= Hinge impulse of an edge-pivoted square plate
{title2=$J_H=K(3a/(2l)-1/4)$}
For a uniform square plate of side $l$ hinged along an edge, $h=l/2$ and $I_H=Ml^2/3$. An <impulse> $K$ normal to the plate, applied a distance $a$ below the centre, gives $v_G=3K(1+2a/l)/(4M)$ and signed hinge <impulse> $J_H=K(3a/(2l)-1/4)$. Therefore the hinge <impulse> vanishes at $a=l/6$ below the centre, a distance $2l/3$ from the hinge. The sign of $J_H$ identifies the reaction direction; its magnitude is $|J_H|$.
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