$A$ uniform disc rotates at $10$ revolutions per second. $A$ torque is applied to it, producing an angular acceleration of $5 \text{ rad s}^{-2}$. After $2 \text{ s}$, its angular velocity is ...... $\text{rad s}^{-1}$ and the number of revolutions completed by the disc in $2 \text{ s}$ is ...... .

$A$ uniform disc of mass $m$ and radius $R$ is pivoted at point $P$ and is free to rotate in a vertical plane. The centre $C$ of the disc is initially in a horizontal position with $P$ as shown in the figure. If it is released from this position,then its angular acceleration when the line $PC$ is inclined to the horizontal at an angle $\theta$ is ............

$A$ wheel having a moment of inertia $2 \; kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \; rpm$ about this axis. The torque required to stop the wheel's rotation in one minute is:

In the following figure,$r_1 = 5\,cm$ and $r_2 = 30\,cm$. If the moment of inertia of the wheel is $1500\,kg\cdot m^2$,then its angular acceleration will be (approximately):

$A$ wheel rotates about its geometric axis at a speed of $60 \ rpm$. If the moment of inertia of the wheel about this axis is $2 \ kg \ m^2$,what torque is required to stop its rotation in one minute?

One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.