learning outcomes

Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement

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

C h a p t e r 1Learning 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 ObservationsWhat can be measured with

the instruments on an aeroplane?

Qualitative ObservationsHow do you measure

artistic beauty?

1.1 Physical QuantitiesQuantitative versus qualitative

• Most observation in physics are quantitative• Descriptive observations (or qualitative) are usually

imprecise



C h a p t e r 11.1 Physical Quantities

• A physical quantity is one that can be measured and consists of a magnitude and unit.

SI units are common today

Measuring length70

km/h

4.5 m

Vehicles Not

Exceeding 1500 kg In Unladen Weight



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Are classified into two types:• Base quantities• Derived quantities

1.1 Physical Quantities

Base quantityis like the brick – the basic building block of a house

Derived quantity is likethe house that wasbuild up from a collectionof bricks (basic quantity)



C h a p t e r 11.2 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




• 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 ÷ volume

In terms of units: Units of density = kg / m3 = kg m−3




• 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 =

timedistance

timevelocity




• Work out the derived quantities for:

Defining equation: Pressure =

In terms of units: Units of pressure =

Defining equation: Work = Force × DisplacementIn terms of units: Units of work =

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

AreaForce

TimedoneWork



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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



C h a p t e r 11.3 Prefixes

• Prefixes simplify the writing of very large or very small quantities

Prefix Abbreviation Powernano n 10−9

micro 10−6

milli m 10−3

centi c 10−2

deci d 10−1

kilo k 103

mega M 106

giga G 109



C h a p t e r 11.3 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 × 10−10 m.

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.



C h a p t e r 11.4 Scalars and Vectors

• Scalar quantities are quantities that have magnitude only. Two examples are shown below:

Measuring Mass Measuring Temperature




• 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




• Vector quantities are quantities that have both magnitude and direction

Magnitude = 100 N

Direction = Left

A Force




• Examples of scalars and vectors

Scalars Vectors

distance displacement

speed velocity

mass weight

time acceleration

pressure force

energy momentum

volume

density



C h a p t e r 11.4 Scalars and VectorsAdding Vectors using Graphical Method• Parallel vectors can be added arithmetically

2 N

4 N

6 N 4 N

2 N

2 N



C h a p t e r 11.4 Scalars and VectorsAdding Vectors using Graphical Method• Non-parallel vectors are added by graphical

means using the parallelogram law–Vectors can be represented graphically by arrows

–The length of the arrow represents the magnitude of the vector

–The direction of the arrow represents the direction of the vector

–The magnitude and direction of the resultant vector can be found using an accurate scale drawing

5.0 cm 20.0 NDirection = right



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• The parallelogram law of vector addition states that if two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram

1.4 Scalars and Vectors



C h a p t e r 11.4 Scalars and VectorsAnother method of Adding Vectors• To add vectors A and B

–place the starting point of B at the ending point of A

–The vector sum or resultant R is the vector joining the starting point of vector A to the ending point of B

–Conversely, R can also be obtained by placing the starting point of A at the ending point of B

–Now the resultant is represented by the vector joining the starting point of B to the ending point of A

• See next slide




A

B

A

B

AB



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1. Scalar quantities are quantities that only have magnitudes

2. Vector quantities are quantities that have both magnitude and direction

3. Parallel vectors can be added arithmetically4. Non-parallel vectors are added by graphical

means using the parallelogram law



C h a p t e r 11.5 Measurement of Length and TimeAccurate Measurement• No measurement is perfectly accurate• Some error is inevitable even with high

precision instruments• Two main types of errors

– Random errors– Systematic errors



C h a p t e r 11.5 Measurement of Length and TimeAccurate Measurement• Random errors occur in all measurements. • Arise when observers estimate the last

figure of an instrument reading• Also contributed by background noise or

mechanical vibrations in the laboratory. • Called random errors because they are

unpredictable• Minimise such errors by averaging a large

number of readings• Freak results discarded before averaging



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Accurate Measurement• Systematic errors are not random but

constant• Cause an experimenter to consistently

underestimate or overestimate a reading• They are due to the equipment being used –

e.g. a ruler with zero error• may be due to environmental factors – e.g.

weather conditions on a particular day• Cannot be reduced by averaging, but they

can be eliminated if the sources of the errors are known

1.5 Measurement of Length and Time



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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• Position eye perpendicularly at the mark on

the scale to avoids parallax errors • Another reason for error: object not align or

arranged parallel to the scale




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• Many instruments do not read exactly zero when nothing is being measured

• Happen because they are out of adjustment or some minor fault in the instrument

• Add or subtract the zero error from the reading shown on the scale to obtain accurate readings

• Vernier calipers or micrometer screw gauge give more accurate measurements




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• Table 1.6 shows the range and precision of some measuring instruments

Instrument Range of measurement

Accuracy

Measuring tape 0 − 5 m 0.1 cm

Metre rule 0 − 1 m 0.1 cm

Vernier calipers 0 − 15 cm 0.01 cm

Micrometer screw gauge

0 − 2.5 cm 0.01 mm




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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 on the main scale.




C h a p t e r 11.5 Measurement of Length and Time• 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



C h a p t e r 11.5 Measurement of Length and Time• 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 the

spindle 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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Precautions when using a micrometer1. Never tighten thimble too much– Modern micrometers have a ratchet to avoid this

2. Clean the ends of the anvil and spindle before making a measurement

– Any dirt on either of surfaces could affect the reading

3. Check for zero error by closing the micrometer when there is nothing between the anvil and spindle

– The reading should be zero, but it is common to find a small zero error

– Correct zero error by adjusting the final measurement




C h a p t e r 11.5 Measurement of Length and TimeTime• Measured in years, months, days, hours,

minutes and seconds• SI unit for time is the second (s).• Clocks use a process which depends on a

regularly repeating motion termed oscillations.



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

uncertainty of 1.7 × 10−15, or accuracy to about one second 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• Mass at the end of the chain

attached to the clock is allowed to fall

• Gravitational potential energy from descending mass is used to keep the pendulum swinging

• In clocks that are wound up, this energy is stored in coiled springs as elastic potential energy.




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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 crystals

vibrating • some watches also make use of coiled

springs to supply the needed energy




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Stopwatch• Measure short intervals of time• Two types: digital stopwatch, analogue

stopwatch• Digital stopwatch more accurate as it can

measure time in intervals of 0.01 seconds.• Analogue stopwatch measures time in

intervals of 0.1 seconds.




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Errors occur in measuring time • If digital stopwatch is used to time a race,

should not record time to the nearest 0.01 s.

• reaction time in starting and stopping the watch will be more than a few hundredths of a second

• an analogue stopwatch would be just as useful




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Ticker-tape Timer• electrical device making use of the oscillations

of a steel strip to mark short intervals of time• steel strip vibrates 50 times a second and makes

50 dots a second on a paper tape being pulled past it

• used only in certain physics experiments




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Ticker-tape Timer• Time interval between two consecutive dots

is 0.02 s• If there are 10 spaces on a pieces of tape,

time taken is 10 × 0.02 s = 0.20 s. • Counting of the dots starts from zero• A 10-dot tape is shown below.




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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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5. Zero error is due to instruments that do not read exactly zero when there is nothing being measured.

6. The time for one complete swing of a pendulum is called its period of oscillation.

7. As the length of the pendulum increases, the period of oscillation increases as well.



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