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Physical Quantities, Units and Measurement

T H E M E O N E : M E A S U R E M E N T

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Learning outcomes

Understand that physical quantities have

numerical magnitude and a unit

Recall base quantities and use prefixes

Show an understanding of orders of magnitude

Understand scalar and vector quantities

Determine resultant vector by graphical method

Measure length with measuring instruments

Measure short interval of time using stopwatches

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Quantitative Observations

What can be measured with theinstruments on an aeroplane?

Qualitative Observations

How do you measureartistic beauty?

1.1 Physical Quantities

Quantitative versus qualitative

Most observation in physics are quantitative

Descriptive observations (or qualitative) are usually imprecise

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A physical quantity is one that can be measured

and consists of a magnitude and unit.

SI units

are

common

today

Measuring length

70km/h

4.5 m

Vehicles

NotExceeding

1500 kg In

Unladen

Weight

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Are classified into two types:

Base quantities

Derived quantities


Base quantityis like the brick the

basic building block of

a house

Derived quantity is like

the house that wasbuild up from a collection

of bricks (basic quantity)

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1.2 SI Units

SI Units International System of Units

Base Quantities Name of Unit Symbol of Unit

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

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This Platinum Iridium

cylinder is the standard

kilogram.

1.2 SI Units

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1.2 SI Units

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1.2 SI Units

Example of derived quantity: area

Defining equation: area = length width

In terms of units: Units of area = m m = m2

Defining equation: volume = length width height

In terms of units: Units of volume = m m m = m2

Defining equation: density = mass volumeIn terms of units: Units of density = kg / m3 = kg m3

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1.2 SI Units

Work out the derived quantities for:

Defining equation: speed =

In terms of units: Units of speed =

Defining equation: acceleration =

In terms of units: Units of acceleration =

Defining equation: force = mass accelerationIn terms of units: Units of force =

time

distance

time

velocity

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1.2 SI Units

Work out the derived quantities for:

Defining equation: Pressure =

In terms of units: Units of pressure =

Defining equation: Work = Force Displacement

In terms of units: Units of work =

Defining equation: Power =In terms of units: Units of power =

Area

Force

Time

doneWork

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Derived

Quantity

Relation with Base and

Derived Quantities Unit

Special

Name

area length width

volume length width

height

density mass volume

speed distance time

acceleration change in velocity

time

force mass acceleration newton

(N)

pressure force area pascal

(Pa)

work force distance joule (J)

power work time watt (W)

1.2 SI Units

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1.3 Prefixes

Prefixes simplify the writing of very large or very

small quantities

Prefix Abbreviation Power

nano n 109

micro 106

milli m 103

centi c 102

deci d 101

kilo k 103

mega M 106

giga G 109

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1.3 Prefixes

Alternative writing method

Using standard form

N 10n where 1 N< 10 and n is an integer

This galaxy is about 2.5 106

light years from the Earth.

The diameter of this atom

is about 1 1010 m.

1
http://upload.wikimedia.org/wikipedia/commons/f/ff/Andromeda_galaxy.jpg

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1. A physical quantity is a quantity that can be

measured and consists of a numerical magnitude

and a unit.

2. The physical quantities can be classified into

base quantities and derived quantities.

3. There are seven base quantities: length, mass,

time, current, temperature, amount of

substance and luminous intensity.

4. The SI units for length, mass and time are metre,kilogram and second respectively.

5. Prefixes are used to denote very big or very small

numbers.

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1.4 Scalars and Vectors

Scalar quantities are quantities that have

magnitude only. Two examples are shown below:

Measuring Mass Measuring Temperature

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Scalar quantities are added or subtracted by using

simple arithmetic.

Example: 4 kg plus 6 kg gives the answer 10 kg

+ =

4 kg

6 kg

10 kg

1

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Vector quantities are quantities that have both

magnitude and direction

Magnitude = 100 N

Direction = Left

A Force

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Examples of scalars and vectors

Scalars Vectors

distance displacement

speed velocity

mass weight

time acceleration

pressure force

energy momentum

volume

density

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1.5 Measurement of Length and Time

Accurate Measurement No measurement is perfectly accurate

Some error is inevitable even with high precision

instruments

Two main types of errors Random errors

Systematic errors

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Length Measuring tape is used to measure relatively long

lengths

For shorter length, a metre rule or a shorter rule

will be more accurate


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Correct way to read the scale on a ruler


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Vernier Calipers Allows measurements up to 0.01 cm

Consists of a 9 mm long scale divided into 10

divisions


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Vernier Calipers The object being measured is between 2.4 cm

and 2.5 cm long.

The second decimal number is the marking on the

vernier scale which coincides with a marking onthe main scale.


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Here the eighth marking on the vernier scale

coincides with the marking at C on the main scale

Therefore the distance AB is 0.08 cm, i.e. the

length of the object is 2.48 cm

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The reading shown is 3.15 cm. The instrument also has inside jaws for measuring internal

diameters of tubes and containers.

The rod at the end is used to measure depth of containers.

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Micrometer Screw Gauge To measure diameter of fine wires, thickness of

paper and small lengths, a micrometer screw

gauge is used

The micrometer has two scales: Main scale on the sleeve

Circular scale on the thimble

There are 50 divisions on the thimble

One complete turn of the thimble moves thespindle by 0.50 mm


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Micrometer Screw Gauge Two scales: main scale and circular scale

One complete turn moves the spindle by 0.50 mm.

Each division on the circular scale = 0.01 mm


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Time Measured in years, months, days, hours, minutes

and seconds

SI unit for time is the second (s).

Clocks use a process which depends on aregularly repeating motion termed oscillations.

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Caesium atomic clock 1999 - NIST-F1 begins operation with an

uncertainty of 1.7 1015, or accuracy to about onesecond in 20 million years


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Time The oscillation of a simple pendulum is an

example of a regularly repeating motion.

The time for 1 complete oscillation is referred to

as the period of the oscillation.


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Pendulum Clock Measures long intervals of time

Hours, minutes and seconds


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Watch also used to measure long intervals of time

most depend on the vibration of quartz crystals

to keep accurate time

energy from a battery keeps quartz crystalsvibrating


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1. The metre rule and half-metre rule are used to

measure lengths accurately to 0.1 cm.

2. Vernier calipers are used to measure lengths to a

precision of 0.01 cm.

3. Micrometer are used to measure length to a

precision of 0.01 mm.

4. Parallax error is due to:

(a) incorrect positioning of the eye

(b) object not being at the same level as the

marking on the scale

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Physical Quantities, Units and MeasurementC h a p t e r 11

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