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--- 183_notes:ucm [2021/02/18 21:09] – stumptyl
+++ 183_notes:ucm [2021/02/18 21:12] (current) – [The Net Force for Uniform Circular Motion] stumptyl
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 ====== Uniform Circular Motion ======
-There are times when you will observe systems that move around some central axis in a very regular fashion. For example, the Moon revolves around the Earth in an orbit that is nearly circular. In doing so, it moves with nearly the same speed (not velocity!) at every location in its orbit. A system whose motion can be modeled as moving in a circular orbit at constant speed is said to execute "uniform circular motion." It is called "uniform" because the speed of the system doesn't change. The velocity is always changing direction, but not size. In these notes, you will read about a special mathematical form that the net force takes when the motion of the system is uniform and circular.
+There are times when you will observe systems that move around some central axis in a very regular fashion. For example, the Moon revolves around the Earth in an orbit that is nearly circular. In doing so, it moves with nearly the same speed (not velocity!) at every location in its orbit. A system whose motion can be modeled as moving in a circular orbit at constant speed is said to execute "uniform circular motion." It is called "uniform" because the speed of the system doesn't change. The velocity is always changing direction, but not size. **In these notes, you will read about a special mathematical form that the net force takes when the motion of the system is uniform and circular.**
 ==== The Net Force for Uniform Circular Motion ====
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 $$ \vec{F}_{net} = \dfrac{mv^2}{R\theta} \langle - \sin \theta, \cos \theta - 1 \rangle $$
-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://en.m.wikibooks.org/wiki/Trigonometry/Power_Series_for_Cosine_and_Sine|what happens to trig functions when their arguments get very small]],
+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://en.m.wikibooks.org/wiki/Trigonometry/Power_Series_for_Cosine_and_Sine|what happens to trig functions when their arguments get very small]],
 \begin{eqnarray*}