Introductory Physics - Physical Quantities, Units and Measurement

Introductory Physics

Physical Quantities, Units and Measurement

(Updated: 20141027)

Presenter

Presentation Notes

Note to author: All numeric figures are to be in Times New Roman (TNR) Regular. All variables and units of measurement are to be in TNR Italics with the exception of capital Greek letters which will remain in TNR Regular. A space is to be inserted between a numeric figure or variable and units of measurement.

Statement of Copyright and Fair Use

The author of this PowerPoint believes that the following presentation contains copyrighted materials used under the Multimedia Guidelines and Fair Use exemptions of U.S. Copyright law applicable to educators and students. Further use is prohibited. If owners of images used in this presentation feel otherwise, please contact the author and he will take them down if other amicable resolutions cannot be agreed upon.

© 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 Symbols The Real Number System Fractions and Decimals Significant Figures Angles and Bearings Indices

3 © Sutharsan John Isles

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Terminology

A feature a noticeable part of something http://simple.wiktionary.org/wiki/feature

What do you notice about the two lines below?

© Sutharsan John Isles

http://simple.wiktionary.org/wiki/feature�

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Terminology

A characteristic a typical feature of something http://simple.wiktionary.org/wiki/characteristic

Compare the vehicles below. What is characteristic of both vehicles?

A limousine An ordinary car


http://simple.wiktionary.org/wiki/characteristic�

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Terminology

A property something that gives an object its characteristics

Observe a piece of rubber band. What do you notice when it is pulled and released? What could you say is characteristic of objects made with the same type of material? Ultimately, what can you say is a property of rubber?

Note: Rubber is not the only elastic material. (Spandex used in stretch jeans, is another example.)


Presenter

Presentation Notes

Note to teacher: Noticeable (feature) – Can be stretched without breaking and returns to its original shape. Characteristic – Anything made of rubber seems to behave in the same way. Property – Elasticity.

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Terminology

Consider the following:

You can feel the effects of a force (throwing you off) as you stand at the edge on a merry-go-round while it is spinning.

You can see that one line is longer than the other.

Physical something that is real in the sense that it can be

seen, felt, etc. (i.e. not imaginary) and can thus be described in terms of what you observe or perceive

http://en.wikipedia.org/wiki/Physical_property


Presenter

Presentation Notes

Note to teacher: Tell students to think in terms of their five senses. (Thus the word feel, as used here, does not refer to things such as love or anger although these can be perceived or results of which may be observed.)

http://en.wikipedia.org/wiki/Physical_property�

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Terminology

A physical property a measurable (or perceived) property of something

observable without having to change the composition or identity of that thing

Examples of physical properties include the following: Length Mass Colour Smell

Temperature Solubility Resistivity Conductivity


Presenter

Presentation Notes

Note to teacher: In philosophy, identity (also called sameness) is whatever makes an entity definable and recognisable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type. (http://en.wikipedia.org/wiki/Identity_%28philosophy%29)

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Terminology

The following are subsets of physical properties:

Mechanical properties Electrical properties Thermal properties Optical properties


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Terminology

A quantity something that can be quantified (given a

number to)

A physical quantity a physical property that can be expressed in

numbers E.g. Length being quantified:

13 cm


Presenter

Presentation Notes

Note to teacher: While colour is a physical property, it cannot be a physical quantity even though it can be expressed in numbers in terms of intensity, hue and saturation. Perception of colour is to a certain extent subjective and thus cannot truly be quantified. References: http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT14/lecture12.html http://www.artinarch.com/core_theory.html

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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


Presenter

Presentation Notes

It should be clear why the French abbreviation (SI) was chosen instead of (IS). SI units are based on the MKS metric system. Thus SI unit is known also as the International Standard Metric System.

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Why SI Units?

Two reasons: Facilitates international trade and

communications Facilitates exchange of scientific findings and

information


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Physical Quantities

These may be divided into base quantities and 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 cd http://www.bipm.org/en/si/si_brochure/chapter2/2-1/


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Presentation Notes

Note to teacher: Draw attention to the fact that only kg is written with a prefix. Explain that the reason is historical. This is also a great opportunity to explain the meaning of the word prefix.

http://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 quadrillion tera T 1012 1 000 000 000 000 trillion giga G 109 1 000 000 000 billion

mega M 106 1 000 000 million kilo k 103 1 000 thousand deci d 10-1 0.1 tenth centi c 10-2 0.01 hundredth milli m 10-3 0.001 thousandth

micro μ 10-6 0.000 001 millionth nano n 10-9 0.000 000 001 billionth http://en.wikipedia.org/wiki/Long_and_short_scales


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Presentation Notes

Note to teacher: Ask the students to guess the reason for why micro is written using the Greek letter µ. This is another great opportunity to teach the spelling (mu) and pronunciation (mew) of the symbol in English. Ask the students to observe the symbols. What do they notice about the symbols which express positive powers of 10 (with the exception of kilo)? Ask the students to think of reasons for why kilo is the only positive power written in lowercase letter. Draw the students’ attention to the ease of representing numbers with many zeros using the index notation.

http://en.wikipedia.org/wiki/Long_and_short_scales�

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Multiples & Submultiples of 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


http://en.wikipedia.org/wiki/Metre�

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


Presenter

Presentation Notes

Note to teacher: The methods shown in these slides are not necessarily the only ways of arriving at the answer. However, the methods shown here appeal to the use of logical thinking based on linguistic and mathematical understanding rather than rote memorisation.

Conversion between multiples & submultiples of a base unit

How do you convert from metres to kilometres? E.g. Convert 70 m to kilometres

Solution Begin with

Recognise that ∴

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1 1000 km m=11

1000m km=

170 70 1000

0.07

m km

km

= ×

=



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

= × ×

= × ×

=

=© Sutharsan John Isles


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

= × ×

= × × ×

= ×


Presenter

Presentation Notes

Note to teacher: Students may alternatively just divide by 10, based on their experience with using a graded ruler.


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

= × ×

= × ×

= × ×


Presenter

Presentation Notes

Note to teacher: Alternatively, students can just multiply 11.5 by 10, based on the recognition that 1 cm = 10 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.


http://www.bipm.org/en/si/si_brochure/chapter1/1-4.html�

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SI Derived Quantities & Units

Name Symbol Derivation Unit area 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 m Note highlighted: Essence of derivation in each case is different. © Sutharsan John Isles

Presenter

Presentation Notes

Highlighted are the parts that show that while the derivation may look the same, the essence of each derivation is different. Note: There should be a space between two different units (for clarity) where applicable. For moment of force, the symbol M is reserved for the torque of a rotating electrical machine.

Trivia

Do you know the full names of scientists after whom the following units were named? Newton Pascal Joule Watt Coulomb Volt Ohm

24 © Sutharsan John Isles

Presenter

Presentation Notes

Note to teacher: The purpose of this activity is to give students a break as well as give them interesting pieces of information which may not necessarily be essential knowledge. The answers are: Isaac Newton Blaise Pascal James P. Joule James Watt Charles-Augustin de Coulomb Alessandro Volta Georg Simon Ohm

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

= ×

= × × × × ×

= × ×


Presenter

Presentation Notes

Note to teacher: While the method presented here may seem unnecessarily long, this is useful for understanding the mathematical reasoning. Once students are familiar with the conversion, they may omit some working. For instance, they may immediately re-write 1 cm as 0.01 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 R and n is an integer.

Depending on the requirement, A can be in any number of significant figures.


Standard Form – Examples

How do you express 0.0008 in standard form? Solution


4

4

80.000810000

8108 10−

=

=

= ×


How do you express 80000 in standard form? Solution


4

80000 8 100008 10

= ×

= ×


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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Presentation Notes

Note to teacher: Inform students that while expressing in standard form makes representation easier, it is not necessarily an accurate representation of the true value.

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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Presentation Notes

Pressure is also a scalar quantity.

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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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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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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? © Sutharsan John Isles

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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.


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.


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.


The Ruler

Look at the ruler shown. What would you say is the degree of

accuracy of this instrument?


The Modern Vernier Callipers


Image source: http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/202.pdf

Can you name the parts of this instrument?

Presenter

Presentation Notes

Note to Teacher: The word calipers can be spelt in two ways.

http://www.mitutoyo.co.jp/eng/useful/catalog/pdf/50.pdf�




Inside jaws

Outside jaws

Screw clamp

Vernier scale Main scale

Depth probe

Presenter

Presentation Notes

Note to Teacher: The word calipers can be spelt in two ways.



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


The Micrometer Screw Gauge



Do you think you can name the parts of this instrument?




Rotating scale

Thimble

Ratchet

Sleeve (with main scale)

Frame

Anvil Spindle

Lock




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


Comparing Accuracies

Note: While the word “accuracy” has been used, it should be noted that no measurement can be said to 100% accurate and there would always be a certain level of uncertainty.

Device Accuracy Ruler 1 mm Vernier Calipers 0.1 mm Micrometer Screw Gauge 0.01 mm


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Acknowledgement

Created by: Sutharsan John Isles References

http://www.wikipedia.org http://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 Limited Poh, 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


http://www.wikipedia.org/�

http://www.bipm.org/en/home/�