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A-Level Physics - Measurements and Their Errors Cheat Sheet by

AQA A-Level Physics Topic 1 - Measurements and Their Errors; made directly in accordance with the AQA 7408 specification

SI units

mass (m)
kilograms (kg)
length (l)
metres (m)
time (t)
seconds (s)
amount of substance (n)
moles (mol)
temper­ature (t)
kelvin (K)
electric current (I)
amperes (A)

Derivation of SI Units

A derived unit is comprised of a combin­ation of SI units.
These can be derived by using the definition of the unit, or their equations eg. F=ma
eg. to find the SI units of force (F), multiply the units of mass and accele­ration to give kgms^-2 (or N)
This means that every unit can be broken down into its SI base units.

Prefixes

Tera (T)
10^12
Giga (G)
10^9
Mega (M)
10^6
Kilo (K)
10^3
Centi (c)
10^-2
Milli (m)
10^-3
Micro (µ)
10^-6
Nano (n)
10^-9
Pico (p)
10^-12
Femto (f)
10^-15
These prefixes could be added before any SI units

Conver­sions between units

It is possible to convert between different units of the same quantity. Here are some examples listed below:
1 eV = 1.6 × 10^–19 J
1 kW h = 3 600 000 J or 3.6 MJ (×10^6)

Types of Errors

Random error
Cause variations in both directions and are usually uncont­rol­lable
Systematic error
Caused by faults in the experi­mental method or apparatus
Zero error
A type of systematic error caused by uncali­brated equipment
Parallax error
A type of systematic error caused by the apparent position of an object due to the viewing angle
 

Reviewing measur­ements

Precise
Consistent and fluctuate around a mean value
Accuracy
A measur­ement that is close to the true value
Repeat­ability
The original person can redo the experi­ement and get the same results
Reprod­uci­bility
A different person does an experiment differ­ently and gets the same results
Resolution
The smallest change in the quantity being measured that gives a recogn­isable change in reading

Uncert­ainty

The bounds in which the accurate value can be expected to lie
They should be given to the same number of signif­icant figures as the data.

Types of Uncert­ainity

Absolute
Uncert­ainty given as a fixed quantity
Fractional
Uncert­ainty as a fraction of the measur­ement
Percentage
Uncert­ainty as a percentage of the measur­ement

Resolution and Uncert­ainity

Readings are when one value is found
Measur­ements are when the difference between 2 readings is found
The uncert­ainty in a reading is +/- half the smallest division
The uncert­ainty in a measur­ement is at least +/- 1 smallest division
The resolution of an instrument will affect its uncert­ainty
Digital readings and given values will either have the uncert­ainty quoted, or assumed to be +/- the last signif­icant digit
For repeated data, the uncert­ainty is half the range

Reducing Uncert­ainity

You can reduce uncert­ainty in the following ways:
• fixing one end of a ruler so there is only uncert­ainty in on reading
• measuring multiple times
• (for fractional and percen­tage) measure larger quantities
 

Combining Uncert­ainties

Adding­/su­btr­acting data - ADD ABSOLUTE UNCERT­AINTIES
Multip­lyi­ng/­diving data - ADD PERCENTAGE UNCERT­AINTIES
Raising to a power - MULTIPLY PERCENTAGE UNCERT­AINITY BY POWER

Uncert­ainties in graphs

Uncert­ainties are shown as error bars on graphs
A line fo best fit on a graph should go through all error bars (excluding anomalies)
The uncert­ainity in a gradient can be found by lines of best and worst fit
This can be done using the gradients of the steepest and shallowest lines of best fits
You can also use these two lines to find the uncert­ainty in the y-inte­rcept

Graph

Estimation of physical quantities

Orders of magnitude are powers of ten which describe the size of an object
These can be used to compare the sizes of objects
Estimation is a skill used to approx­imate the values of physical quanti­ties, in order to make compar­isons, or to check if a value calculated is reason­able.

Variables

Dependant
The variable that is being measured
Indepe­ndent
The variable that is being changed
Control
Other variables that stay the same
       
 

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