1. The problem statement, all variables and given/known data A particle initially sits on top of a large smooth sphere of radius R. The particle begins to slide down the sphere without friction. At what angle . does the particle lose contact with the sphere? 2. Relevant equations g=9.8m/s2 perhaps? (Is this dependent on the acceleration?) 3. The attempt at a solution It seems like the angle that the particle loses contact with the sphere is possibly dependent on the acceleration of the particle. If so, I don't know how to mathematically explain this relationship. If the angle is equal to x, sinx will give a tangent vector of a magnitude proportional to the size of the angle, but I don't know if that gets me anywhere. My second guess is that the particle either loses contact with the sphere at 90 degrees, or 45 degrees. I know that the particle cannot possibly hold on to the sphere without an adhesive property after 90 degrees. I do not know if a particle would be able to stay on the sphere past 45 degrees though.