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The jerking motion is precisely the sloshing dynamics that I plan to discuss in the research paper, although it's out of my scope mathematically speaking. I plan to write about it in terms of my visual findings upon conducting the experiment.haruspex said:That would be a steady state condition, but if we are taking the water as inviscid it will never be achieved.
As a simplification, I would treat the water as a frictionless solid, as though it were ice (but not stuck to the cylinder, as it was in the video you posted). It might be possible to solve this model, but still tricky enough. As @jbriggs wrote, it will behave like a pendulum, but with the complication of the interaction with the cylinder, which will roll in a jerky fashion.
It is not clear to me whether that is what @mostafaelsan2005 means by "sloshing dynamics", or if he is thinking of more complex motion.
Certainly the ice model overlooks that the surface of the water would not remain flat; a lower centripetal force would be required along the centre line of the water surface than at the edges. But intuitively I feel that is quite a minor effect. It could be studied in isolation merely as water slopping back and forth in a bowl.
Lnewqban said:The way I see it (perhaps erroneously, as many other times):
The liquid inside should be only affected by the linear acceleration of both centers of mass, cylinder and liquid.
The surface of that liquid should adopt certain angle (tan a/g) respect to the horizon.
The value of that linear acceleration (a) should be lower than of an equivalent mass freely sliding down the slope, because the rotational acceleration of the cylinder alone should be slowing that rate of linear acceleration down.
As the level of liquid changes, the location of its CM respect to the central axis of the cylinder and point of contact and moment should change as well.
That's what I believe as well, though I plan to conduct a preliminary experiment in order to make sure of it. Conceptually I see it as if it is a less steep slope it won't behave in terms of sloshing dynamics due to the initial angle it is displaced at.haruspex said:It will depend greatly on the angle of the slope. Tests on steep slopes of sufficient length would be nontrivial to conduct.
mostafaelsan2005 said:which is the reason that the moment of inertia cannot be easily found as a particular value as it changes as it goes down the ramp based on how much water is in the shell).
It’s the large “step” change in acceleration that starts the water rocking. It’s sitting there at rest, then it almost instantly goes to some value ##a##. The steeper angle scales the magnitude of that step change, which likely scales the effect of “sloshing”.mostafaelsan2005 said:Conceptually I see it as if it is a less steep slope it won't behave in terms of sloshing dynamics due to the initial angle it is displaced at.
The point of a having a "moment of inertia" is that you can then multiply it by a rotation rate to get a number for angular momentum. For a rigid object, this works out well. A rigid object has a rotation rate. Its moment of inertia can be computed with an integral or found in a table on Wikipedia.mostafaelsan2005 said:the moment of inertia cannot be easily found as a particular value as it changes as it goes down the ramp based on how much water is in the shell
I don’t see how the angle the eater surface makes to the wall of the can is interesting.mostafaelsan2005 said:modeling the initial angle that the water makes with respect to the can based on how much water is in it
If it is full, what angle is there?mostafaelsan2005 said:identical to the full cylinder model but just with the added variable of there being an angle of the water