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## Homework Statement

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?

## Homework Equations

g=9.8m/s

_{2}perhaps? (Is this dependent on the acceleration?)

## 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.