From 32b9a32a8a2bbf793c34a20e4e99098b68b23bb9 Mon Sep 17 00:00:00 2001 From: magicalsoup Date: Thu, 24 Sep 2020 19:15:30 -0400 Subject: [PATCH 1/5] Update 'docs/sph3u7.md' --- docs/sph3u7.md | 15 ++++++++++++--- 1 file changed, 12 insertions(+), 3 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 0ac9314..2136be9 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -36,6 +36,9 @@ 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 +115,7 @@ 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. (eg if a ruler can measure to $0.1cm$, the uncertainty would $0.005 cm$) - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude. !!! example @@ -142,9 +145,9 @@ Error bars represent the uncertainty of the data, typically representing that da (Source: Kognity) The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes. -$$m_{best fit} ± m_{max}-m_{min}$$ +$$m_{\text{best fit}} ± \dfrac{m_{\max}-m_{\min}}{2}$$ The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines. -$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$ +$$\text{intercept}_{\text{best fit}} ± \dfrac{\text{intercept}_{\max} - intercept_{\min}}{2}$$ ## 1.3 - Vectors and scalars @@ -166,6 +169,9 @@ $$\vec{a} = (1, 1)$$ - The **magnitude** of a vector can be expressed as the absolute value of a vector. $$|\vec{a}| = 1 \text{ m}$$ +!!! info "Reminder" + Remember that the **minimum magnitude** for any vector must be $`\ge 0`$ + ### Adding/subtracting vectors diagrammatically 1. Draw the first vector. @@ -179,6 +185,9 @@ When subtracting a vector, **negate** the vector being subtracted by giving it a (Source: Kognity) +!!! 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. -- 2.48.0 From 3821d854bcbd4869701bfa3a7d2049970777a1cb Mon Sep 17 00:00:00 2001 From: magicalsoup Date: Thu, 24 Sep 2020 19:45:57 -0400 Subject: [PATCH 2/5] Update 'docs/sph3u7.md' --- docs/sph3u7.md | 25 +++++++++++++++++++++++-- 1 file changed, 23 insertions(+), 2 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 2136be9..beb7ac1 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -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 + +|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 (Source: Kognity) 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. -$$\text{intercept}_{\text{best fit}} ± \dfrac{\text{intercept}_{\max} - intercept_{\min}}{2}$$ +$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - intercept_{\min}}{2}$$ ## 1.3 - Vectors and scalars -- 2.48.0 From 2ba7f391f1264ce86792fa04423dd65e8c11151e Mon Sep 17 00:00:00 2001 From: magicalsoup Date: Thu, 24 Sep 2020 19:53:12 -0400 Subject: [PATCH 3/5] Update 'docs/sph3u7.md' --- docs/sph3u7.md | 15 +-------------- 1 file changed, 1 insertion(+), 14 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index beb7ac1..f7edbd2 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -18,26 +18,13 @@ 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 - -|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). + Example: $10m$ (10 meters). ### Metric prefixes -- 2.48.0 From 5cb0a7de4770d8fb793f8ecd131774761f8208c6 Mon Sep 17 00:00:00 2001 From: magicalsoup Date: Thu, 24 Sep 2020 19:59:22 -0400 Subject: [PATCH 4/5] Update 'docs/sph3u7.md' --- docs/sph3u7.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index f7edbd2..87149e0 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -123,7 +123,7 @@ 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 uncertainty is half of the smallest scale. (eg if a ruler can measure to $0.1cm$, the uncertainty would $0.005 cm$) + - 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 @@ -163,6 +163,7 @@ $$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - intercep !!! note "Definition" - **Scalar:** A physical quantity with a numerical value (magnitude) and a unit. - **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.** + - The **minimum magnitude** for any vector must be $`\ge 0`$ ??? example - Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more. @@ -177,8 +178,6 @@ $$\vec{a} = (1, 1)$$ - The **magnitude** of a vector can be expressed as the absolute value of a vector. $$|\vec{a}| = 1 \text{ m}$$ -!!! info "Reminder" - Remember that the **minimum magnitude** for any vector must be $`\ge 0`$ ### Adding/subtracting vectors diagrammatically -- 2.48.0 From 27dfe046b8a8458e9a14a8e3666e61b79a35d6ad Mon Sep 17 00:00:00 2001 From: magicalsoup Date: Thu, 24 Sep 2020 20:23:00 -0400 Subject: [PATCH 5/5] Update 'docs/sph3u7.md' --- docs/sph3u7.md | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 87149e0..e9f452a 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -22,10 +22,6 @@ Every other SI unit is derived from the fundamental SI units. Memorise these! Note that on an assesment, you are expected to derive the SI unit expression given the equation of unit. For example Force = mass x acceleration = mass x distance / time / time = $kg \times m \times s^{-2}$. -!!! note "Definition" - Physical Quantity: must always be expressed as the product of **magnitude**(number) and a **unit**. - Example: $10m$ (10 meters). - ### Metric prefixes Every SI unit can be expanded with metric prefixes. @@ -155,7 +151,7 @@ Error bars represent the uncertainty of the data, typically representing that da The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes. $$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}} ± \frac{\text{intercept}_{\max} - intercept_{\min}}{2}$$ +$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept} _{\min}}{2}$$ ## 1.3 - Vectors and scalars -- 2.48.0