1For relative angular acceleration,
\alpha = lim \Delta t\rightarrow 0 \; \frac{\Delta \omega }{\Delta t}
Let \omega _{1}=\omega _{2}+\Delta \omega
\Delta \phi =\frac{arc}{radius}=\frac{\Delta \omega }{\omega _{1}}
\frac{\Delta \phi }{\Delta t}=\omega _{2} \Rightarrow \alpha =\omega _{1}\omega _{2}