Neglecting the moment of inertia of the “light rod” and the tiny rotational energy the “small heavy ball” obtains in the “ride” part of the problem (the ball only rotates through an angle of about π/4), the situation at the end of the ride is dynamically identical to this following well- known problem in theoretical mechanics:1 “A particle is placed on top of a smooth sphere of radius a. If the particle is slightly disturbed, at what point will it leave the sphere?” (Note that the “particle” is not assumed to rotate any more than the ball on the rod does. The assumption is that it slides frictionlessly down the sphere.)

Let the angle θ be measured from the vertical and let θs be the separation angle as shown in the figure. For arbitrary θ < θs, there are two forces acting on the ball: mg...
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