$A$ pulley has the shape of a uniform solid disc of mass $2 \ kg$ and radius $0.5 \ m$. $A$ string is wrapped over its rim and is pulled by a force of $2.5 \ N$. The pulley is free to rotate about its axis. Initially,the pulley is at rest. Find the angular velocity of the pulley just after $10 \ s$. (in $rad/s$)

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 = $ ...... $s$.

$A$ uniform disc of mass $5\,g$ and radius $1\,cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque,that will make the system rotate about $AB$ at $25$ rotations per second in $5\,s$,is close to:

What is the physical quantity of the time rate of the angular momentum?

$A$ crew of scientists has built a new space station. The space station is shaped like a wheel of radius $R,$ with essentially all its mass $M$ at the rim. When the crew arrives,the station will be set rotating at a rate that causes an object at the rim to have radial acceleration $g,$ thereby simulating Earth's surface gravity. This is accomplished by two small rockets,each with thrust $T$ newtons,mounted on the station's rim. How long a time $t$ does one need to fire the rockets to achieve the desired condition?

$A$ 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 ....... $rad \ s^{-1}$.