Torsional stiffness ($K_{\phi }=dN/d\phi$)

The derivative of an axial torque with respect to relative end-rotation angle, evaluated at the operating configuration. In a linear torsion spring, $N=K_{\phi }\phi$.

For a uniform rod of length $L$ and twist per unit length $\tau$, the end-rotation angle is $\phi =L\tau$. The chain rule gives $K_{\tau }=L{K}_{\phi }$, where $K_{\phi }$ is the torsional stiffness. If a source defines a normalized torque $M=N/(2\pi )$, its derivative is $dM/d\tau =K_{\tau }/(2\pi )$.