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Topic 1: MeasurementsSl UnitsBase Quantity - chosen and arbitrarily definedDerived Quantity, defined based on combination of base quantitiesBase Quantities - mass, length, time, electric current, temperature & amount of substance

Errors and UncertaintiesFig1.2 Comparing systematic errors and random errors

Fig 1.1 Prefixes to remember:Prefix Symbol Multiples Prefix symbol Multiplescenti c 102kilo k tou milli to'M 10b mtcro u 1o't8a G 10' nano n 10'tera T 10r2 pico p to"

Definition Systematic Errors Random ErrorsAn error of measurement whichcause a random set of readings tospread consistentlv around a meanvalue different from the trub value.

An error of measurement that causesan unpredictable scatter of readjngsabout a mean value such that eachreading has an eoual chance of beinghieher or lower than the meanJalue.Characteristic Cannot be reduced or eliminated by

taking the average of readings.

Can be eliminated by carefuldesignof an experiment and goodexperimental techniques.

Cannot be eliminated, but can beminimized by taking the average ofrepeated readings.

Examples (1) zero errors of instruments{2) heat loss to surroundings(3) background count rate of a GMcounter (H2)

(1) human reaction time(2) parallax error

llPaee

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Fis 1.3 Accuracy vs precisionPrecision

Note: m is the physicallquantity;N is its frequency of occurrence;mo is the true value of the quantity.

EigL.4 Absolute and fractional (or percentage) errors

Good precision Good precision6ood accuracy

Poor precision

Absolute error Fractional error Percentage erlorSymbol At &I' Ar- x lo0c6

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Fig 1-5 Calculation of errorSum Difference Product Quotient ExponentialTvAz Lr Lv hz Ax

w=(t-2*o.L)m r=(o-34:o.o5)'rr y=(S_6:o-z)rnS*'+x-2y3rlr + tr * zAr

2wy& alar^.= +:+- A'ArAI&-:r +:+z-

z -.Lz dz always has only 1 significant figurez will then follow the num ber of decimal place which 6z has.e.g. zlaz=(42 17) mmot z: Lz = (99O l40) mmor z:t\z= (3.+i0.2)mmor ziLz= (3.94 1o.07)mm

Steps to calculate the value of a phvsical qua ntitv in term ofthe uncertainW(1) Express the unknown quantity asthe subject.l2l Calculate the value ofthe unknown quantity without the uncertainty.(3) Use Fig. 1.5 above to find the uncertainty of unknown quantity.(4) Express uncertainty to 1sf.(5) Round tbe quantityto the same dp as the uncertainty.(6) Express answer to standard form (not always compulsory but good practice)\71 Write the quantity with its uncertainty and the unitiNote: unit should be written outside bracket)

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Scalars and VedorsWhilst scalars can be added or subtracted by simple arithmetic, vectors cannot - both theirmasnitudes and directions must be taken into account.Vector resolutionLet v be the vectorto be resolved.Tips: {1)the 2 resolved components must be 9Oo apart;

(2) the 2 resolved components must encompass the original vector v;{3) the component adjacent to the labeled angle is the 'cos' one (the other must

therefore bethe'sin' one).

vsin0vsinPI

-_r v cos pFu rther ti p: Whe n solving q u estions that involve th e calculation of resu lta nt of vectors, it isusuallV easter to resolve the individualforces into their respedive veatical and horizontalcomponents first, {10 cos45') N 10N

145'I -> (10 sin45') N

7N(7 sinTs') N

(7 cos75')*

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Now proceed to add up the horizontal and vertical components. Remember to obey the signconvention you have defined.Practice

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