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| 183_notes:ucm [2021/02/18 21:09] – [Uniform Circular Motion] stumptyl | 183_notes:ucm [2021/02/18 21:12] (current) – [The Net Force for Uniform Circular Motion] stumptyl | ||
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| $$ \vec{F}_{net} = \dfrac{mv^2}{R\theta} \langle - \sin \theta, \cos \theta - 1 \rangle $$ | $$ \vec{F}_{net} = \dfrac{mv^2}{R\theta} \langle - \sin \theta, \cos \theta - 1 \rangle $$ | ||
| - | In fact, this is the //average// net force in this situation. You cannot get a more accurate estimate on this average net force without considering shorter times steps. That is, situations where the angular distance is very small. If you do consider such situations, the average net force becomes the instantaneous net force at the location. To do this, we make the approximation that $\theta$ is very small. In calculus, you might have seen [[https:// | + | In fact, this is the //average// net force in this situation. You cannot get a more accurate estimate on this average net force without considering shorter times steps. That is, situations where the angular distance is very small. If you do consider such situations, the average net force becomes the instantaneous net force at the location. |
| \begin{eqnarray*} | \begin{eqnarray*} | ||