applied things to remember

SI units:

• Mass = kg

• Length = m

• Time = s

• Speed = m/s

• Acceleration = m/s^2

• Weight = N or kg m/s^2

• Force = weight

forces

• Weight - acts vertically downwards

• Normal reaction - force perpendicular to surface when object is in contact (opposite of weight)

• Friction - force opposing motion between 2 rough surfaces

• Tension - if object is being pulled by string, force on object = tension in string

• Thrust/Compression - if object is being pushed by light rod, thrust/compression in rod is acting on object

• Buoyancy - upward force on body that allows it to float

• Air resistance - opposes motion (weight)

Particle assumptions

• rotational forces and air resistance can be ignored

• mass of object is concentrated at single point

• dimensions of object = negligible

Air resistance negligible/smooth surface assumptions

• Ignore frictional effects on object/between object and surface due to air resistance

rod assumptions

• all dimensions but 1 = negligible

• mass concentrated along a line

• no thickness

• rigid

lamina

object has area but negligible thickness

• mass is distributed across flat surface

uniform body

• mass distributed evenly

• mass is concentrated at single point at centre (centre of mass

light object

• mass is small compared to other masses e.g. string/pulley

• treat object as = 0 mass

• tension the same at both ends of a light string

smooth surface

assume that there is no friction between surface and objects

rough surface

• any surface that is not smooth

• objects in contact experience a frictional force if moving

wire

• rigid thin length of metal

• treat as one-dimensional

smooth and light pulley

• all pulleys are smooth and light

• pulley has no mass

• tension is same on either side of pulley

bead

• particle with hole in it for threading

• moves freely along wire/string

• tension is same on either side of bead

peg

• support from which body can be suspended/rested

• dimensionless and fixed

• can be rough or smooth as specified

gravity

• force of attraction between all objects

• acceleration due to gravity = g

• assume all objects with mass are attracted towards earth

• earth’s gravity is uniform and acts vertically down

• g is constant, taken as 9.8m/s² unless stated otherwise

magnitude of displacement vector

distance

magnitude of velocity vector

speed

if v = ai + bj, magnitude =

|v| = sq root (a²+b²)

population

whole set of items that are of interest

census

observes/measures every member of a population

sample

selection of observations taken from a subset of the population, used to find out information about the population as a whole

census v sample

	Advantages	Disadvantages
census	Should give completely accurate result	Time consuming and expensive Cannot be used when testing process destroys item Hard to process such large quantity of data
sample	Less time consuming and cheaper Fewer people needed Less data to process	Data may not be as accurate Sample may not be large enough to give information about small sub-groups of population

three types of random sampling

• simple random sampling

  • sampling frame (list of people/things), allocate each with unique number, choose numbers at random

• systematic sampling

  • required elements chosen at regular intervals from ordered list

• stratified sampling

  • population divided into mutually exclusive strata (e.g. males and females), random sample taken from each

  • number sampled in stratum = (no in stratum/no in population) x overall sample size

simple random sampling advantages vs disadvantages

Advantages	Disadvantages
Free of bias Easy and cheap for small populations/samples Each sampling unit has known and equal chance of selection	Not suitable when population size large, potentially time consuming, expensive Sampling frame needed

systematic sampling advantages vs disadvantages

Advantages	Disadvantages
Simple, quick to use Suitable for large samples/populations	Sampling frame needed Can introduce bias if sampling frame not random

stratified sampling advantages vs disadvantages

Advantages	Disadvantages
Sample accurately reflects population structure Guarantees proportional representation of groups within population	Population must be classified clearly into distinct strata Selection within each stratum suffers from same disadvantages as simple random sampling

two types of non-random sampling

• quota sampling

  • interviewer/researcher selects sample reflecting characteristics of whole population

• opportunity sampling

  • taking sample from people who are available at the time of study and who fit the criteria you are looking for

quota sampling: advantages vs disadvantages

Advantages	Disadvantages
Allows small sample to still be representative of population No sampling frame needed Quick, easy, inexpensive Allows for easy comparison between different groups within population	Non-random sampling can intoduce bias Population must be divided into groups - costly/inaccurate Increasing scope of study increases number of groups, adding time and expense Non-responses are not recorded as such

opportunity sampling advantages vs disadvantages

Advantages	Disadvantages
Easy to carry out Inexpensive	Unlikely to provide representative sample Highly dependent on individual researcher

continuous variable

variable that can take any value in a given range e.g. time (2, 2.1, 2.01 secs)

discrete variable

variable that can only take specific values in a given range (eg. number of girls in a family)

class boundaries (in grouped frequency tables)

tell you maximum and minimum values in each class
FOR CONTINUOUS: OFTEN THEY HAVE BEEN ROUNDED

E.G. UPPER CLASS BOUNDARY FOR 30-31MM = 31.5

midpoint of class (in grouped frequency table)

average of class boundaries (1/2 x lower c.b + upper c.b)

class width (in grouped frequency table)

upper class boundary - lower class boundary (difference between c.bs)

UK locations in large data set

• Leuchars: town in Scotland

• Leeming: village in North Yorkshire

• Heathrow: hamlet in Greater London

• Hurn: village in Dorset (South West England)

• Camborne: town in Cornwall (South West England)

• total daily sunshine, mean windspeed, max gust = unknown for first half of may 1987

international locations in large data set

• Beijing: capital city of China

• Perth: capital city of Western Australia (state of Australia)

• Jacksonville: city in Florida (state of USA)

• only have:

  • daily mean temp

  • daily total rainfall

  • daily mean pressure

  • daily mean windspeed

LDS locations near coast

• jacksonville

• perth

• camborne

• hurn

• leuchars

total days LDS covers

184 days

LDS locations in different hemispheres

• perth in southern hemi, has winter when UK in summer

LDS: UK great storm and effects

• 15-16 october 1987

• wind speeds high

• south and south-east affected

• skews some variables (wind/gust/rain)

• won’t have much impact on some (sunshine/cloud cover)

time periods of LDS

• May to October 1987

• May to October 2015

variables in LDS

• daily mean (air) temp in °C to 1dp

• daily total rainfall in mm to 1dp

• daily total sunshine in hr to 1dp

• daily maximum relative humidity as % to nearest integer

• daily mean windspeed and direction in knots (1kn=1.15mph) given to nearest integer and degrees to nearest 10

• daily maximum gust and direction in knots

• cloud cover in Oktas (1/8ths of sky covered by cloud, discrete data)

• daily mean visibility in decametres (1Dm = 10m) horizontally

• daily mean pressure in hectopascals (1hPa = 100Pa = 1 millibar)

daily mean air temp in LDS

average of hourly temperature readings between 0900-0900 GMT

daily total rainfall in LDS

measured for 24hrs starting at 0900 GMT
- ‘tr’ (trace of rain) = less than 0.05mm, use 0 or 0.025

daily maximum relative humidity in LDS

if above 95% - associated with mist and fog

daily mean windspeed and direction in LDS

• windspeed described using Beaufort conversion (calm, light etc)

• wind direction given as cardinal direction (NESW)

• averaged for 24 hours starting at 0000GMT

daily maximum gust and direction in LDS

• same units as windspeed+direction

• maximum instantaneous speed over 24 hours

suvat

outliers using quartiles

either:

greater than Q3+k(Q3-Q1)

less than Q1-k(Q3-Q1)

variance =

mean of the squares - square of the means

standard deviation =

sq root variance

binomial distribution

mutually exclusive

no outcomes in common (do not overlap)
P(A or B) = P(A) + P(B)

independent events

one event has no effect on another

P(A and B)= P(A) x P(B)

discrete uniform distribution

when all probabilities are the same

newton’s first law

object at rest will stay at rest, object moving at constant velocity will continue moving with constant velocity unless unbalanced force acts on it

newton’s second law

F=ma

W=

mg