# What shape of object will roll down the fastest through the decline piece of wood on Earth?

What shape of object will roll down the fastest through the decline piece of wood if travelling with a straight line assuming there are frictionless ramp to stop them from going to the side given the same amount of material with their smoothness being the same? Could it be sphere or a partial sphere with cross section trimmed off? Please also including the distribution of the mass. Is the mass focused in the center given much faster velocity to roll down? What about the 3D shape generate from other curve for example, elliptical or hyperbola, etc...

In addition, I know that a hollow cylinder will roll down slower a solid-centered cylinder.

Interesting thing to learn from this video is that the density doesn't matter, bigger cylinder VS smaller cylinder are the same, even the weight doesn't matter in his experiments...

• Hollow should roll faster (atleast accelerate), unless your friction becomes an issue. Partial sphere can fall on its side but basically a suitable compromise between stability and possility to hollow it down and lower friction that does not fall over is best. As light as possible as it has least amount of innertia to accelerate but produces enough force to overcome stick friction. OTOH it also climbs worst back up again. Aug 31 '16 at 20:25
• Not sure I understand your question. You seem to be asking what shape of an item will roll down faster on an inclined plane with normal Earth atmosphere, correct? But do the different shapes also include the distribution of their matter within the outer shape? And their mass? And their smoothness?
– Jens
Aug 31 '16 at 21:01
• Joojaa, hollow is slower. Have a look at the video. World nenowned physics Professeor Lewin from MIT makes a strong case for solid sections. Aug 31 '16 at 21:02
• Just a minor pedantic point that has always irritated me about these brain teaser questions: if the ramp is truly frictionless, the items will not roll. They'll all slide at the same acceleration. (I'm happy to be corrected if anyone thinks I'm wrong though.)
– Andy
Sep 1 '16 at 8:11