@@ -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
@@ -97,10 +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 **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.
@@ -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
@@ -123,13 +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 $(x ± \Delta x, y ± \Delta y)$
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.
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"
@@ -216,7 +218,7 @@ $$
To find the resultant direction, use inverse tan to calculate the angle of the vector using the lengths of its components.
$$
\vec{c}_{direction} = \tan^{-1}\frac{c_y}{c_x}
\theta_{c} = \tan^{-1}(\frac{c_y}{c_x})
$$
### Multiplying vectors and scalars
@@ -228,6 +230,43 @@ $$\vec{v} × s = (|\vec{v}|×s)[\theta_{v}]$$
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.
- 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)
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