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Imagine we have a particle sitting on top of a sphere of radius R. The sphere is inertially fixed. A small disturbance force sets the particle in motion from its unstable equilibrium point atop the sphere. Theta is measured from the vertical to the position of the particle. Assume this angle is formed from the center of the circle. At what angle will the particle separate from the sphere? I really can't think of a geometrical condition that must be true for this problem. I've determined the velocity as a function of theta, assuming the only forces are the normal and weight (no friction - the sphere is smooth).
Perhaps this occurs when the horizontal component of the velocity is greater than the rate of change of the sphere's curvature in the x direction?
Any hints, ideas? Thanks
Perhaps this occurs when the horizontal component of the velocity is greater than the rate of change of the sphere's curvature in the x direction?
Any hints, ideas? Thanks