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

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $(\alpha - \beta t)$ at time $t,$ where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

$A$ disc is rotating with an angular velocity $\omega_0$. $A$ constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{\omega_0}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest?

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 has a moment of inertia $5 \times 10^{-3} \, kg \, m^2$ and is making $20 \, rev/sec$. The torque needed to stop it in $10 \, sec$ is $............. \times 10^{-2} \, N-m$. (in $\pi$)

$A$ torque of $10^5 \ N \cdot m$ is applied to a disc of mass $10 \ kg$ and radius of gyration $50 \ m$. What is the value of the angular acceleration in $rad/s^2$?