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For local cold magnetocentrifugal acceleration, the field must guide the gas and enforce approximate corotation with its disk footpoint in the sub-Alfvénic launching region. Let that footpoint be $R=R_f$, and keep its field-line angular velocity ${\Omega }_f=\Omega (R_f)$ constant along the field. In this rotating frame the relevant effective potential isThe footpoint is a critical point because ${\partial }_R\Phi (R_f,0)=R_f{\Omega }_f^2$ and ${\partial }_z\Phi (R_f,0)=0$. The meridional Hessian matrix there isTake distance $\ell$ along a smooth outward magnetic field line whose initial tangent is $(\sin \alpha ,\cos \alpha )$ in the $(R,z)$ plane. Since the gradient of $V$ vanishes at the footpoint, field-line curvature does not contribute to its second derivative. ConsequentlyA negative quadratic coefficient gives a downhill displacement and acceleration without thermal assistance. The magnetocentrifugal launching criterion in a flattened power-law potential is thereforeAngles are measured from the vertical, with $0\le \alpha <\pi /2$. Below the critical angle the footpoint is a local minimum along the field, so a cold particle cannot cross the initial potential barrier. At equality the quadratic test is marginal; higher derivatives and the unspecified field curvature can decide the outcome. The threshold is a local condition for launch, not proof that the wind escapes along an arbitrary global field geometry. The spherical point-mass limit $\lambda =1$, $\beta \to 1$ recovers ${\alpha }_{\mathrm{crit}}=30^{\circ }$, consistent with Ogilvie's discussion of cold disk winds, section 9.9.