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1. A point mass is on a fixed hemisphere under the influence of a g field.

2. A hoop is on a fixed hemisphere under the influence of a g field.

I have found the equations of motion, etc... no probs there.

I found that the point mass will leave the sphere at a smaller angle than the hoop. Here the angle is measured w.r.t the vertical.

I would not have guesed this and am wondering if anyone has a good conceptual explanation for this. thanks