Cheatography

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

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

### 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