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PHYSICAL QUANTITY AND RELATED TERMSTRANSCRIPT
Introductory Physics
Physical Quantities, Unitsand Measurement
(Updated: 20150702)
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© Sutharsan John Isles 2
Expected Prior Knowledge
It is assumed that you know the following sufficiently well. If you feel that you do not know them sufficiently, please visit those topics in your books before continuing further:
Mathematical SymbolsThe Real Number SystemFractions and DecimalsSignificant FiguresAngles and BearingsIndices
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Terminology
A featurea noticeable part of somethinghttp://simple.wiktionary.org/wiki/feature
What do you notice about the two lines below?
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Terminology
A characteristica typical feature of somethinghttp://simple.wiktionary.org/wiki/characteristic
Compare the vehicles below. What is characteristic of bothvehicles?
A limousine An ordinary car
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Terminology
A propertysomething that gives an object its characteristics
Observe a piece of rubber band. What do you notice whenit is pulled and released? What could you say ischaracteristic of objects made with the same type ofmaterial? Ultimately, what can you say is a property ofrubber?
Note: Rubber is not the only elastic material. (Spandex usedin stretch jeans, is another example.)
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Terminology
Consider the following:
You can feel the effects of a force (throwing you off) as youstand at the edge on a merry‐go‐round while it is spinning.
You can see that one line is longer than the other.
Physicalsomething that is real in the sense that it can beseen, felt, etc. (i.e. not imaginary) and can thus bedescribed in terms of what you observe or perceivehttp://en.wikipedia.org/wiki/Physical_property
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Terminology
A physical propertya measurable (or perceived) property of something observable without having to change the composition or identity of that thing
Examples of physical properties include thefollowing:
LengthMassColourSmell
TemperatureSolubilityResistivityConductivity
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Terminology
The following are subsets of physical properties:
Mechanical propertiesElectrical propertiesThermal propertiesOptical properties
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Terminology
A quantitysomething that can be quantified (given a number to)
A physical quantitya physical property that can be expressed in numbers
E.g. Length being quantified: 13 cm
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Units
There are two common systems of units:SI units (Système International d’Unités)
E.g. metre, kilogram, second
The British engineering system (a.k.a. imperial system of units)
E.g. foot, pound, second
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Why SI Units?
Two reasons:Facilitates international trade and communicationsFacilitates exchange of scientific findings and information
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Physical Quantities
These may be divided into base quantitiesand derived quantities.Base quantities are expressed in base units.Derived quantities are expressed in derived units.There are seven base quantities and thus seven base units.
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SI Base Quantities & Units
Quantity Symbol Unit Abbreviation
Length l metre m
Mass m kilogram kg
Time t seconds s
Electric current I ampere A
Thermodynamic temperature T kelvin K
Amount of substance n mole mol
Luminous intensity Iv candela cdhttp://www.bipm.org/en/si/si_brochure/chapter2/2‐1/
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Common SI Prefixes for Units
Prefix Symbol Value Decimal Equivalent Scale (Short)peta P 1015 1 000 000 000 000 000 quadrilliontera T 1012 1 000 000 000 000 trilliongiga G 109 1 000 000 000 billion
mega M 106 1 000 000 millionkilo k 103 1 000 thousanddeci d 10-1 0.1 tenthcenti c 10-2 0.01 hundredthmilli m 10-3 0.001 thousandth
micro μ 10-6 0.000 001 millionthnano n 10-9 0.000 000 001 billionthhttp://en.wikipedia.org/wiki/Long_and_short_scales
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Multiples & Submultiplesof SI Units – The Metre
Multiples Submultiples
Value Symbol Name Value Symbol Name
103 m km kilometre 10-1 m dm decimetre
106 m Mm megametre 10-2 m cm centimetre
109 m Gm gigametre 10-3 m mm millimetre
1012 m Tm terametre 10-6 m μm micrometre
1015 m Pm petametre 10-9 m nm nanometre
http://en.wikipedia.org/wiki/Metre
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Conversion between multiples and submultiples of a base unit
How do you convert from kilometres to metres?E.g. Convert 3 km to metres
Solution
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3 3 3 1000 1 3000
kmm
m
= × ×= × ×=
kilo metre
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Conversion between multiples & submultiples of a base unit
How do you convert from metres to kilometres?E.g. Convert 70 m to kilometres
SolutionBegin with
Recognise that
∴
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1 1000 km m=11
1000m km=
170 70 1000
0.07
m km
km
= ×
=
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Conversion between multiples & submultiples of a base unit
How do you convert from millimetres to metres?
E.g. Convert 45 mm to metres
Solution
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145 45 metre1000
145 1 1000
45 10000.045
mm
m
m
m
= × ×
= × ×
=
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Conversion between multiples & submultiples of a base unit
How do you convert from millimetres to centimetres?
E.g. Convert 13 mm to centimetres
Solution
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113 13 metre1000
1 113 1 100 10
113 10
1.3
mm
m
cm
cm
= × ×
= × × ×
= ×
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Conversion between multiples & submultiples of a base unit
How do you convert from centimetres to millimetres?
E.g. Convert 11.5 cm to millimetres
Solution
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111.5 11.5 metre1001011.5 1
10001115 1
1000115
cm
m
m
mm
= × ×
= × ×
= × ×
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SI Derived Quantities & Units
Derived units are defined as products of powers of the base units.http://www.bipm.org/en/si/si_brochure/chapter1/1‐4.html
There are derived units expressed only in terms of base units.
E.g. square metres [m2], metres per second [m/s], etc.
There are also derived units with special names, usually names of scientists, and symbols for their units.
E.g. Newtons [N], Pascal [Pa], etc.
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SI Derived Quantities & Units
Name Symbol Derivation Unitarea A m × m m2
volume V m2 × m m3
speed, velocity v m ÷ s m/s
acceleration a m/s ÷ s m/s2
density ρ kg ÷ m3 kg/m3
force F kg × m/s2 kg m/s2 = N
pressure P N ÷ m2 N/m2 = Pa
energy, work E, W N × m N m = J
power P J ÷ s J/s = W
electrical charge Q A × s A s = C
electric potential difference V W ÷ A W/A = V
electrical resistance R V ÷ A V/A = Ω
moment of force (torque) τ (or M) N × m N mNote highlighted: Essence of derivation in each case is different.
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Trivia
Do you know the full names of scientists after whom the following units were named?
NewtonPascalJouleWattCoulombVoltOhm
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Conversion between multiples & submultiples of derived units
How do you convert from squared centimetres to squared metres?
E.g. Convert 8 cm2 to squared metres
Solution
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2
2
2
8 1 8 1 11 1 8 1
100 10018 1
100000.0008
cm cm cm
m m
m
m
= ×
= × × × × ×
= × ×
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Standard Form
Also called the scientific notation, it is a way of representing numbers that are too large or too small.It is generally denoted as A × 10n, where 1 ≤ A < 10 and A c R and n is an integer.Depending on the requirement, A can be in any number of significant figures.
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Standard Form – Examples
How do you express 0.0008 in standard form?Solution
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4
4
80.000810000
8108 10−
=
=
= ×
Standard Form – Examples
How do you express 80000 in standard form?Solution
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4
80000 8 100008 10
= ×
= ×
Standard Form – Examples
One of the best estimates to a number called the Avogadro’s Number is 602,214,141,070,409,084,099,072. If only the first 4 digits of this number were significant, how would you express this number in standard form?Solution
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6022141410704090840990726022000000000000000000006.022 10
≈
= ×
http://www.americanscientist.org/issues/pub/an-exact-value-for-avogadros-number
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Scalar and Vector Quantities
A scalar quantity has magnitude only and is completely described by a certain number with appropriate units.
E.g. The distance is 7 m.
Other examples of scalar quantities include mass, time and temperature.
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Scalar and Vector Quantities
A vector quantity has both a magnitude and a direction and can be represented by a straight line in a particular direction.
E.g. The displacement is 5 m in the direction 045°.
Other examples of vector quantities include velocity, force and momentum.
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Scalar and Vector Quantities
Why is it useful to understand which quantity is a vector and which quantity is a scalar?
Consider the following formula where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time for which the vehicle accelerated:
v = u + at
Solve for a when v = 10 m/s, u = 0 m/s and t = 2 s.Solve for a when u = 10 m/s, v = 0 m/s and t = 2 s.What do you observe about the answers?
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Scalar and Vector Quantities
The formula for a vector quantity is designed with the allowance for positive and negative values and difference in meaning for each.Acceleration is a vector quantity.
A negative acceleration is actually a deceleration.
Negative values indicate “going in or doing the opposite”.Can a scalar quantity have a negative value?
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Scalar and Vector Quantities
Temperature is a scalar quantity.While temperatures may have negative values, they do not represent a change in direction.A temperature reading at any point in time is a static figure.
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Precision and Accuracy
The term precision refers to how consistently an instrument measures something.Accuracy, on the other hand, refers to how close the measured value is to the actual value.Thus, an instrument can be precise, but inaccurate.
E.g.A clock that is consistently one minute late at any point in time.
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Notes on Accuracy
How accurate the reading is, is dependent on the type of instrument being used. This is referred to the degree of accuracy.It is important to keep in mind the sensitivity and stability of the instrument when measuring, especially in the case of thermometers. These can affect accuracy as well.
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The Ruler
Look at the ruler shown.What would you say is the degree of accuracy of this instrument?
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The Modern Vernier Callipers
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Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/202.pdf
Can you name the parts of this instrument?
The Modern Vernier Callipers
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Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/202.pdf
Inside jaws
Outside jaws
Screw clamp
Vernier scale Main scale
Depth probe
The Modern Vernier Callipers
Invented by Pierre Vernier.The word “vernier” is now used to refer to certain movable parts of measuring instruments.Measures to an accuracy of 0.01 cm or 0.1 mm
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The Micrometer Screw Gauge
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Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/50.pdf
Do you think you can name the parts of this instrument?
The Micrometer Screw Gauge
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Rotating scale
Thimble
Ratchet
Sleeve (with main scale)
Frame
Anvil Spindle
Lock
Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/50.pdf
The Micrometer Screw Gauge
The first micrometric screw was invented by William Gascoigne and the modern day MSG is a result of a series of adaptations by other inventors.Measures to an accuracy of 0.001 cm or 0.01 mm
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Comparing Accuracies
Note:While the word “accuracy” has been used, it should be noted that no measurement can be said to be 100% accurate and there would always be a certain level of uncertainty.
Device AccuracyRuler 1 mmVernier Calipers 0.1 mmMicrometer Screw Gauge 0.01 mm
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Acknowledgement
Created by: Sutharsan John IslesMathematica fonts by Wolfram Research, Inc.References
http://www.wikipedia.orghttp://www.bipm.org/en/home/Giancoli, D.C. (2005). Physics: Principles with applications. Upper Saddle River, NJ: Pearson Education, Inc.Duncan, T. (2000). Advanced physics. London, UK: Hodder Murray.Chang, R. (1994). Chemistry. Hightstown, NJ: McGraw‐Hill, Inc.Hughes, E. (1888). Hughes electrical and electronic technology (10th ed.). Harlow, England: Pearson Education LimitedPoh, L.Y. (2007). Effective guide to ‘O’ Level Physics (2nd ed.). Singapore: Pearson Education South Asia Pte Ltd.Billstein, R., Libeskind, S. & Lott, J.W. (2001). A problem solving approach to mathematics for elementary school teachers. (7th ed.). Reading, MA: Addison Wesley Longman
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