How can I design a roller project to roll down an incline as slow as possible?

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To design a roller project that descends an incline as slowly as possible, focus on maximizing rotational energy while minimizing kinetic energy. The roller must have a uniform radius between 0 and 0.5 meters and a mass between 0.25 kg and 0.5 kg. Utilize formulas for potential energy conversion into kinetic and rotational energy, emphasizing shapes that yield higher rotational energy, such as spheres, cylinders, or rings. Understanding the relationship between these energy types will guide the design. This approach will help achieve the goal of slow descent on the ramp.
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Homework Statement


I have to make something that will roll down an incline as slow as possible. It needs to have a uniform radius of 0-.5m and have a mass between .25kg and .5kg. The ramp it needs to go down is a pine board 12' long, with a starting height of 6", and the ramp is 7.5" wide. I am not necessarily looking for how to do it exactly, but just help with what formulas and such to use. This stuff is beyond my limited knowledge of physics.


Homework Equations


Dont know any, that's why I am here.



The Attempt at a Solution


I don't really know where to start for this project. If it makes a difference, it is not a graded one for school, but for an after school science league competition. I am just looking for something to get me going in the right direction. thanks
 
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As it rolls down the ramp, potential energy will be converted into kinetic energy plus rotational energy. The more that goes into RE rather than KE, the slower it will go down. Find formulas for the rotational energy for rollers of various shapes (sphere, cylinder, ring ...). Choose the one that has the largest rotational energy for a given rolling speed.
 

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