An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$belt drive. The motor pulley is $8\,cm$ in radius,and the tension in the $V-$belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be ...... $kW$.

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

What does the time rate of change of angular momentum represent?

$A$ non-uniform rod $OA$ of linear mass density $\lambda = \lambda_0 x$ (where $\lambda_0$ is a constant) is suspended from the ceiling with a hinge joint at $O$ and a light string as shown in the figure. Find the angular acceleration of the rod just after the string is cut.

Which of the following are correct expressions for torque acting on a body?
$A. \ \vec{\tau}=\vec{ r } \times \vec{ L }$
$B. \ \vec{\tau}=\frac{ d }{ dt }(\vec{ r } \times \vec{ p })$
$C. \ \vec{\tau}=\vec{ r } \times \frac{ d \vec{ p }}{ dt }$
$D. \ \vec{\tau}= I \vec{\alpha}$
$E. \ \vec{\tau}=\vec{ r } \times \vec{ F }$
($\vec{ r }=$ position vector; $\vec{ p }=$ linear momentum;
$\vec{ L }=$ angular momentum; $\vec{\alpha}=$ angular acceleration;
$I=$ moment of inertia; $\vec{ F }=$ force; $t =$ time)
Choose the correct answer from the options given below:

$A$ torque of $30 \ Nm$ is applied for $15 \ s$ on a stationary wheel of mass $5 \ kg$. The moment of inertia of the wheel is $2 \ kg \ m^2$. The angular displacement of the wheel in $10 \ s$ is ....... $rad$.