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## Physics in addition to Physical Measurement Topic 1.2 Measurement in addition to Uncertainties The S.I

Armitage, Dan, Field Editor has reference to this Academic Journal, PHwiki organized this Journal Physics in addition to Physical Measurement Topic 1.2 Measurement in addition to Uncertainties The S.I. system of fundamental in addition to derived units St in addition to ards of Measurement SI units are those of the Système International dUnités adopted in 1960 Used as long as general measurement in most countries

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Fundamental Quantities Some quantities cannot be measured in a simpler as long as m in addition to as long as convenience they have been selected as the basic quanitities They are termed Fundamental Quantities, Units in addition to Symbols The Fundamentals Length metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temp Kelvin K Amount of a substance mole mol Derived Quantities When a quantity involves the measurement of 2 or more fundamental quantities it is called a Derived Quantity The units of these are called Derived Units

The Derived Units Acceleration ms-2 Angular acceleration rad s-2 Momentum kgms-1 or Ns Others have specific names in addition to symbols Force kg ms-2 or N St in addition to ards of Measurement Scientists in addition to engineers need to make accurate measurements so that they can exchange in as long as mation To be useful a st in addition to ard of measurement must be Invariant, Accessible in addition to Reproducible 3 St in addition to ards ( as long as in as long as mation) The Metre :- the distance traveled by a beam of light in a vacuum over a defined time interval ( 1/299 792 458 seconds) The Kilogram :- a particular platinum-iridium cylinder kept in Sevres, France The Second :- the time interval between the vibrations in the caesium atom (1 sec = time as long as 9 192 631 770 vibrations)

Conversions You will need to be able to convert from one unit to another as long as the same quanitity J to kWh J to eV Years to seconds And between other systems in addition to SI KWh to J 1 kWh = 1kW x 1 h = 1000W x 60 x 60 s = 1000 Js-1 x 3600 s = 3600000 J = 3.6 x 106 J J to eV 1 eV = 1.6 x 10-19 J

SI Format The accepted SI as long as mat is ms-1 not m/s ms-2 not m/s/s i.e. we use the suffix not dashes Uncertainity in addition to error in measurement Errors Errors can be divided into 2 main classes R in addition to om errors Systematic errors

Mistakes Mistakes on the part of an individual such as misreading scales poor arithmetic in addition to computational skills wrongly transferring raw data to the final report using the wrong theory in addition to equations These are a source of error but are not considered as an experimental error Systematic Errors Cause a r in addition to om set of measurements to be spread about a value rather than being spread about the accepted value It is a system or instrument value Systematic Errors result from Badly made instruments Poorly calibrated instruments An instrument having a zero error, a as long as m of calibration Poorly timed actions Instrument parallax error Note that systematic errors are not reduced by multiple readings

R in addition to om Errors Are due to variations in per as long as mance of the instrument in addition to the operator Even when systematic errors have been allowed as long as , there exists error. R in addition to om Errors result from Vibrations in addition to air convection Misreading Variation in thickness of surface being measured Using less sensitive instrument when a more sensitive instrument is available Human parallax error Reducing R in addition to om Errors R in addition to om errors can be reduced by taking multiple readings, in addition to eliminating obviously erroneous result or by averaging the range of results.

Accuracy Accuracy is an indication of how close a measurement is to the accepted value indicated by the relative or percentage error in the measurement An accurate experiment has a low systematic error Precision Precision is an indication of the agreement among a number of measurements made in the same way indicated by the absolute error A precise experiment has a low r in addition to om error Limit of Reading in addition to Uncertainty The Limit of Reading of a measurement is equal to the smallest graduation of the scale of an instrument The Degree of Uncertainty of a measurement is equal to half the limit of reading e.g. If the limit of reading is 0.1cm then the uncertainty range is 0.05cm This is the absolute uncertainty

Reducing the Effects of R in addition to om Uncertainties Take multiple readings When a series of readings are taken as long as a measurement, then the arithmetic mean of the reading is taken as the most probable answer The greatest deviation or residual from the mean is taken as the absolute error Absolute/fractional errors in addition to percentage errors We use ± to show an error in a measurement (208 ± 1) mm is a fairly accurate measurement (2 ± 1) mm is highly inaccurate In order to compare uncertainties, use is made of absolute, fractional in addition to percentage uncertainties. 1 mm is the absolute uncertainty 1/208 is the fractional uncertainty (0.0048) 0.48 % is the percentage uncertainity

Combining uncertainties For addition in addition to subtraction, add absolute uncertainities y = b-c then y ± dy = (b-c) ± (db + dc) Combining uncertainties For multiplication in addition to division add percentage uncertainities x = b x c then dx = db + dc x b c Combining uncertainties When using powers, multiply the percentage uncertainty by the power z = bn then dz = n db z b

St in addition to ard Graphs – hyperbola again An inverse square law graph is also a hyperbola i.e. y 1/x2 or y = k/x2 where k is the constant of proportionality Non-St in addition to ard Graphs You need to make a connection between graphs in addition to equations If this is a graph of r against t2 plotted from data having an expected relationship r = at2/2 +r0 where a is a constant Then the gradient is a/2 in addition to the y-intercept is r0 – it is not the case that r t2, it is a linear relationship The intercept is there as long as e important too

## Armitage, Dan Field Editor

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