$A$ rigid lamina is rotating about an axis passing perpendicular to its plane through point $O$ as shown in the figure. The angular velocity of point $B$ with respect to $A$ is ....... $rad/s$.

$A$ rigid rod of length $\ell$ is sliding. At some instant,the position of the rod is as shown in the figure. End $A$ has a constant velocity $v_0$ along the $x$-axis. At $t = 0$,the rod is vertical with end $B$ at $y = \ell$. Which of the following statements is correct?

In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. Then,its angular acceleration $\alpha_2$ is (given that there is no slipping):

Write the formula expressing the relationship between linear velocity and angular velocity for a particle in rotational motion.

$A$ spool of mass $M$ and radius $R$ is unwinding under gravity as a string is pulled. What is the acceleration of the spool?

$A$ cord is wound round the circumference of a wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is $I$. $A$ weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$,the angular velocity of the wheel will be