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I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane

I was able to derive an equation for acceleration for the case of a fully solid cylindrical shell and then used law of conservation of energy to determine equations for the velocity of a solid and hollow cylinder and I understand that the moment of inertia's of the aforementioned cans can also be found easily using the radius. However, I am finding difficulty in finding a method to determine the moment of inertia for cans that are partially filled other than the parallel axis theorem which I am not sure can be applied to this scenario. Furthermore, I am also unsure about the actual experiment that I am doing to answer the initial research question (I have access to a motion sensor and photogate sensor) and was wondering if I should simply measure the final velocities and relate it to varying moment of inertias if it is possible to calculate but would appreciate any alternatives to this experiment. Finally, I am not sure if I should treat the water as an inviscid fluid as that would mean there would be no effects on the moment of inertias but the mass would still change so that would affect it in that regard, right? For now I have been treating it as an inviscid fluid for the purpose of the derivations that I have made.

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The problem is that the water does not rotate with the can. Instead it forms a pool in the bottom part of the can and sloshes around as the can rolls. The resistance to motion will be due to the force needed to make the water flow, and this is impossible to calculate in any simple way. There is certainly no simple equation for it, though it might be possible to come up with an empirical equation. It would be interesting to see if this is possible with the data you collect.

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  • $\begingroup$ Where would I start in order to find an empirical equation for this? $\endgroup$
    – Mostafa ElSanousi
    Commented Jul 5, 2023 at 4:54
  • $\begingroup$ @MostafaElSanousi Can you measure the velocity as a function of time? Or only the final velocity? The problem with measuring only the final velocity is that the drag the water causes is probably not constant as I suspect it will increase with increasing angular velocity. $\endgroup$
    – John Rennie
    Commented Jul 5, 2023 at 5:00
  • $\begingroup$ I am not sure how I would do that as I have a photogate sensor but it can only measure the velocity at a particular point on the ramp. I can tweak the experiment as I haven't fully decided on what I will be measuring (my investigation is open ended since i only mentioned dynamics and not a specific independent/dependent variable so I will make it more specific once I decide on an experiment). I have a motion sensor as well so I can only make a displacement-time graph $\endgroup$
    – Mostafa ElSanousi
    Commented Jul 5, 2023 at 7:58

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