1. The problem statement, all variables and given/known data My uncle gave me this problem: A very small ball of mass m is at the very top of a big ball of radius r and is pushed very lightly (initial velocity is basically zero). What is the angle θ that the small ball's position vector (originating from the origin of the big ball) makes with the vertical y axis as the small ball comes off of (or departs from) the big ball? PLEASE TELL ME ONLY IF I'M ON THE RIGHT TRACK OR NOT! IF I'M NOT, A HINT WOULD BE GREATLY APPRECIATED (sorry for the all-caps, but I just need a little push in the right direction, not the fully worked out solution). 2. Relevant equations ƩF=ma 3. The attempt at a solution The normal force N exerted on the small ball by the big ball is N=mgcosθ. ma(y)=mg-Ncosθ a(y)=g-gcosθcosθ ma(x)=Nsinθ a(x)=mgcosθsinθ a(x) and a(y) being the accelerations of the ball in the x and y coordinates, respectively. Once I got the accelerations, I was sort of stuck. I'm not really sure what to do next. One thing I've though of is to think of under what conditions the small ball has departed. What I came up with was that when x>rsinθ, the small ball has departed. (x being the x position of the small ball). I tried integrating the acceleration in the x direction twice to get position, but that didn't really help. Does anybody have any hints? Thanks very much.