The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t) = 2t^3 - 6t^2$. The torque on the wheel becomes zero at $t = $ ...... $s$.

$A$ particle of mass $m$ moves in a circular path of radius $r$,under the action of a force which delivers constant power $P$ and increases its speed. The angular acceleration of the particle at time $t$ is proportional to:

$A$ mass of $10 \ kg$ is attached to one end of a massless rod and rotated in a circle of radius $30 \ cm$ with an angular velocity of $10 \ rad/s$. If the body is brought to rest in $10 \ s$ by applying a brake,the magnitude of the torque applied will be ...... $N-m$.

$A$ 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 $\pi \ N$)

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:

$A$ constant torque of $400 \ Nm$ acts on a wheel having a moment of inertia of $100 \ kg \ m^2$ about its central axis. The angular velocity acquired in $4 \ s$ is ....... $rad \ s^{-1}$.