Suppose I make a pendulum consisting of a long string connected to a hollow sphere, then fill the sphere half way with water and set the pendulum in motion by giving all the water and the sphere some initial horizontal velocity. What does the surface of the water do?

  • $\begingroup$ In the approx of small oscillation and the sway of the water not affecting the simple pendulum motion, the surface assumes the equipotential in the net acceleration of the sphere...how to get that equipotential across sphere volume seems difficult $\endgroup$ – lineage Aug 7 '19 at 19:42
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    $\begingroup$ I'm a great believer in letting nature provide answers to simple questions like this. The shape of the container will make very little difference. Try hanging a bucket half full of water on a long rope, and gently start it swinging. See what happens. $\endgroup$ – S. McGrew Aug 7 '19 at 22:45
  • $\begingroup$ @S.McGrew, I respectfully (partially) disagree. The pendulum is usually studied in the approximation of small oscillations, so that the DE is nice and solvable. This is a theoretical construct. Another famous related example is the Newton's bucket. I highly doubt that Sir Isaac used to rotate buckets (at his time, handmade, and pretty asymmetrical and unbalanced) half-filled with water and hanging on a rope. Another way to look at it: you do an experiment not to "see what happens", but to confirm (or, conversely, falsify, as Sir Karl idealized it) a model, itself built on a theory. $\endgroup$ – kkm Aug 8 '19 at 3:00
  • $\begingroup$ OK, I'll agree to disagree. In my experience, observations usually precede theory. Targeted, carefully designed experiments then follow to confirm, refine, or falsify the theory. $\endgroup$ – S. McGrew Aug 8 '19 at 15:10

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