In the motion of a spinning top at any one place,does the point in the spinning top remain stationary or does the line remain stationary?

$A$ 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).

What is the linear velocity if angular velocity $\vec{\omega} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$?

$A$ block of mass $2\,kg$ hangs from the rim of a wheel of radius $0.5\,m$. On releasing from rest,the block falls through $5\,m$ height in $2\,s$. The moment of inertia of the wheel will be ...... $kg \cdot m^2$.

When a ceiling fan is switched off,its angular velocity falls to $\frac{1}{3}$ of its initial value while it makes $24$ rotations. How many more rotations will it make before coming to rest?

Two particles of equal mass $m$ at $A$ and $B$ are connected by a rigid light rod $AB$ of length $L$ lying on a smooth horizontal table. An impulse $J$ is applied at $A$ in the plane of the table and perpendicular to $AB$. Then the velocity of the particle at $A$ is: