If you roll a sphere, a ring, and a hoop down an incline, which shape will win the race? It turns out that the mass and radius don't matter; only the shape! Note: If we neglect air drag, the speed at the bottom of the ramp can easily be calculated with energy conservation: E at top = E at bottom gives Mgh = (1/2) Mv^2 + (1/2) I v^2 / R^2, in which R is the radius of the object. I = (2/5) MR^2 for a solid sphere, (1/2) MR^2 for a disc, and MR^2 for a ring (hoop), and h is the vertical height of the ramp. SPOILER ALERT: note that the ring [MR^2] has the largest coefficient of MR^2 on its moment of inertia (its mass is distributed far from its center), so it loses the race. The disc [(1/2) MR^2] comes in 2nd place and the sphere [(2/5) MR^2] wins, as its mass is distributed closer to its center. Again, mass and radius actually cancel out of consideration, but the DISTRIBUTION of mass is of the utmost importance! Solid spheres beat discs and hoops. always lose.

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