The direction of the angular velocity vector is along which of the following?

$A$ bob of mass $m$ is tied by a massless string whose other end is wound on a flywheel (disc) of radius $R$ and mass $m$. When released from rest,the bob starts falling vertically downwards. If the bob has covered a vertical distance $h$,then the angular speed of the wheel will be (There is no slipping between the string and the wheel,$g$ is the acceleration due to gravity).

As shown in the figure,a mass $m = 500 \ g$ hangs from the rim of a wheel of radius $r = 20 \ cm$. When released from rest,the mass falls $2.0 \ m$ in $8 \ s$. Then the moment of inertia of the wheel is .......... $kg \cdot m^2$. $(g = 10 \ m/s^2)$

Let $\vec{A}$ be a unit vector along the axis of rotation of a purely rotating body and $\vec{B}$ be a unit vector along the velocity of a particle $P$ of the body away from the axis. The value of $\vec{A} \cdot \vec{B}$ is

$A$ rod of length $l$ and mass $m$ lies on a fixed horizontal smooth table. $A$ cord is led through a pulley,and its horizontal part is attached to one end of the rod,while its vertical part is attached to a block of mass $m_1$. Assume the pulley and the cord are ideal. The maximum possible acceleration of the rod's centre of mass $C$ (for all possible values of masses $m$ and $m_1$) at the moment of releasing the block $m_1$ is $\frac{g}{n}$. Find the value of $n$.

What is a rigid body?