From c3aaec3194d52cc469b2e21cf7e759273ba9740b Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 24 Sep 2020 20:39:28 -0400 Subject: [PATCH 1/5] phys: fix factual errors --- docs/sph3u7.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index cd43666..6bc0378 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -112,7 +112,7 @@ 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, half of the most precise reading is uncertain. - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude. !!! example @@ -142,16 +142,16 @@ 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. -$$m_{best fit} ± m_{max}-m_{min}$$ +$$m_{best fit} ± \frac{m_{max}-m_{min}}{2}$$ The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines. -$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$ +$$intercept_{best fit} ± \frac{intercept_{max} - intercept_{min}}{2}$$ ## 1.3 - Vectors and scalars !!! 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.** + - **Vector:** A physical quantity with a **non-negative** numerical value (magnitude), a unit, and a **direction.** ??? example - Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more. From 100d81345a500e5c423cd4c1237d76f7321b2737 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 24 Sep 2020 20:40:54 -0400 Subject: [PATCH 2/5] phys: make latex text use text --- docs/sph3u7.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 6bc0378..accfb50 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -142,9 +142,9 @@ 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. -$$m_{best fit} ± \frac{m_{max}-m_{min}}{2}$$ +$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$ The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines. -$$intercept_{best fit} ± \frac{intercept_{max} - intercept_{min}}{2}$$ +$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept}_{\min}}{2}$$ ## 1.3 - Vectors and scalars From 90905dbcdc8045e8327855957892cec360dd71b4 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 24 Sep 2020 20:43:48 -0400 Subject: [PATCH 3/5] phys: improve metric prefixes and add physical quantites review --- docs/sph3u7.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index accfb50..0d7befe 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -4,6 +4,9 @@ The course code for this page is **SPH3U7**. ## 1.1 - Measurements in physics +!!! reminder + All physical quantities must be expressed as a **product** of a magnitude and a unit. For example, ten metres should be written as $10 \text{ m}$. + ### Fundamental units Every other SI unit is derived from the fundamental SI units. Memorise these! @@ -20,7 +23,7 @@ Every other SI unit is derived from the fundamental SI units. Memorise these! ### Metric prefixes -Every SI unit can be expanded with metric prefixes. +Every SI unit can be expanded with metric prefixes. Note that the difference between many of these prefixes is $10^3$. !!! example milli + metre = millimetre ($10^{-3}$) m From eb9cc762d81b1964d1d40b102b7045506a692c93 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 24 Sep 2020 21:00:35 -0400 Subject: [PATCH 4/5] phys: add tail-to-tail --- docs/sph3u7.md | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 0d7befe..c0eb195 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -172,13 +172,18 @@ $$|\vec{a}| = 1 \text{ m}$$ ### Adding/subtracting vectors diagrammatically 1. Draw the first vector. -2. Draw the second vector with its *tail* at the *head* of the first vector. +2. Draw the second vector with its tail at the head of the first vector. 3. Repeat step 2 as necessary for as many vectors as you want by attaching them to the *head* of the last vector. -4. Draw a new (**resultant**) vector from the *tail* of the first vector to the *head* of the last vector. +4. Draw a new ("resultant") vector from the tail of the first vector to the head of the last vector. (Source: Kognity) -When subtracting a vector, **negate** the vector being subtracted by giving it an opposite direction and then add the vectors. +When subtracting exactly one vector from another, repeat the steps above, but instead place the second vector at the **tail** of the first, then draw the resultant vector from the head of the second vector to the head of the first vector. Note that this only applies when subtracting exactly one vector from another. + +!!! example + In the diagram above, $\vec{b}=\vec{a+b}-\vec{a}$. + +Alternatively, for any number of vectors, negate the vector(s) being subtracted by **giving it an opposite direction** and then add the negative vectors. (Source: Kognity) From 40ebf911f69b78988e2791ae33766bb60a39fad2 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 24 Sep 2020 21:06:19 -0400 Subject: [PATCH 5/5] phys: merge data into blocks, reduce non-example admonitions --- docs/sph3u7.md | 12 +++--------- 1 file changed, 3 insertions(+), 9 deletions(-) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index c0eb195..c1b1c47 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -100,10 +100,7 @@ The order of magnitude of a number can be found by converting it to scientific n ### Uncertainties -Uncertainties are stated in the form of [value] ± [uncertainty]. A value is only as precise as its absolute uncertainty. Absolute uncertainty of a **measurement** is usually represented to only 1 significant digit. - -!!! note - Variables with uncertainty use an uppercase delta for their uncertainty value: $a ± \Delta a$ +Uncertainties are stated in the form of $a±\Delta a$. A value is only as precise as its absolute uncertainty. Absolute uncertainty of a **measurement** is usually represented to only 1 significant digit. - The absolute uncertainty of a number is written in the same unit as the value. - The percentage uncertainty of a number is the written as a percentage of the value. @@ -126,13 +123,10 @@ See [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf) for h ### Error bars -Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical. +Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical. A data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$ (Source: Kognity) -!!! note - On a graph, a data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$ - ### Uncertainty of gradient and intercepts !!! note "Definition" @@ -189,7 +183,7 @@ Alternatively, for any number of vectors, negate the vector(s) being subtracted ### 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. +Vectors can be broken up into two **component vectors** 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. $$\vec{F}_x + \vec{F}_y = \vec{F}$$ !!! info "Reminder"