Contact loss on a smooth sphere
= Contact loss on a smooth sphere
A particle released from an infinitesimal displacement near the top of a smooth sphere has $v^2=2gR(1-\cos\theta)$. The <normal reaction> vanishes when $mg\cos\theta=mv^2/R$, giving $\cos\theta=2/3$. The travelled arc is $R\arccos(2/3)$, whereas the vertical drop is $R/3$.