Particle motion analysis in a vertical circular loop using limit concepts

Abstract In this work, we will analyze the condition to a particle leave the contact with a vertical circular loop. This is a typical problem shows in textbooks of Physics, here we will present three different forms to solve it. For that, we will use only fundamental math concepts, it means without use differential calculus. We will show you that, although this analysis is been constructed in intuitive principles, it is equivalent to what is traditional show in textbooks. Overall we will discuss a special case, where a similar deduction of ours leave a false conclusion.