What is the direction of angular velocity for a rigid body?

In the rotational motion of a rigid body,all particles of the body have

The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = kr^2 / 2$,where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O$,which of the following statements is (are) true?
$(A)$ $v = \sqrt{\frac{k}{2m}} R$
$(B)$ $v = \sqrt{\frac{k}{m}} R$
$(C)$ $L = \sqrt{mk} R^2$
$(D)$ $L = \sqrt{\frac{mk}{2}} R^2$

What is rotational motion and an axis of rotation?

Two blocks of mass $1\ kg$ and $2\ kg$ are connected with each other by a spring of spring constant $60\ N/m$. If the velocity given to the block of mass $2\ kg$ at the natural length is $6\ m/s$,find the maximum velocity of the $1\ kg$ block in the subsequent motion (in $m/s$).

For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?