An electric motor is started from rest to produce a torque. It acquires an angular acceleration given by $\alpha = 3t - t^2$. The angular acceleration becomes zero after $2 \ s$. Calculate the angular velocity after $6 \ s$.

$A$ disc of mass $M \ kg$ and radius $R \ m$ is rotating at an angular speed of $\omega \ rad/s$ when the motor is switched off. Neglecting the friction at the axle,the force that must be applied tangentially to the wheel to bring it to rest in time $t$ is ...............

The angular speed of a motor wheel is increased from $1200 rpm$ to $3120 rpm$ in $16 s$. The angular acceleration of the motor wheel is

Two circular discs of radius $10 \ \text{cm}$ each are joined at their centres by a rod of length $30 \ \text{cm}$ and mass $600 \ \text{g}$ as shown in the figure. If the mass of each disc is $600 \ \text{g}$ and the applied torque between the two discs is $43 \times 10^{5} \ \text{dyne cm}$,the angular acceleration of the discs about the given axis $AB$ is . . . . . . $\text{rad/s}^{2}$.

Consider a $20\, kg$ uniform circular disk of radius $0.2\, m$. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F = 20\, N$ through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50\, rad/s$. The value of $n$,to the nearest integer,is.......... [Given: In one complete revolution,the disk rotates by $6.28\, rad$]

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