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phys: misc fixes and improvements #9

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docs/sph3u7.md
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@ -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
eggy commented 2020-09-24 20:03:03 -04:00
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This isn’t a definition, and I think it can instead be either a warning or rewritten to be integrated into the page somewhere.

To conform with the rest of the repository, unless they are proper nouns, definitions should be in sentence case and should be bolded:

**Physical quantity**: A measurable property of an object or system, expressed as a product of a magnitude (number) and a unit, in that order.

This isn't a definition, and I think it can instead be either a warning or rewritten to be integrated into the page somewhere. To conform with the rest of the repository, unless they are proper nouns, definitions should be in sentence case and should be bolded: `**Physical quantity**: A measurable property of an object or system, expressed as a product of a magnitude (number) and a unit, in that order.`
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
eggy commented 2020-09-24 19:34:33 -04:00
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This information seems like it is already there in the text box above the image.

This information seems like it is already there in the text box above the image.
magicalsoup commented 2020-09-24 19:59:18 -04:00
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No, I would highly argue that people do not remember this fact from looking at the diagram or the textbox. In addition, I wrote this here due to the fact that it was not clearly stated.

No, I would highly argue that people do not remember this fact from looking at the diagram or the textbox. In addition, I wrote this here due to the fact that it was not clearly stated.
<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.