# How does the amount of liquid in a cylindrical can affect its motion when rolling down an inclined plane?

I am currently working on my physics extended essay for IB and I have chosen to investigate how the amount of water in a cylinder affects its motion down an inclined plane. I am planning to carry out an experiment by varying the amount of water in a can and measuring its velocity down an incline.

Do you have any suggestions on how I would be able to calculate the rotational inertia of the can for each trial using data for its velocity? What are some other variables that I would be able to measure?

This is my first time posting here, so please let me know if you would like more details about my question. Thank you so much for your help!

• Maybe you could see this question : Rotational Motion down an inclined plane. Also, this site could help : Rolling Race. This pdf is also a relevant read: Effects of a fluid in a can rolling down an incline. – Firefox1921 Jun 18 at 7:59
• @Firefox1921 thank you! I have seen the pdf before and got a little confused about the way they determined the rotational inertia. It writes that ". Determination of the rotational inertia for all objects will be done by performing linear fits (y = a + bx) to velocity vs. time plots and using the slope to represent the acceleration (v˙ = a) in equation 2." Does this assume that the acceleration is constant? – grace Jun 18 at 8:14
• If you see the formula given, acceleration will be constant for a particular body with a defined MI as well as a constant mass, right? Acceleration is the slope for a v-t plot, it has to be constant for a particular body. – Firefox1921 Jun 18 at 8:20
• @Firefox1921 Oh I see. But wouldn't the value of R change during the motion as the centre of mass would change as the liquid moves around? – grace Jun 18 at 8:35
• R is the radius of the cylinder. It has to be constant, otherwise, the object won't even be a cylinder at multiple instances of time. Why will it change? – Firefox1921 Jun 18 at 8:37

If you are dealing with water, then it will behave nearly like an inviscid fluid, meaning that, aside from a very thin boundary layer near the wall, the fluid will not be rotating as the can rolls down the incline. Basically treating the water as inviscid is equivalent to allowing the water to slip at the wall. This would prevent the can rotation from propagating into the fluid. So the water would move down the incline as a non-rotating body while the can would rotate around it (and would have rotational inertia). The problem could be modeled that way.

A very highly viscous fluid, on the other hand, would behave as a rigid body stuck to the wall whose center of mass is offset from the axis. It would be possible to model this situation also.

Another situation that might not be too hard to analyze would be a moderately viscous fluid that fills the can.

However, other situations would be pretty difficult to get a handle on. For example, the case of a moderately viscous fluid that does not fill the can.

In my judgment the range of possibilities of % fill and fluid viscosity is too broad to be tractable right now. I think you need to narrow the range of possibilities that you are willing to consider.

• Thank you! Do you think it would be easier/more interesting if I choose to do my investigation on varying the viscosity of the liquid (e.g oils at different temperatures) in the can instead? – grace Jun 19 at 12:03
• I would use either a full can with fluids of different viscosities or an partially filled can with a low viscosity fluid, like water, with different degrees of fill. – Chet Miller Jun 19 at 12:06