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There is a question concerning the Physics of a small child's tall that has been bothering me for some time now. I have investigated this to a small degree, but I have not been able to find a satisfactory answer and I believe the resulting answer must be of an elementary nature.

My newborn son has a small plastic toy that is an ellipsoid filled with small, plastic balls (approximately 10-15 balls). The ellipsoid can be revolved around an axis of revolution (the axis of revolution is the major axis of the planar ellipse) and when one spins the ellipsoid, the small, plastic balls find there way (almost immediately) to the plane that is perpendicular to the axis of revolution and contains the minor axis of the planar ellipse where they continue to spin in said plane as long as their speed is sufficiently large.

Spinning ellipsoid

In the image, the red curve is a metal rod (elephant's arms) that keep the ellipsoid in suspension, the green line is the axis of revolution, and the blue curve is the curve that the small, plastic, balls move to (almost immediately) and rotate along as long as the speed is sufficiently fast enough.

Is there an elementary explanation (elementary = 2 undergraduate courses in Physics) for what I am observing? I am also interested in any explanation of what I am observing that would lead me to learning something new.

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2 Answers 2

It's not hard to see why the balls tend to rotate along the blue curve.

There are 3 forces on each of the rotating balls: the weight, the force due to the contact with the surface of the ellipsoid, and the friction. Friction is what makes the balls start and stop rotating, and it's tangential to the circle in which the balls are rotating. The weight makes things a tad more complicated, but it's not very relevant to your question.

The contact force (also called normal force) is the key here. It is always perpendicular to the surface, so if the ball is not rotating along the blue line, there will be a component of this force pointing towards the blue curve. See this diagram (I'm only showing the normal force):

force diagram

The end result is that the blue curve is the only stable path for the balls.

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The rotation of the ellipse requires the small balls to move in a circle,(the normal betweeen the ball and the ellipose provides the centrepetal force) and the curvature of the ellipse requires the balls to move in a circle as u described.

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