$A$ 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 ....... $rad/s$.

Explain angular velocity and angular acceleration about a fixed axis,derive the equations of rotational motion,and write the analogy between the equations of linear motion and rotational motion.

$A$ wheel starting from rest gains an angular velocity of $10 \ rad/s$ after being uniformly accelerated for $5 \ s$. The total angle through which it has turned is

Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$ and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum,is given by

The instantaneous velocity of point $B$ of a rod of length $L = 0.5 \ m$ is $v = 3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. The angular velocity of the rod for the minimum velocity of end $A$ is:

Two masses $400 \ g$ and $350 \ g$ are suspended from the ends of a light string passing over a heavy pulley of radius $2 \ cm$. When released from rest, the heavier mass is observed to fall $81 \ cm$ in $9 \ s$. The rotational inertia of the pulley is . . . . . . $kg \cdot m^2$. $(g = 9.8 \ m/s^2)$