Minimum velocity to complete a vertical circular loop: a kinematic approach

In this simple study is presented an alternative method for the classic problem of finding the minimum velocity necessary to complete a vertical loop of radius $R$. Unlike the usual approaches of introductory textbooks of basic physics, which use the concept of force (normal and weight), in this study only kinematics and geometrics concepts are applied to find the known value for the minimum velocity $v_{\mathrm{\text{min}}}=\sqrt{gR}$.

Keywords:
kinematic; circular motion; projectile motion