# How does the viscosity of a fluid affect the angular speed and resultant force of a cylinder that is rolling?

*This is not a homework question - I'm taking the iB and need to understand how liquid properties affects certain variables of a cylinder for my Extended Essay.

So basically, here's the scenario: There's a cylinder that's rolling down a ramp with a known liquid of known viscosity inside it.

I want to know how changing the viscosity of the liquid will affect the angular speed and resultant force and therefore the translational speed of the cylinder at the end of the ramp.

In my experiment, I used a PVC pipe of radius 10cm and inside it is half filled with water. Moreover, I vary the viscosity by adding corn syrup to the water and finding the viscosity using this method: http://www.wikihow.com/Measure-Viscosity

Moreover, I changed the volume of the liquid inside for each viscosity. I found a positive linear relationship between volume and translational speed. As volume increases, speed increases. I also do not understand why this happens. I've attempted to explain it using moment of inertia and conservation of energy but it didn't work because all the mass is cancelled in the equation. I'm guessing it's due to slosh dynamics but I can't seem to find much information on it.

TL;DR I want to know how liquid viscosity and liquid volume affects speed.

• What does "I changed the volume of the liquid inside for each viscosity" mean? Did you start with an empty cylinder and added more and more liquid until full? Because I would expect stable results for empty and full case, and unstable/fluctuating results for the half-full cases. – Steeven May 4 '17 at 7:13
• I started with an empty PVC pipe until half filled – IntJ May 4 '17 at 15:30
• Note that you would expect a full solid cylinder to roll down a ramp faster than a hollow cylinder; see here. Note also that you would expect a cylinder filled with zero-viscosity fluid to act basically like a hollow cylinder, since the fluid wouldn't rotate with the cylinder; and a cylinder filled with a high-viscosity fluid would act like a solid cylinder, since the fluid would rotate perfectly with the cylinder. But the half-filled cylinder (which you're asking about here) is much trickier. – Michael Seifert Dec 19 '18 at 16:06

But when containing a mixed phase of liquid/gas, the moment-of-inertia $I$ is not fixed. The liquid can move around and since $I=\int r^2\;dm$ depends on distance, this splashing around will severally change $I$.
Such changes in $I$ will change the angular speed $\omega$ during the motion, since $K=\frac 12 I \omega^2$ must be constant.
The viscosity only changes the liquids ease of moving around inside the cylinder. The higher the viscosity, the slower are the fluctuations in $I$ due to the content displacing itself. In other words, I would expect higher viscosity to make the motion more stable with less sudden changes by evening out the bumps and changes in $I$.