Add 'docs/cie3mz.md'

docs/cie3mz.md

@@ -0,0 +1,2 @@
+
+## Introduction

docs/sph3u7.md

@@ -18,6 +18,10 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
 | Amount of substance | Mole | mol |
 | Luminous intensity | Candela | cd |
 
+!!! info "Reminder"
+    Note that on an assesment, you are expected to derive the SI unit expression given the equation of unit.
+    For example Force = mass x acceleration = mass x distance / time / time = $kg \times m \times s^{-2}$. 
+
 ### Metric prefixes
 
 Every SI unit can be expanded with metric prefixes.
@@ -36,6 +40,9 @@ Every SI unit can be expanded with metric prefixes.
 | peta- | P | $10^{15}$ | f | femto- |
 | exa- | E | $10^{18}$ | a | atto- |
 
+!!! note
+    For easier memorization, notice that most of these prefixes are in multiples of $3$. 
+
 ### Significant figures
 
  - The leftmost non-zero digit is the **most significant digit**.
@@ -112,7 +119,7 @@ Uncertainties are stated in the form of [value] ± [uncertainty]. A value is onl
 To determine a measurement's absolute uncertainty, if:
 
  - the instrument states its uncertainty, use that.
- - an analog instrument is used, the last digit is estimated and appended to the end of the reported value. The estimated digit is uncertain by 5 at its order of magnitude.
+ - an analog instrument is used, the uncertainty is half of the smallest scale.
  - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
 
 !!! example
@@ -142,9 +149,9 @@ Error bars represent the uncertainty of the data, typically representing that da
 <img src="/resources/images/error-slopes.png" width=700>(Source: Kognity)</img>
 
 The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
-$$m_{best fit} ± m_{max}-m_{min}$$
+$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
 The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
-$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
+$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept} _{\min}}{2}$$
 
 
 ## 1.3 - Vectors and scalars
@@ -152,6 +159,7 @@ $$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
 !!! note "Definition"
     - **Scalar:** A physical quantity with a numerical value (magnitude) and a unit.
     - **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.**
+        - The **minimum magnitude** for any vector must be $`\ge 0`$
 
 ??? example
     - Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
@@ -166,6 +174,7 @@ $$\vec{a} = (1, 1)$$
  - The **magnitude** of a vector can be expressed as the absolute value of a vector.
 $$|\vec{a}| = 1 \text{ m}$$
 
+
 ### Adding/subtracting vectors diagrammatically
 
 1. Draw the first vector.
@@ -179,6 +188,9 @@ When subtracting a vector, **negate** the vector being subtracted by giving it a
 
 <img src="/resources/images/vector-subtract-direction.png" width=700>(Source: Kognity)</img>
 
+!!! note
+    Notice that when we are subtracting vectors ($\vec{a} - \vec{b}$), we have **tail** to **tail** and the difference vector has a direction from ($\vec{b} to \vec{a}$)
+
 ### Adding/subtracting vectors algebraically
 
 Vectors can be broken up into two vectors (**"components"**) laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.
@@ -216,7 +228,7 @@ $$
 To find the resultant direction, use inverse tan to calculate the angle of the vector using the lengths of its components.
 
 $$
-\vec{c}_{direction} = \tan^{-1} \frac{c_y}{c_x}
+\theta_{c} = \tan^{-1}(\frac{c_y}{c_x})
 $$
 
 ### Multiplying vectors and scalars
@@ -228,6 +240,43 @@ $$\vec{v} × s = (|\vec{v}|×s)[\theta_{v}]$$
 !!! example
     $$3 \text{ m} · 47 \text{ ms}^{-1}[N20°E] = 141 \text{ ms}^{-1}[N20°E]$$
 
+## 2.1 - Motion
+
+### Models
+
+A **scientific model** is a simplification of a system based on assumptions used to explain or make predictions for that system.
+
+!!! note "Definition"
+    - **System**: An object or a connected group of objects.
+    - **Point particle assumption**: An assumption that models a system as a blob of matter. It is more reliable if the size and shape of the object(s) do not matter much.
+    - **Uniform motion**: The type of motion in which the speed of an object is constant.
+
+### Displaying motion
+
+Motion can be expressed visually using a **motion diagram** or a **position-time graph**.
+
+// TODO: insert motion diagram here because kognity bad
+
+A **position-time graph** expands on the motion diagram by specifying a precise **position** value on the vertical axis in addition to time on the horizontal axis. The line of best fit indicates the object's speed, as well as if it is accelerating or decelerating.
+
+<img src="/resources/images/position-time-graph.png" width=700>(Source: Kognity)</img>
+
+When the slope is:
+
+ - linear, the object is moving at a constant speed.
+ - exponential, the object is accelerating.
+ - logarithmic, the object is decelerating.
+
+## 2.2 - Forces
+
+## 2.3 - Work, energy, and power
+
+## 2.4 - Momentum and impulse
+
+## 3.1 - Thermal concepts
+
+## 3.2 - Modelling a gas
+
 ## Resources
 
  - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)