loop problem, "critical velocity" 1. The problem statement, all variables and given/known data First I'd like to ask a general question, if a body enters a loop (like a rollercaster loop) and PASSES the heighest point, assuming there's no friction, will it neccasserlly complete the loop or can it's orbit around the loop still decay? I was told this is so by my professor. according to my textbook there's a term called "critical velocity" which it says is the "minimum speed a body must have WHEN reaching the heighest point in order to complete a full circle", also an equation is given critical speed = square root of g * R. R being the radius of the loop. In my mind, the latter two statements completely contridict one another, so one of them must be wrong. bottom line the question is as follows a block approches a loop of radius = 2 meters, what is the minimal velocity can be, when entering the loop, in order for it to REACH the heighest point of the loop. friction is negliable. 3. The attempt at a solution my attempt at solution is simple 1/2mv^2 = mgh(enery conservation, since at start of loop height is equel to zero, and at the heighest point the velocity is zero v^2 = 2 g h v = 39.2 but according to my text book this is false. for a reason I do not understand, it the equation must look like this 1/2mv^2 = mgh + squareroot(g * R). why must it have a speed at the height point in order to cross it? I don't get this "critical speed" thing, I really don't. I'm desperate for help.