Answer
In case A, there are points on the rod that have the same tangential speeds.
Work Step by Step
$$v_T=r\omega$$
In case A, the axis of rotation $R$ divides the rod into 2 sections: the left one and the right one. Any point $A$ on the left side will have a corresponding point $A'$ on the right side such that the distance $RA=RA'=r$, meaning the tangential speeds at $A$ and $A'$ are equal to each other.
In case B, because the axis of rotation $R$ lies at one end, each point $A$ on the rod will have a different value of $RA=r$; therefore, there are no points on the rod that have the same tangential speeds.
