= Two hinged rods sliding on a floor
{title2=$\dot\theta^2=\frac{3g}{2l}\frac{\sin\alpha-\sin\theta}{1+3\sin^2\theta}$}
Two equal uniform rods of length $2l$ and mass $M$, one pivoted to the floor and the other endpoint sliding on it, have arch coordinates $B=(2l\cos\theta,2l\sin\theta)$ and $C=(4l\cos\theta,0)$. The <kinetic energy decomposition about the center of mass> gives $T=\tfrac43Ml^2(1+3\sin^2\theta)\dot\theta^2$, while gravitational <potential energy> is $2Mgl\sin\theta$. <Conservation of energy> from rest at angle $\alpha$ gives the displayed equation and hinge impact <speed> $\sqrt{6gl\sin\alpha}$, provided contact is maintained. The endpoint's normal reaction becomes negative during this constrained fall if $\sin\alpha>35/54$; a unilateral floor then permits detachment and the constrained formula no longer describes the entire motion.
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