Rolling Cans

(Created prior to 1993)


Question:  Rolling Cans, why do they roll different?
I was rolling cans of soup with my students the other day and we 
noted that they rolled down a ramp in very different ways.  Some rolled slowly 
and gained speed while others seemed to leap away after a slow start.  Some 
stopped quickly once they were off the ramp and others continued on for a 
considerable distance.  Could someone please help me with the physics of this 
phenomenon?
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Sounds like a really fun experiment!  Of course, it all depends 
on what is in the can.  If the can contains very viscous material, or 
essentially solid material, like a can of molasses, it will roll as a solid 
body, with the inside having exactly the same angular speed as the outside.  
If the can contains a liquid, then the inside can behave quite differently, 
and if there are several different materials inside, you could have quite 
complex interactions, with heavy solid materials trying to stay on the bottom 
of the can all the time, and therefore preventing its rotation to some extent, 
for example.  The basic physics is that of rotational angular momentum 
coupling to the gravitational force pulling the can down the plane, and the 
rotation caused by the fact that the surface of the can rolls, rather than 
sliding.  There should be some treatments of slightly less complex systems 
(wheels rolling down inclined planes, for example) in a mechanics text that 
discusses moments of inertia.  Then, on the inside of your can, you have a 
fluid mechanics problem, which should be treated in books that discuss 
viscosity, since fluid motion in a rotating cylinder is a standard measure of 
viscosity.  And finally you have possible solid objects that are sliding 
against the can on the inside, causing a frictional force.  Hopefully, with 
all these elements, you can at least model most of the different behaviors you 
saw!

Arthur Smith
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How about doing some experiments in which you control some of the 
variables Arthur Smith mentioned?  Roll a can containing pure water, another 
containing molasses, another containing water and sand...do some experiments 
at constant volume (full cans) and others at constant weight.  Vary the size 
of the can, keeping the contents fixed, and do this for several different 
contents.  See if you can justify the results against the physical principles 
Arthur Smith described.

Topper
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