Cheatography

# Physical Quantities, Units and Measurement Cheat Sheet by peaceknight05

Physics Notes for Unit 1

### Physical Quantities

 Physical attributes that are measurable are known as Physical Quanti­ties. A physical quantity always consists of a numerical magn­itude and a unit.

### Examples of Physical Quantities

 200 km 12.3 dB 23 Hz 47.3 °C 300 kN

### Accuracy of Measur­ement

 Accu­racy refers to the closeness of a measured value to a standard or known value.

### Precision

 Prec­ision refers to the closeness of two or more measur­ements to each other.

### Random Errors

 It occurs in all measur­ements. It occurs whenever an observer estimates the last figure of a reading on an instru­ment. Causes: - human reaction time - background noise - mechanical vibrations It cannot be predicted. It can be reduced by taking large numbers of readings and averaging them.

### Systematic Errors

 It is not random but constant. It may cause an observer to consis­tently undere­stimate or overes­timate a reading. Causes: - zero error of an instru­ment: any indication that a measuring system gives a false reading when the true value of a measured quantity is zero It can be eliminated if we know the sources of the errors.

### Taking Measur­ements

 Different measuring instru­ments are used for measuring different quanti­ties. The choice of instrument will affect the precision of the measur­ement we obtain. The precision of an instrument is usually equal to the smallest division of the instrument with a few exceptions such as the thermo­meter, ammeter and voltmeter.

### SI Units and Base Quantities

 The Inter­nat­ional System of Units is the modern form of the metric system, and is the most widely used system of measur­ement. It is comprised of a system of units built on seven base units.

### The Seven Base Units

 Length metre m Mass kilogram kg Time second s Electric Current ampere A Temper­ature kelvin K Amount of Substance mole mol Luminous Intensity candela cd

### Defini­tions of Base Units

 second The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unpert­urbed ground­-state hyperfine transition frequency of the caesiu­m-133 atom, to be 9,192,­631,770 when expressed in the unit Hz, which is equal to s−1. metre The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299,79­2,458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs. kilogram The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.6260­701­5×1­0−34 when expressed in the unit J⋅s, which is equal to kg⋅m2­⋅s­−1, where the metre and the second are defined in terms of c and ΔνCs. ampere The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.6021­766­34×­10−19 when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of ΔνCs. kelvin The kelvin, symbol K, is the SI unit of thermo­dynamic temper­ature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.3806­49×­10−23 when expressed in the unit J⋅K−1, which is equal to kg⋅m2­⋅s­−2­⋅K­−1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs. mole The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.0221­407­6×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. candela The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monoch­romatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm⋅W−1, which is equal to cd⋅sr⋅­W−1, or cd⋅sr⋅­kg­−1­⋅m­−2­⋅s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
Not necessary inform­ation

### Prefixes and Orders of Magnitude

 The SI system also establ­ishes a set of twenty prefixes to unit names and unit symbols that may be used when specifying multiples and fractions of the units. This is useful for expressing physical quantities that are either very big or very small.

### Table of Prefixes

 yotta Y 1024 zetta Z 1021 exa E 1018 peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deka da 101 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 femto f 10-15 atto a 10-18 zepto z 10-21 yocto y 10-24
In O-Levels, the only prefixes that you need to know are nano, micro, milli, centi, deci, kilo, mega and giga.

### Examples of Orders of Magnitudes

 3,900 YHz Highest energy gamma wave ray detected 30.86 Zm One gigaparsec 30 Eg Mass of the rings of Saturn 30 PHz Frequency of an X-Ray 9.461 Tm The distance light travels in a year 0.3 Gm/s Speed of light in a vacuum 12.742 Mm Diameter of the earth 16.5 kN Bite force of a 5.2m Saltwater Crocodile 2.4 hg Average mass of a grand piano 7 dag Average mass of an adult human 1.1 dJ Energy of an American half-d­ollar falling 1 metre 1.6667 cHz 1 rpm 2.75 mm/s Fastest recorded speed of a snail 0.3 μm/s Calculated speed of an amoeba (lower bound) 1.6 nN Force required to break a typical covalent bond 50 pK Lowest temper­ature produced 1 fg Mass of a HIV-1 virus 1.65 ag Mass of double­-st­randed DNA molecule consisting of 1,578 base pairs 3 zJ Energy of a van der Waals intera­ction between atoms 0.0000­000­00016 ym One Planck length