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phys: misc fixes and improvements #9

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@ -18,6 +18,27 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
### Derived units
These are units that are derived from SI units, meaning that they can be broken down into an expression of SI units. These are also known as **preferred units**.
TODO: add more derived units
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.`
|Name|Symbol|Concept|Broken down into SI units|
|---|---|---|---|
|Newton|$N$|Force or weight|$$\frac{Kg \times m}{s^2}$$|
|Joule|$J$|Energy or work|$$\frac{kg \times m^2}{s^2}$$|
|Watt|$W$|Power|$$\frac{kg \times m^2}{s^3}$$|
|Pascal|$Pa$|Pressure|$$\frac{kg}{m \times s^2}$$|
!!! 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 = $kg \times m \times s^{-2}$.
!!! note "Definition"
Physical Quantity: must always be expressed as the product of **magnitude**(number) and a **unit**.
Example: $$10m$$ (10 meters).
### Metric prefixes
Every SI unit can be expanded with metric prefixes.
@ -145,9 +166,9 @@ 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.
$$m_{\text{best fit}} ± \dfrac{m_{\max}-m_{\min}}{2}$$
$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
$$\text{intercept}_{\text{best fit}} ± \dfrac{\text{intercept}_{\max} - intercept_{\min}}{2}$$
$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - intercept_{\min}}{2}$$
eggy commented 2020-09-24 19:57:31 -04:00
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The last “intercept” is missing \text.

The last "intercept" is missing `\text`.
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eggy commented 2020-09-24 19:32:33 -04:00
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This can be moved into the description of magnitude or elsewhere instead of taking up valuable screen space in its own box.

This can be moved into the description of magnitude or elsewhere instead of taking up valuable screen space in its own box.
## 1.3 - Vectors and scalars