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--- course_planning:course_notes:momentum [2014/07/08 12:17] – [Definition of Momentum] caballero
+++ course_planning:course_notes:momentum [2014/07/08 12:31] (current) – [Momentum] caballero
@@ Line 1: / Line 1: @@
 ===== Momentum =====
-A [[course_planning:course_notes:momentum_principle|central principle of mechanics]] involves the relationship between momentum and force. In these notes, you will read about the concept of momentum.
+A [[course_planning:course_notes:momentum_principle|central principle of mechanics]] involves the relationship between momentum and force. In these notes, you will learn about the concept of momentum, and when it is ok to use the approximate form of the momentum vector.
 ==== Changes in Motion ====
@@ Line 19: / Line 18: @@
 $$\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$$
+==== When does the $\gamma$ factor matter? ====
+For most motion that is fair from the speed of light, the $\gamma$ factor will not matter so much. For example, consider the following table of speeds.
+^  $\mathbf{|\vec{v}|}$ m/s  ^  $\mathbf{|\vec{v}|/c}$  ^  $\mathbf{\gamma}$  ^
+|         0  |       0  |   1.0000  |
+|         3  |    1e-8  |   1.0000  |
+|       300  |    1e-6  |   1.0000  |
+|       3e6  |    1e-2  |   1.0001  |
+|       3e7  |     0.1  |   1.0050  |
+|     1.5e8  |     0.5  |   1.1547  |
+|   2.997e8  |   0.999  |  22.3663  |
+|  2.9997e8  |  0.9999  |  70.7124  |
+|       3e8  |       1  |  Infinite! Impossible!  |
+For most purposes, $\gamma \approx 1$, so we can often use the approximate formula for the momentum vector,
+$$\vec{p} = m\vec{v}$$