\begin{align*} & \text{ the sphere position vector}\\\\ &\mathbf R= \left[ \begin {array}{c} r\cos \left( \theta \right) \sin \left( \phi \right) \\ r\sin \left( \theta \right) \sin \left( \phi \right) \\ r\cos \left( \phi \right) \end {array} \right]\\\\ &\text{from here you obtain the velocity}\\\\ &\mathbf v=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\cos \left( \theta \right) \cos \left( \phi \right)\dot{\phi} -r\sin \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \sin \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\sin \left( \theta \right) \cos \left( \phi \right)\dot{\phi} +r\cos \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \cos \left( \phi \right) {\dot{r}}-r\sin \left( \phi \right)\dot{\phi} \end {array} \right]\\ \end{align*} you can also write the velocity \begin{align*} &\mathbf v=\dot{r}\,\mathbf e_r+r\,\dot{\phi}\,\mathbf e_\phi+r\,\sin(\phi)\,\dot{\theta}\,\mathbf e_\theta\\\\ &\text{where $~\mathbf e~$ are unit vectors}\\\\ &\mathbf e_r=\frac{\frac{\partial\mathbf{R}}{\partial r}}{\left|\frac{\partial\mathbf{R}}{\partial r}\right|}=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) \\ \sin \left( \theta \right) \sin \left( \phi \right) \\ \cos \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\phi=\frac{\frac{\partial\mathbf{R}}{\partial \phi}}{\left|\frac{\partial\mathbf{R}}{\partial \phi}\right|}=\left[ \begin {array}{c} \cos \left( \theta \right) \cos \left( \phi \right) \\ \sin \left( \theta \right) \cos \left( \phi \right) \\ -\sin \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\theta= \frac{\frac{\partial\mathbf{R}}{\partial \theta}}{\left|\frac{\partial\mathbf{R}}{\partial \theta}\right|}=\left[ \begin {array}{c} -\sin \left( \theta \right) \\ \cos \left( \theta \right) \\ 0 \end {array} \right] \end{align*}

those

$p_r$ momenta towards $\mathbf{e}_r$

$p_\phi$ momenta towards $\mathbf{e}_\phi$

$p_\theta$ momenta towards $\mathbf{e}_\theta $

\begin{align*} & \text{ the position vector}\\\\ &\mathbf R= \left[ \begin {array}{c} r\cos \left( \theta \right) \sin \left( \phi \right) \\ r\sin \left( \theta \right) \sin \left( \phi \right) \\ r\cos \left( \phi \right) \end {array} \right]\\\\ &\text{from here you obtain the velocity}\\\\ &\mathbf v=\frac{\partial\mathbf{R} }{\partial r}\,\dot{r}+ \frac{\partial\mathbf{R} }{\partial \phi}\,\dot{\phi}+ \frac{\partial\mathbf{R} }{\partial \theta}\,\dot{\theta}\\ &\mathbf v=\mathbf e_r\,\dot{r}+\mathbf e_\phi\,r\,\dot{\phi}+\mathbf e_\theta\,r\,\sin(\phi)\,\dot{\theta}\\\\ &\text{where $~\mathbf{e}~$ are unit vectors} \end{align*} those

$p_r$ momenta towards $\mathbf{e}_r$

$p_\phi$ momenta towards $\mathbf{e}_\phi$

$p_\theta$ momenta towards $\mathbf{e}_\theta $

\begin{align*} & \text{ the sphere position vector}\\\\ &\mathbf R= \left[ \begin {array}{c} r\cos \left( \theta \right) \sin \left( \phi \right) \\ r\sin \left( \theta \right) \sin \left( \phi \right) \\ r\cos \left( \phi \right) \end {array} \right]\\\\ &\text{from here you obtain the velocity}\\\\ &\mathbf v=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\cos \left( \theta \right) \cos \left( \phi \right)\dot{\phi} -r\sin \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \sin \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\sin \left( \theta \right) \cos \left( \phi \right)\dot{\phi} +r\cos \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \cos \left( \phi \right) {\dot{r}}-r\sin \left( \phi \right)\dot{\phi} \end {array} \right]\\ \end{align*} you can also write the velocity \begin{align*} &\mathbf v=\dot{r}\,\mathbf e_r+r\,\dot{\phi}\,\mathbf e_\phi+r\,\sin(\phi)\,\dot{\theta}\,\mathbf e_\theta\\\\ &\text{where $~\mathbf e~$ are unit vectors}\\\\ &\mathbf e_r=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) \\ \sin \left( \theta \right) \sin \left( \phi \right) \\ \cos \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\phi=\left[ \begin {array}{c} \cos \left( \theta \right) \cos \left( \phi \right) \\ \sin \left( \theta \right) \cos \left( \phi \right) \\ -\sin \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\theta= \left[ \begin {array}{c} -\sin \left( \theta \right) \\ \cos \left( \theta \right) \\ 0 \end {array} \right] \end{align*}

those

$p_r$ momenta towards $\mathbf{e}_r$

$p_\phi$ momenta towards $\mathbf{e}_\phi$

$p_\theta$ momenta towards $\mathbf{e}_\theta $

\begin{align*} & \text{ the sphere position vector}\\\\ &\mathbf R= \left[ \begin {array}{c} r\cos \left( \theta \right) \sin \left( \phi \right) \\ r\sin \left( \theta \right) \sin \left( \phi \right) \\ r\cos \left( \phi \right) \end {array} \right]\\\\ &\text{from here you obtain the velocity}\\\\ &\mathbf v=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\cos \left( \theta \right) \cos \left( \phi \right)\dot{\phi} -r\sin \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \sin \left( \theta \right) \sin \left( \phi \right) {\dot{r}}+r\sin \left( \theta \right) \cos \left( \phi \right)\dot{\phi} +r\cos \left( \theta \right) \sin \left( \phi \right) \dot\theta \\ \cos \left( \phi \right) {\dot{r}}-r\sin \left( \phi \right)\dot{\phi} \end {array} \right]\\ \end{align*} you can also write the velocity \begin{align*} &\mathbf v=\dot{r}\,\mathbf e_r+r\,\dot{\phi}\,\mathbf e_\phi+r\,\sin(\phi)\,\dot{\theta}\,\mathbf e_\theta\\\\ &\text{where $~\mathbf e~$ are unit vectors}\\\\ &\mathbf e_r=\frac{\frac{\partial\mathbf{R}}{\partial r}}{\left|\frac{\partial\mathbf{R}}{\partial r}\right|}=\left[ \begin {array}{c} \cos \left( \theta \right) \sin \left( \phi \right) \\ \sin \left( \theta \right) \sin \left( \phi \right) \\ \cos \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\phi=\frac{\frac{\partial\mathbf{R}}{\partial \phi}}{\left|\frac{\partial\mathbf{R}}{\partial \phi}\right|}=\left[ \begin {array}{c} \cos \left( \theta \right) \cos \left( \phi \right) \\ \sin \left( \theta \right) \cos \left( \phi \right) \\ -\sin \left( \phi \right) \end {array} \right]\\\\ &\mathbf e_\theta= \frac{\frac{\partial\mathbf{R}}{\partial \theta}}{\left|\frac{\partial\mathbf{R}}{\partial \theta}\right|}=\left[ \begin {array}{c} -\sin \left( \theta \right) \\ \cos \left( \theta \right) \\ 0 \end {array} \right] \end{align*}

those

$p_r$ momenta towards $\mathbf{e}_r$

$p_\phi$ momenta towards $\mathbf{e}_\phi$

$p_\theta$ momenta towards $\mathbf{e}_\theta $