183_notes:momentum

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183_notes:momentum [2021/02/04 23:05] – [Changes in Motion] stumptyl183_notes:momentum [2021/02/04 23:07] (current) – [When does the $\gamma$ factor matter?] stumptyl
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 ==== Definition of Momentum ==== ==== Definition of Momentum ====
  
-//Momentum is a [[:183_notes:scalars_and_vectors|vector]] that quantifies the "ease" with which an object's motion can be changed.//+**Momentum** is a [[:183_notes:scalars_and_vectors|vector]] that quantifies the "ease" with which an object's motion can be changed.
  
 More formally, it is the product of the object's mass (a scalar), its velocity (a vector), and a proportionality constant  (that takes into account [[https://en.wikipedia.org/wiki/Special_relativity|relativistic motion]]). Mathematically, we represent the momentum like this: More formally, it is the product of the object's mass (a scalar), its velocity (a vector), and a proportionality constant  (that takes into account [[https://en.wikipedia.org/wiki/Special_relativity|relativistic motion]]). Mathematically, we represent the momentum like this:
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 $$\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$$ $$\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$$
  
-where $c$ is the speed of light in vacuum ($c = 3.00 \times 10^8 \dfrac{m}{s}$).+where **$c$** //is the speed of light in vacuum// **($c = 3.00 \times 10^8 \dfrac{m}{s}$).**
 ==== When does the $\gamma$ factor matter? ==== ==== When does the $\gamma$ factor matter? ====
  
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 |       3e8  |        |  Infinite! Impossible!  | |       3e8  |        |  Infinite! Impossible!  |
  
-For most purposes, $\gamma \approx 1$, so we can often use the approximate formula for the momentum vector,+For most purposes, __//$\gamma \approx 1$//__, so we can often use the approximate formula for the momentum vector,
  
 $$\vec{p} = m\vec{v}$$ $$\vec{p} = m\vec{v}$$
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