Category:Central Forces
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This category contains results about Central Forces.
Definitions specific to this category can be found in Definitions/Central Forces.
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.
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.
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