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--- 183_notes:ap_derivation [2014/11/20 18:06] – caballero
+++ 183_notes:ap_derivation [2014/11/20 18:06] (current) – caballero
@@ Line 1: / Line 1: @@
 ===== Derivation of the Angular Momentum Principle ====
-Consider a single particle (mass,  $m$ ) that is moving with a momentum  $p$ . This particle experiences a net force $F_{net}$, which will change the particle's momentum based on the momentum principle,
+Consider a single particle (mass,  $m$ ) that is moving with a momentum $\vec{p} $. This particle experiences a net force$ \vec{F}_{net}$, which will change the particle's momentum based on the momentum principle,
-$$F_{net} = \dfrac{d\vec{p}}{dt}$$
+$$\vec{F}_{net} = \dfrac{d\vec{p}}{dt}$$
 Now, if we consider the cross product of the momentum principle with some defined lever arm (e.g., the origin of coordinates),  $\vec{r}$ , we can show this results in the angular momentum principle.
@@ Line 25: / Line 25: @@
  $\vec{\tau}_{net} = \dfrac{d}{dt}\left(\vec{r} \times \vec{p}\right) - m \underbrace{\vec{v} \times \vec{v}}_{=0}$
-And thus, we have the angular momentum principle in it's derivative form,
+And thus, we have the angular momentum principle in its derivative form,
  $\vec{\tau}_{net} = \dfrac{d}{dt}\left(\vec{r} \times \vec{p}\right)$