$A$ wheel having a moment of inertia of $4 \,kg \cdot m^2$ about its symmetrical axis rotates at a rate of $240 \,rpm$ about it. The torque required to stop the rotation of the wheel in one minute is ............ $N \cdot m$.

$A$ massless rod of length $2l$ has equal point masses $m$ attached to its two ends as shown in the figure. The rod is rotating about an axis passing through its centre and making an angle $\alpha$ with the axis. The magnitude of the rate of change of angular momentum of the rod,i.e.,$\left|\frac{dL}{dt}\right|$,is equal to:

$A$ pulley of radius $2 \ m$ is rotated about its axis by a force $F = (20t - 5t^2) \ N$ (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 \ kg \ m^2$,the number of rotations made by the pulley before its direction of motion is reversed is approximately equal to: (in $.5$)

Two equal and opposite forces are applied tangentially to a uniform disc of mass $M$ and radius $R$ as shown in the figure. If the disc is pivoted at its centre and free to rotate in its plane,the angular acceleration of the disc is ............

$A$ torque of $50 \ N \cdot m$ causes a wheel to rotate from rest through $200 \ rad$ in $5 \ s$. The value of the angular acceleration produced is ...... $rad/s^2$.

$A$ constant torque is applied to a wheel undergoing uniform circular motion,causing its angular momentum to change from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of this torque is .......