Moment of inertia of a beer can

[Zack-UK]

Homework Statement

Hello there! Right now I am preparing for my exam, but I am having some problems with an experiment which we had earlier this year on class. It was an experiment, in which we rolled canned beers down an incline, one with beer in it, and one with no beer in it. The experiment showed, that the can with beer in it reached bottom first, and had a much larger acceleration.
The answer is then; why does the can with beer in it reach bottom first, and does the liquid take part in the rotation of the beer can?

As far as i can see then the reason that the can with liquid reaches bottom first is that it has lots of mass, but almost no moment of inertia. Therefore the net force on the can is greater, and it is easier to get the can rotating. In this statement, I have claimed, that the only mass contributing to the moment of inertia, is the masse of the can. Is this right? Or could anybody please answer the question "does the liquid take part in the rotation of the beer can?" then I would be happy.

I need your help, thanks :)

Homework Equations

The Attempt at a Solution

 

[berkeman]

Welcome to the PF. Interesting question. BTW, was emptying some of the beer cans a precursor to the experiment? Just curious.

I would have thought that the liquid in the can would have gained some rotational motion via vicous interaction with the inner can wall, but maybe that effect is small... The best way for you to tell would be to list your experimental data and match that to some amount of motion of the liquid inside. Model it as the can, with a solid cylinder inside, mounted on an axle down the center of the can. So the can rotates at the rate dictated by its motion down the ramp, and the inner mass accelerates at some smaller rate. You should be able to match that slower rate to the actual motion of the full can down the ramp that you recorded.

 

[thomate1]

Hello there! It sounds like you are on the right track with your thinking. The moment of inertia of an object is a measure of its resistance to rotational motion. It takes into account both the mass and the distribution of that mass in the object. In the case of a beer can, the liquid inside does contribute to the total mass of the can, but it is not distributed evenly throughout the can. This means that the moment of inertia of the can is primarily determined by the mass and shape of the can itself, rather than the mass of the liquid inside.

In terms of the experiment you described, the can with beer in it likely reached the bottom first because it had a larger net force acting on it due to its lower moment of inertia. The liquid inside may have contributed to this by sloshing around and shifting the center of mass of the can, making it easier for the can to rotate and reach the bottom faster.

In conclusion, the liquid does play a role in the rotation of the beer can, but its effect is primarily through its contribution to the overall mass of the can. I hope this helps and good luck on your exam!