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--- 183_notes:localg [2021/02/04 23:32] – [Motion of Systems Due to Near-Earth Gravitational Forces] stumptyl
+++ 183_notes:localg [2024/01/11 20:56] (current) – hallstein
@@ Line 12: / Line 12: @@
 ==== The Gravitational Acceleration ====
-Countless experiments near the surface of the Earth have shown that the force that the Earth exerts on a system with mass is the product of the system's mass ( $m$ ) and the local gravitational acceleration ( $\vec{g}$ ).where we have defined "up" as positive  $y$ -direction and the magnitude of the gravitational acceleration ( $g$ ) is equal to **9.81  $\dfrac{m}{s}$ .**
+Countless experiments near the surface of the Earth have shown that the force that the Earth exerts on a system with mass is the product of the system's mass ( $m$ ) and the local gravitational acceleration ( $\vec{g}$ ).where we have defined "up" as positive  $y$ -direction and the magnitude of the gravitational acceleration ( $g$ ) is equal to **9.81 $\dfrac{m}{s^2}$.**
+{{  183_notes:week2_m2m.png?350}}
-\\
  Mathematically, we represent this force like this:
  $\vec{F}_{Earth} = m\vec{g}$
-{{ 183_notes:localg.png?400}}
 where the local gravitational acceleration is directed towards the center of the Earth. In your typical "flat-Earth" models,((By "flat-Earth", I mean [[http://en.wikipedia.org/wiki/Geographical_distance#Flat-surface_formulae|the distance over which the Earth is curved is much larger than any distance the system will travel]] not that [[https://en.wikipedia.org/wiki/Modern_flat_Earth_societies|the Earth is truly flat as some might think]].)) you will say the gravitational acceleration points "downward", which we typically consider to be the negative  $y$ -direction. In this case,
- $\vec{g} =  \langle 0, -g, 0\rangle \approx \langle 0, -9.81, 0\rangle \dfrac{m}{s}$
+$$\vec{g} =  \langle 0, -g, 0\rangle \approx \langle 0, -9.81, 0\rangle \dfrac{m}{s^2}$$
 We also accept some variation in  $\vec{g}$  from [[http://en.wikipedia.org/wiki/Gravity_anomaly|place to place]].