$A$ sphere is rotating about a diameter.

What is rotational motion? Explain it with an example.

$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

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?
$(A)$ $v = \sqrt{\frac{k}{2m}} R$
$(B)$ $v = \sqrt{\frac{k}{m}} R$
$(C)$ $L = \sqrt{mk} R^2$
$(D)$ $L = \sqrt{\frac{mk}{2}} R^2$

$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. If $dv/dt = 0$,then the angular acceleration of the ladder when $\alpha = 45^o$ is:

What is pure translational motion?