(adsbygoogle = window.adsbygoogle || []).push({}); 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/s_{2}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.

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# Homework Help: Frictionless sphere, falling particle

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