be:

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

$A$ tangential force $F$ is applied on a disc of radius $R$,due to which it deflects through an angle $\theta$ from its initial position. The work done by this force would be

$A$ thin rod of length $l$ and mass $m$ oscillates in a vertical plane about a horizontal axis passing through one of its ends. If the maximum angular velocity of the rod is $\omega$,what is the maximum height reached by its center of mass?