$A$ disc of mass $10 \ kg$ and radius $0.1 \ m$ is rotating at $120 \ rpm$. $A$ retarding torque brings it to rest in $10 \ s$. If the same torque is due to a force applied tangentially on the rim of the disc, then the magnitude of the force is: (in $\pi \ N$)

$A$ solid disc of radius $20 \, \text{cm}$ and mass $10 \, \text{kg}$ is rotating with an angular velocity of $600 \, \text{rpm}$ about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc to rest in $10 \, \text{s}$ is $x \pi \times 10^{-1} \, \text{Nm}$. Find the value of $x$.

If $I, \alpha$ and $\tau$ are the moment of inertia,angular acceleration,and torque respectively of a body rotating about an axis with angular velocity $\omega$,then:

$A$ homogeneous disc with a radius $0.2\, m$ and mass $5\, kg$ rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula $\omega = 2 + 6t$. The tangential force applied to the rim of the disc is ........ $N.$

Two small balls with masses $m$ and $2m$ are attached to both ends of a rigid rod of length $d$ and negligible mass. If the angular momentum of this system is $L$ about an axis $(A)$ passing through its centre of mass and perpendicular to the rod,then the angular velocity of the system about $A$ is:

$A$ wheel is rotating at a rate of $900$ revolutions per minute about its axis. When the power source is cut off,it comes to rest in $1$ minute. The angular retardation of the wheel in $rad/s^2$ is: