A rod can rotate about a fixed vertical axis. The mass is non$-$uniformly distributed along the length of the rod. A horizontal force of constant magnitude and always perpendicular to the rod is applied at the end. Which of the following quantity $($after one rotation$)$ will not depend on the information that through which end the axis passes? $($Assuming initial angular velocity to be zero$)$

$(1)$ angular momentum

$(2)$ kinetic energy

$(3)$ angular velocity

$(4)$ none of these