\begin{definition}[Definition:Central Force]
Consider a particle $p$ of mass $m$ moving in the plane under the influence of a force $\mathbf F$.
Let the position of $p$ at time $t$ be given in polar coordinates as $\left\langle{r, \theta}\right\rangle$.
Let $\mathbf F$ be expressed as:
:$\mathbf F = F_r \mathbf u_r + F_\theta \mathbf u_\theta$
where:
:$\mathbf u_r$ is the unit vector in the direction of the radial coordinate of $p$
:$\mathbf u_\theta$ is the unit vector in the direction of the angular coordinate of $p$
:$F_r$ and $F_\theta$ are the magnitudes of the components of $\mathbf F$ in the directions of $\mathbf u_r$ and $\mathbf u_\theta$ respectively.
:600px
Let $\mathbf F$ have no component perpendicular to $\mathbf u_r$.
That is, such that $F_\theta = 0$.
Then $\mathbf F$ is referred to as a '''central force'''.
\end{definition}