Part of JME-04 — Rotational Motion & Moment of Inertia

Rolling Race — Which Body Wins?

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All bodies start from rest at the top of the same incline. Which reaches the bottom first?

Acceleration a = g*sintheta(1+k2/R2)\frac{theta}{(1 + k^2/R^2)}. Larger a means faster.

Bodyk2k^2/R2R^2Factor 11+k2/R2\frac{1}{1+k^2/R^2}Rank
Solid sphere2/5 = 0.405/7 = 0.7141st (fastest)
Solid cylinder1/2 = 0.502/3 = 0.6672nd
Hollow sphere2/3 = 0.673/5 = 0.6003rd
Ring11/2 = 0.5004th (slowest)

Sliding block (no rotation): k2k^2/R2R^2 = 0, a = g*sin(theta). Always faster than any rolling body.

Critical insight: Mass and radius cancel out. A tiny marble and a huge bowling ball (both solid spheres) reach the bottom at the same time.

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