Rolling-1

\begin{flalign*} v_{A}&=v_{A,O}+v_{O,Earth} &\\ &=v_{A,O}-v_{P,O}& \\ &=\boldsymbol{\omega}\times \mathbf{r} - \boldsymbol{\omega}\times (-\mathbf{R})& \\ &=\boldsymbol{\omega}\times(\mathbf{r}+\mathbf{R})&\\ &=\boldsymbol{\omega}\times \boldsymbol{\rho}& \\ \end{flalign*}