$A$ string is wrapped around the rim of a wheel with a moment of inertia of $0.20 \ kg \cdot m^2$ and a radius of $20 \ cm$. The wheel is free to rotate about its axis and is initially at rest. The string is now pulled with a force of $20 \ N$. What will be the angular velocity of the wheel after $5 \ s$ in $rad/s$?

$A$ 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 $.5$)

Four masses of $2 \ kg$ each are attached to an axle by spokes of length $1/4 \ m$ as shown in the figure. $A$ force $F = 24 \ N$ is applied at the end of a spoke of length $1/2 \ m$ at an angle of $30^{\circ}$ to produce an angular acceleration $\alpha$. The value of $\alpha$ is ........ $rad/s^2$.

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 subjected to a torque of $1000 \ N-m$ and rotates with a moment of inertia of $200 \ kg-m^2$ about an axis passing through its center. What will be the angular velocity of the wheel after $3 \ s$?

$A$ 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 .......