I have found similar problems to this elsewhere on the forum, but I still can't seem to understand it: 1. The problem statement, all variables and given/known data A mass rests on the top of a frictionless fixed sphere with radius R, and begins with an infinitesimally small velocity to slide off. At what angle theta (measured from the horizontal) will it loose contact with the sphere? 3. The attempt at a solution I used the conservation of mechanical energy E = 1/2mv^2 - mgR(sin(theta)+1), plugged in -2Rmg for E (since initially the mass is at rest and at the top of the sphere) and derived v^2 = 2gR(sin(theta)-3). Assuming that the centripetal force is mg(sin(theta)) - Fn , and equal to v^2/R, I wrote: 2mgR(sin(theta)-3) = mgR(sin(theta)) - FnR. Now, at the point where the mass looses contact, Fn = 0, so 2mgR(sin(theta)-3) = mgR(sin(theta)) When I solve for theta I get arcsin(6)??? I fear I have made some grievous conceptual error, and I would greatly appreciate any help you can give.