Detailed study notes for physics and engineering students containing helpful diagrams and formulas. The notes are separated by chapter according to the textbook Principles and Practice of Physics.
Translational = movement of the object to another
NOTES – PHYS1032A
location (taking care to move any relevant external
influences as well)
CHAPTER 1 – Foundations
Note: Mathematical expressions of laws exhibit translational
1. The Scientific Method
symmetry w/r/t time and space (location).
The iterative process by which experimentally validated
theories are developed from observations.
3. Matter and the Universe
Observations of patterns in a naturally occurring
Universe = matter + energy combined with space + time in
phenomenon are used to induce a hypothesis (which uses
which all events happen. Concepts describe the universe and
a model and assumptions) that predicts the outcome of
in physics we use physical quantities to express these
the phenomenon. These predictions must be tested
concepts; eg. length, mass, temp, time…
experimentally to prove either accurate or inaccurate.
Length is a standard measured in meters and because of the
If prediction = inaccurate then rerun the test / revise
vast range of size scales in the universe, order of magnitude
hypothesis / rethink assumptions/ re-examine
is used to round off values to the nearest power of 10. For
observations.
0.3 -> 3 OM = 1 ; For 3 -> 30 OM = 10
If prediction = accurate repeatedly then it becomes a law /
Note: First write the quantity in scientific notation with the least
theory. Note: A law tells us what happens under certain
number of significant digits eg. 1.8 ×102 has an OM of 1 × 102
conditions in terms of relationships and a theory tells us
Atoms made up of subatomic protons and neutrons in the
why it happens by explaining the basic processes and
nucleus and a tenuous cloud of electrons are the basic
relationships. Laws and theories are subject to retesting.
building block of the universe.
Inductive reasoning is the argument from specific to
Atoms attract one another at small distances but resist being
general while deductive reasoning is the argument from
squeezed together. The arrangement of atoms in a material
general to specific.
determines its properties. Clusters can be identified such as
subatomic particles, atom, matter and star clusters.
2. Symmetry 4. Time and Change
An object exhibits symmetry when certain operations can Time is a physical quantity that allows us to determine the
be performed to it without changing its appearance. If a sequence in which related events occur.
procedure to an experiment leaves its result unchanged Absolute time is the notion that time is the same for all
then that experiment possesses symmetry. observers in the universe, regardless of their location or
Reflectional = two sides showing a mirror image across a motion.
reflection axis. Time flows irreversibly in a single direction, ie. The arrow of
Rotational = turning the object a certain amount ° about a time only points forward, time is an infinite continual
fixed point progression of events past, present and future.
Adapted from Principles and Practice of Physics
, Time allows us to establish a causal relationship between NA = 6.0221413 × 1023 (one mol means 6.022 × 1023 of
events through the principle of causality that states anything) is the number of atoms in 1 mol of a substance
whenever event A causes event B, all observers see event A Number density: number of objects per unit volume n =
happening first. N/V
Change is the transition from one state to another, we can Mass density: amount of mass per unit volume ρ = m/V
study these changes but remarkably some properties remain 7. Significant digits
unchanged which give rise to conservational laws. Leading zeroes before any nonzero digit are not significant
0.0037
5. Representations Trailing zeroes that come after the decimal are significant
Making a visual representation of information given by 5.290
organising it so that it is meaningful. Zeroes between nonzero digits are significant 4009
A mental movement from concrete to abstract useful in When adding or subtracting quantities, the number of
constructing models to solve problems as it aids in the decimal places in the result is the same as the number of
visualisation of the scenario. decimal places in the input quantity with the fewest
decimal places
6. Physical Quantities and SI units When multiplying or dividing quantities, the number of
Length M significant digits in the result is the same as the number of
Mass Kg significant digits in the input quantity with the fewest
Time S significant digits
Volume m or dm3
3
Energy J
Temperature ° or K Chapter 2 – Motion in One Dimension
Amount of substance Mol
Electric current A 1. Dimensional Analysis
Mass -> [M] in kg
kilo 103 milli 10-3 Length -> [L] in m [ M x L x Tx ]
mega 106 micro 10-6 Time -> [T] in s
giga 109 nano 10-9
terra 1012 pico 10-12 2. Position and Displacement (x components)
peta 1015 femto 10-15 Position is a vector that specifies the location of an object
exa 1018 atto 10-18 along a reference axis. This vector runs from the origin to
zetta 1021 zepto 10-21 the product of the x coordinate and the unit vector î. r⃗ =x î
yotta 1024 yocto 10-24 Displacement is a vector pointing from the initial position of
an object to its final position. It is essentially a change in
the x coordinate of the object Δ ⃗r =⃗r f −⃗
ri
Adapted from Principles and Practice of Physics
, Distance a scalar quantity describing the length covered by An object’s average speed is a scalar quantity describing
a moving object along its path of motion. the total distance travelled divided by the time taken to
Displacement is represented graphically by an arrow that travel it
points from the initial position to the final position . Velocity is a vector that gives the time rate of change in
Δ ⃗r =Δx î =x f −x i the position of an object.
The x component of an object’s velocity is the x component
Distance = |x f −x i| in one dimension
of its displacement divided by the time taken to travel it
Distance is always ≥ displacement (because the total path
x 2−x 1 Δ r⃗ Δx ⋅ l^
length travelled is greater than the change in position from v=v av= or v av =
⃗ or ⃗
v av ( l^ )=
initial to final) t 2−t 1 Δt Δt
3. Representing motion The gradient of a position time graph indicates velocity v x
but speed is |v x| and speed in general is > velocity
Average speed ≠ average velocity when the motion
involves a change of direction
5. Scalars and Vectors
⃗ x l^ a vector is specified by a magnitude and direction
b=b
¿arrow symbol reminds us that vectors have a direction in
space and obey different rule to scalars)
Δ ⃗q= ⃗0 is the notation for the zero vector
To add two vectors, place the tail of the second vector of
the sum at the tip of the first vector; the vector of the sum
runs across both
To subtract a vector from another, place their tails at the
same point and then draw a vector from the tip of the
vector being subtracted to the tip of the vector you are
subtracting.
Note: a unit vector is a unitless vector of magnitude one used to
specify a direction in space.
4. Average Speed and Average Velocity
When an object is in motion its position changes w/r/t time 6. Motion at Constant Velocity
The average speed/velocity tells us how fast an object An object moving at constant velocity will move the same
moves over a given time interval; understand that the distance for every second of its motion eg. 10m/s is 10
slower an object moves, the greater time interval it needs meters every second
to cover a given distance / change position
Adapted from Principles and Practice of Physics
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