Units and Measurement 2.ppt

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 the
instruments on an aeroplane?
Qualitative Observations
How do you measure
artistic 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
70
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
Base quantity
is like the brick – the
basic building block of
a house
Derived quantity is like
the house that was
build 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 ÷ volume
In terms of units: Units of density = kg / m3 = kg m−3

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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 × acceleration
In 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
done
Work

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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 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

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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 × 10−10 m.

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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

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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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Adding Vectors using Graphical Method
• Parallel vectors can be added arithmetically
2 N
4 N
6 N 4 N
2 N
2 N

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Adding 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 N
Direction = 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

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Another 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

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A
B
A
B
A
B

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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 arithmetically
4. Non-parallel vectors are added by graphical
means using the parallelogram law

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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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• 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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• Systematic errors are not random but constant
• Cause an experimenter to consistently
underestimate or overestimate a reading
• They 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

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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.

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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 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 micrometer
1. 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

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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 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.

Units and Measurement 2.ppt

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