The relationship between internal torque $\mathrm{T}$ in a shaft and its angle of twist $\mathrm{\varphi }$ is given by:

$\mathrm{\varphi }=\frac{\mathrm{TL}}{\mathrm{JG}}$

Therefore, the torque-twist relationships for shafts $\left(1\right)$ and $\left(2\right)$ can be expressed as:

${\mathrm{\varphi }}_1=\frac{{\mathrm{T}}_1{\mathrm{L}}_1}{{\mathrm{J}}_1{\mathrm{G}}_1} \mathrm{and} {\mathrm{\varphi }}_2=\frac{{\mathrm{T}}_2{\mathrm{L}}_2}{{\mathrm{J}}_2{\mathrm{G}}_2}$