# Assume a spool rolls down a slope with its body (not its ends) in contact with the slope

I was doing a little mental exercise and imagined the above scenario. I can intuitively see that in the described case, the smaller the diameter of the spool body, the larger the proportion of the spool's potential energy at the top ends up as rotational kinetic energy (in the spool ends mostly) than in linear kinetic energy by the time the spool reaches the bottom of the slope.

In one extreme, the spool might be thought of as just a solid cylinder (i.e., the spool ends are the same diameter as the spool body) and it accelerates fairly quickly downhill and has a decent amount of linear (x direction) velocity by the time it reaches the bottom of the slope.

At the other extreme, picture the spool body as just a thin (but very strong!) cylindrical wire with all the spool's mass in disks hanging off the sides of the slope. In this case, assuming that gravity can impart enough torque to get the spool rolling, the spool will roll very slowly downhill and much more of the potential energy will be transformed to rotational kinetic energy by the time the spool reaches the bottom of the slope and the linear kinetic energy will be fairly small (i.e., the spool as a whole will be moving slowly in the x direction).

Now, if you wanted to actually build something more along the lines of the second case, what are the sorts of things that you need to consider when modeling such a system, i.e., what factors are involved? I thought of things like coefficients of friction in the spool body and slope surface, air resistance/drag, size (radius) of the spool ends, restitution/deformation characteristics of the materials in contact (spool body and slope), angle of the slope, strength of the materials used, and gravity of course. What else needs to be considered and what are the equations involved in modeling this? Thanks.

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 These kinds of games are played for classroom demos on a regular basis. Demo intended for a first year introductory course. You can model the basic behavior with nothing more than conservation of energy and a no-slip condition. – dmckee♦ Jul 30 '12 at 22:32