Introductory Physics - Physical Quantities, Units and Measurement

Introductory Physics
Physical Quantities, Units
and 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 Symbols
The Real Number System
Fractions and Decimals
Significant Figures
Angles and Bearings
Indices
3© Sutharsan John Isles

4
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

5
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

6
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.)

7
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

8
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

9
Terminology
The following are subsets of physical
properties:
Mechanical properties
Electrical properties
Thermal properties
Optical properties

10
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

11
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

12
Why SI Units?
Two reasons:
Facilitates international trade and
communications
Facilitates exchange of scientific findings and
information

13
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.

14
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/

15
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

16
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

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
17
3 3
3 1000 1
3000
km
m
m
= × ×
= × ×
=
kilo metre

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
∴
18
1 1000km m=
1
1
1000
m km=
1
70 70
1000
0.07
m km
km
= ×
=

How do you convert from millimetres to
metres?
E.g. Convert 45 mm to metres
Solution
19
1
45 45 metre
1000
1
45 1
1000
45
1000
0.045
mm
m
m
m
= × ×
= × ×
=
=

How do you convert from millimetres to
centimetres?
E.g. Convert 13 mm to centimetres
Solution
20
1
13 13 metre
1000
1 1
13 1
100 10
1
13
10
1.3
mm
m
cm
cm
= × ×
= × × ×
= ×
=

How do you convert from centimetres to
millimetres?
E.g. Convert 11.5 cm to millimetres
Solution
21
1
11.5 11.5 metre
100
10
11.5 1
1000
1
115 1
1000
115
cm
m
m
mm
= × ×
= × ×
= × ×
=

22
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.

23
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.

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

submultiples of derived units
How do you convert from squared centimetres
to squared metres?
E.g. Convert 8 cm2 to squared metres
Solution
25
2
2
2
8 1 8
1 1
1 1 8 1
100 100
1
8 1
10000
0.0008
cm cm cm
m m
m
m
= ×
= × × × × ×
= × ×
=

26
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.

Standard Form – Examples
How do you express 0.0008 in standard form?
Solution
4
4
8
0.0008
10000
8
10
8 10−
=
=
= ×

How do you express 80000 in standard form?
Solution
4
80000 8 10000
8 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
23
602214141070409084099072
602200000000000000000000
6.022 10
≈
= ×
http://www.americanscientist.org/issues/pub/an-exact-value-for-avogadros-number

30
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.

31
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.

32
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?

33
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?

34
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?

Inside jaws
Outside jaws
Screw clamp
Vernier scale
Main scale
Depth probe

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 be 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

45
Acknowledgement
Created by: Sutharsan John Isles
Mathematica fonts by Wolfram Research, Inc.
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

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