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--- book:chap2:2.1_motivation_and_outline [2021/10/25 15:42] – abril
+++ book:chap2:2.1_motivation_and_outline [2022/04/01 19:59] (current) – jv
@@ Line 1: / Line 1: @@
+[[forcestorques|2. Balancing Forces and Torques]]
+  * **  2.1 Motivation and outline: forces are vectors **
+  * [[  2.2 Sets| 2.2 Sets ]]
+  * [[  2.3 Groups| 2.3 Groups ]]
+  * [[  2.4 Fields| 2.4 Fields ]]
+  * [[  2.5 Vector spaces| 2.5 Vector spaces ]]
+  * [[  2.6 Physics application balancing forces| 2.6.  Physics application: balancing forces]]
+  * [[  2.7 The inner product | 2.7 The inner product]]
+  * [[  2.8 Cartesian coordinates | 2.8 Cartesian coordinates]]
+  * [[  2.9 Cross products --- torques| 2.9 Cross products — torques ]]
+  * [[ 2.10 Worked example Calder's mobiles| 2.10 Worked example: Calder's mobiles ]]
+  * [[ 2.11 Problems| 2.11 Problems ]]
+  * [[ 2.12 Further reading| 2.12 Further reading ]]
+----
 ===== 2.1 Motivation and outline: forces are vectors =====
@@ Line 10: / Line 26: @@
 Finally, also a displacement involves a length specification and a direction.
-<WRAP 115px left>
+<WRAP 115px left #fig_middlePage >
 {{book:chap2:middle_page_dot.png?direct&400|}}
-<wrap lo>The displacement of the red point from the bottom left corner to the the middle of the page
+Figure 2.1: The displacement of the red point from the bottom left corner to the the middle of the page
 can either be specified by the direction $\theta$  and the distance $R$ (polar coordinates, top),
-or by the distances $x$ and $y$ along the sides of the paper (Cartesian coordinates, bottom).}</wrap>
+or by the distances $x$ and $y$ along the sides of the paper (Cartesian coordinates, bottom).
-\label{figure:middlePage}
 </WRAP>
-<WRAP box round>**Example 1.1** <wrap em>Displacement of a red dot from the lower left corner to the middle of a paper</wrap> \\
+<WRAP box round>**Example 2.1** <wrap em>Displacement of a red dot from the lower left corner to the middle of a paper</wrap> \\
-This displacement is illustrated in \cref{figure:middlePage}.
+This displacement is illustrated in [[#fig_middlePage|Figure 2.1]].
 It can either be specified in terms of the distance $R$ of the point from the corner
 and the angle $\theta$ of the line connecting the points and the lower edge of the paper
@@ Line 78: / Line 94: @@
 $f : A \to A$.
 When an operation $\circ$ takes two elements of a set $A$ and returns a single element of $A$ we write ((Here $A \times A$ is the set, $(a_1, a_2)$, of all pairs of elements $a_1, a_2 \in A$.
-Further details will be given in \Defin{SetOperations} below.)) $\circ : A \times A \to A$.
+Further details will be given in [[book:chap2:2.2_sets#Def_SetOperations|Definition 2.3]] below.)) $\circ : A \times A \to A$.
 Equipped with the mathematical tool of vectors we will explore the physical concepts of forces and torques,
 and how they are balanced in systems at rest.
 ~~DISCUSSION|Questions, Remarks, and Suggestions~~