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Whenever I put an ice-cube into a glass of hot water, so that it melts quickly, and it is initially rotating slowly, I noticed that its rotational speed increases as it melts and 'shrinks'. Why?

I thought of conservation of angular momentum, but does that really apply here? The part of the ice that melts into water would be 'carrying' off some of the ice-cube's angular momentum as it breaks away and diffuses into the surrounding water. So I see no reason for the remaining ice-cube to rotate faster.

I can only think of one possible reason, and it is just a guess: The friction between the water and ice causes the melting part to form eddies that spin in the opposite direction to the ice-cube, and so the ice-cube loses much less momentum in melting since its boundary is actually moving together with the adjacent eddy boundaries. If the eddies expand as the ice-cube shrinks, it seems we would have to conclude that the ice-cube must rotate faster to preserve total angular momentum.

But such an analysis seems very weird, and cannot be a proper picture of what is really happening since the 'number' of eddies must decrease as the ice-cube shrinks, so they must combine in some manner, and I have no idea how any of this works out.

So, what really is spinning the ice?

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    $\begingroup$ A video of the ice cubes melting/spinning would be useful $\endgroup$ – binaryfunt Dec 31 '18 at 12:34
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    $\begingroup$ Whenever I have observed this phenomenon, I've thought it was correlated with air bubbles near the white center of the cube breaching the surface of the ice, rather than with the transparent solid ice near the edges of a fresh cube. A video would help to confirm that everyone is discussing the same effect. $\endgroup$ – rob♦ Dec 31 '18 at 17:08
  • $\begingroup$ @rob: I don't have the tools to make a proper video, but I don't think it's difficult to reproduce. My ice is made from rather pure boiled water but it does have air bubbles trapped in it. Even if air bubbles breach the surface of the ice (which they do in my case), how could it cause the ice to rotate faster? That is what I cannot understand. Either the rotational momentum is not taken away by whatever is leaving the ice (whether melted water or air) sufficiently, or the energy from the heat gradient is contributing, such as Lewis Miller suggests. $\endgroup$ – user21820 Dec 31 '18 at 17:34
  • $\begingroup$ My ice-cube is also not cube-shaped (due to the ice-tray) but look like this without the ice spike. I doubt that the air bubbles are trapped in some intrinsically asymmetric way such that their escape imparts a non-negligible torque. $\endgroup$ – user21820 Dec 31 '18 at 17:37
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    $\begingroup$ scifun.chem.wisc.edu/wop/Vortex.html, uw.physics.wisc.edu/~wonders/Vortex.html $\endgroup$ – sammy gerbil Dec 31 '18 at 19:55
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The same physics that explains why water tends to rotate when you drain your bathtub also answers this question. In both situations there is a downward flow of water that accentuates the residual rotation that remains after the vessel has been filled. In the case of your bathtub the downward flow results from opening the drain. For the ice cube in hot water the downward flow is created when the just melted water sinks because it is colder than the surrounding water. This downward flow creates a vortex and it is the interaction between the ice cube and the vortex that causes the increase in rotational speed ot the ice cube.

There is an urban legend that claims that the direction of spin in drains is associated with the coriolis effect and differs between the northern and southern hemispheres. While this may be true of hurricanes and cyclones, it is too small an effect to apply to bathtub drains or glasses of hot water with ice cubes. For these smaller scale systems the rotation direction is dictated by the residual rotation created when the vessel was filled. This small residual rotation may not be noticeable until the downward flow accentuates it.

Edit: @sammygerbil has found a website that discusses this phenomenon and attributes it to the same mechanism I outlined above.

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  • $\begingroup$ So you're saying that the temperature gradient is powering the whirlpool. It would be interesting to see visual evidence of such a motion in the water melting off a dyed ice-cube. I only noticed this effect when the water was relatively hot, so your suggestion is actually quite plausible. $\endgroup$ – user21820 Dec 31 '18 at 16:10
  • $\begingroup$ Two more "not a questions" 1. geometry(when ice melt, it geometric shape change from a cubic to more likely a slim of ice, which made the original rotational axis become the one(of two) that easily to be rotated.) 2. I still a little bit suspicious about the main cause to be "current" caused by the diffusion. I was thinking maybe rotational momentum was conserved because melting did not do a good job at taking away rotational momentum.(The rotational energy was taken away by the fraction force, but not melting) $\endgroup$ – ShoutOutAndCalculate Dec 31 '18 at 16:56
  • $\begingroup$ For a sense of the scale of the Coriolis effect in a human-sized water vessel, see these synchronized multi-hemispheric videos. $\endgroup$ – rob♦ Dec 31 '18 at 17:31
  • $\begingroup$ @rob: I love SmarterEveryDay and Veritasium, but it strikes me as odd that they didn't analyze the possible confounding variables. Firstly, if it was at random, then the probability of the water swirling each way would be 1/2. Secondly, even if repeating the experiment many times yields the same result, it may be due to an irregularity in the outlet hole or pipe, which can easily decide the direction of swirling, and it would be extremely difficult to prove that no such irregularity was there... $\endgroup$ – user21820 Dec 31 '18 at 17:56
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    $\begingroup$ @descheleschilder You are probably right that the primary reason for the speed-up of the ice cube spin is not its decreasing size. I suspect that it is really its interaction with the vortex that makes it speed up. That was really what I meant by "the mechanism" in my answer.. The website found by Sammy actually suggests that the ice cube be "carefully placed" in the water while it (the water) is still rotating after being stirred. The questioin suggests that it was the ice cube that was "slowly rotating." I'll edit my answer to remove the reference to the decreasing size of the cube. $\endgroup$ – Lewis Miller Jan 7 '19 at 16:17
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This is a very nice question, to start with! Let me turn to what is already described in the website sent in by sammygerbil. When the rotating ice cube melts, the cold melting water is moving downwards under the cube, taking away angular momentum from it. The vortex beneath the rotating cube gets less when approaching the bottom because the rotational momentum is taken up by the hot water surrounding it.
The downward moving cold water attracts hot water (the cold water moving downwards must be filled up by other water and this can be both hot water or melting water, but the hot water prevails, as might be clear) which gains linear momentum, and this linear momentum is subsequently conversed (by a torque acting on the cube caused by the attracted hot water) in an increased angular momentum of the ice cube.
So I don't think the cube gets to spin faster because a smaller cube is easier to rotate in the whirlpool, because the whirlpool beneath the melting cube also gets smaller while melting (scale invariance).

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