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PHYSICS ND ME SUREMENT IN

EVERYD Y LIFE

[ ] Physical Quantities nd Units

Physical quantity:

Any number that is used to describea physical phenomenonquantitatively.

Consists of:- Basic quantities.- Derived Quantities.

International System, SI Unit:

The most common unit used byscientists and engineers around theworld

Basic quantities & SI Units

Quant i t ies SI Uni ts Symbols

Time second [s]

Length meter [m]

Mass kilogram [kg]

Current ampere [A]

Temperature Kelvin [K]

Amount of

Substance mole [n]

(Light Intensity) candela [cd]

Derived Quantities:

Combinations of the basic quantities.

- Units for derived quantities can bededuced if the definitions are given

Determining the Derived Units:

- Example:

i) Define the quantity:

Density ()is the mass (m) of an

object per unit volume (V).

Hence the defining equation in SI

units:

= m / V

(kg / m3)

This gives the derived SI unit for

density as kilograms per cubic

meter, (kg / m3).

ii) What are the units of ?

*(Clue : The relationship between the

circumference (c) and the diameter

(d) of a circle is given by the

equation c= d

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If length is measured in meters, then

= c /d

(m / m)

Thus the constant has no units,

because they cancel out. It is

unitless or dimensionless constant.

Unit Prefixes

Pref ix Symbo l Factor

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 10-6

Nano n 10-9

Pico p 10-12

Femto f 10-15

Unit Consistency and Conversions

- Equation must always bedimensionally consistent

- example:

d= 10m, v = 2ms-1

and t = 5s

d = vt

In terms of unit:

Conversion of Unit

- When converting between units,write down the units explicitly in thecalculations and treat them like anyalgebraic quantity.

- In particular, take advantage of thefact that multiplying or dividing anequation by a factor of 1 does notalter and equation.

- Example:

Express 979.0 m in feet.

(3.281 feet = 1 meter)

Solution:

Use (3.281 feet / 1 meter) as a conversion factor to multiply the

equation Length = 979.0 meters

Length = (979.0 m)(1)

= (979.0 meters) (3.281 feet / 1 meter)

= 3212 feet

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Significant Figures

- Measured quantities containuncertainty.

- Only retain figures that containmeaningful information.

- Signi f icant f igures(sometimescalled significant digits) is:

all non-zero digits plus zeros thatdo not just hold a place before orafter a decimal point.

used to indicate the number ofmeaningful digits.

- The number of s.f. of a numericalquantity is the number of reliablyknown digits it contains.

example: 2.91mm (3s.f.)

- For a measured quantity, s.f. isusually defined as all of the digitsthat can be read directly from theinstrument used in making the

measurement plus one uncertaindigit that is obtained by estimatingthe fraction of the smallest division ofthe instruments scale.

- Zeros at the beginning of anum ber are not signi f icant. They

merely locate the decimal po int .

e.g. 0.0254 (3 s.f. - 2,5,4)

- Zeros w ithin a num ber aresigni f icant.

e.g. 104.6 m (4 s.f. - 1,0,4,6)

- Zeros at the end of a number afterthe decimal poin t are signi f icant.

e.g. 2705.0 m (5 s.f. - 2,7,0,5,0)

- In a who le num ber withou t adecimal point that end in one ormore zeroes ..

How Many Significant Figures

0.089 2

1.089 4

12000 2

12001 5

300.0 4

300.01 5

0.0105 3

0.01 1

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*Addition and Subtraction

*Multiplication and Division

- Result should have the same

number of significant figures as theleast accurate number

Scientific Notation

- The result of a calculation usuallyhas no more significant figures thanthe input data

Mathematical

operation

Significant figures in

result

Multiplication or

division

No more than in numb

with the fewest

significant figures

e.g. 0.745 x 2.2 /

3.885=0.42

Addition or

subtraction

Determined by the

number with the

smallest uncertainty

e.g.27.153+138.2

11.74=153.6

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Accuracy and precision

- Accuracy:

How close a measurement is to

being correct.

- Precision:

The number of significant figures(or the uncertainties) in ameasurement.

For gravitational acceleration

near the earth,

g = 9.532706 m/s2 and g = 9.7 m/s

2.

Which is more

(i) precise?

(ii) accurate?

*(Greater precision does notmean greater accuracy! )