An automobile engine develops $200 \ hp$ at $6000 \ rpm$. The corresponding torque is ......... $N \cdot m$.

Write the Newton's second law for rotational motion about a fixed axis.

$A$ string is wrapped around the rim of a wheel of moment of inertia $0.40 \ kg \cdot m^2$ and radius $10 \ cm$. The wheel is free to rotate about its axis. Initially,the wheel is at rest. The string is now pulled by a force of $40 \ N$. The angular velocity of the wheel after $10 \ s$ is $x \ rad/s$,where $x$ is $\qquad$

$A$ disc of mass $25 \ kg$ and radius $0.2 \ m$ is rotating at $240 \ r.p.m.$ $A$ retarding torque brings it to rest in $20 \ s$. If the torque is due to a force applied tangentially on the rim of the disc,then the magnitude of the force is:

$A$ 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 .......

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 ........ $rad/s^2$.