Download Definitions of Physical Quantities

Physical Quantities
Definition,
Types,
Symbols and
Units.
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Definitions of Physical Quantities
A physical quantity is a physical property that
can be quantified by measurement.
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Types of physical quantities
• Scalar quantities
are quantities that have magnitude only; they
are independent of direction.
(time, temperature, mass, density, energy,…)
• Vector quantities
are quantities that have magnitude and
direction.
(displacement, velocity, moment, force, ….)
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Symbols for physical quantities
Usually, the symbols for physical quantities
are chosen to be a single letter of the Latin or
Greek alphabet, and are often printed in italic
type (F, t, m, ……).
Often, the symbols are modified by subscripts
and superscripts, to specify what they refer to
- for instance Ek is usually used to denote
kinetic energy and cp heat capacity at constant
pressure.
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Physical Quantities
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Vector presentation
• When vectors are written, they are
represented by a single letter in bold type or
with an arrow above the letter, such as or .
Some examples of vectors are displacement
(e.g. 120 cm at 30°) and velocity (e.g. 12
meters per second north). The only basic SI
unit that is a vector is the meter. All others are
scalars. Derived quantities can be vector or
scalar, but every vector quantity must involve
meters in its definition and unit.
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Vector notation
• Vectors are distinguished from scalars by
writing them in special ways. A widely used
convention is to denote a vector quantity in
bold type, such as A, and that is the
convention that will be used. you may also
encounter the notation Ū or ḛ.
• The magnitude of a vector A is written as |A|.
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Representation of vectors in Cartesian coordinates
The vector can be represented by its
components (magnitude)in (x,y,z) directions.
The direction of the vector can be
represented by a unit vector u = i + j + k,
so:
v = vx i + vy j + vz k
where the units can be anything
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Representation of vectors in Cartesian coordinates
(cont.)
• F = Fx i + Fy j + k
Where:
Fx = F cos α
Fy = F cos β
Fz = F cos γ
α, β and γ are the angles the force
vector (F) making with x, y and z
axis respectively. And
F = √ Fx 2 + Fy 2 + Fz 2
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Vector Mathematical Operation
(adding, subtracting, multiplying ..)
• you have to consider both
the magnitude and the direction.
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Vectors Addition
Adding two vectors in Cartesian form v1 and v2
v3 = v1 + v2
v3 = (vx1 i + vy1 j + vz1 k) +(vx2 i + vy2 j + vz2 k)
v3 = (vx1 + vx2) i + (vy1 + vy2) j + (vz1 + vz2) k
That is, the components of a sum are the sums of
the components.
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Units of physical quantities
• Most physical quantities Q include a unit.
Neither the name of a physical quantity,
nor the symbol used to denote it, implies
a particular choice of unit.
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Systems of Units
• The Imperial units or the Imperial system is a
collection of English units, first defined in the Weights
and Measures Act of 1824, later refined (until 1959)
and reduced. The units were introduced in the United
Kingdom and its colonies, including Commonwealth
countries, but excluding the then already independent
United States.
• The United States customary system (also called
American system or, more rarely, "English units") is the
most commonly used system of measurement in the
United States. It is similar but not identical to the
British Imperial units.
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Systems of Units (cont.)
• The most widely used system of units and
measures around the world is the Systeme
International d'Unites (SI), the modern form of
the metric system. This originated in France,
where in 1790 the French Academy of Science
was commissioned to design a new system of
units (the International System of Unit).
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International system of units (SI)
• Basic units:
Physical quantity
SI unit
Unit symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Degree of temperature
kelvin
K
Amount of substance
mole
mole
Light (luminous) intensity
candela
cd
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International system of units (SI) (cont.)
• Associated with basic units are a variety of
supplementary derived units.
• Derived units:
Derived quantity
SI unit
Unit symbol
Area
square meter
m2
Volume
cubic meter
m3
Velocity
meter per second
m/s
Acceleration
meter per second square
m/s2
Density
Kilogram per cubic meter
Kg/m3
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International system of units (SI) (cont.)
• Derived units with special names and symbol:
Physical quantity
SI unit
Unit symbol
Force, Weight
newton
N = kg m/s2
Work, Energy, Quantity of Heat
joule
J=Nm
Power
watt
W = N m/s = J/s
Pressure, Stress
pascal
Pa = N/m2
Electric charge
coulomb
C=As
Electric potential
volt
V = W/A
Electric capacitance
frad
F = A s/V
Electric resistance
ohm
Ω = V/A
Frequency
hertz
Hz = s-1
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International system of units (SI) (cont.)
• In the International system of unit, a unit is
chosen for a particular purpose and larger and
smaller are obtained by applying a prefix to
this unit and multiplying or dividing by 10 or
power of 10.
• Larger units, obtained by multiplying by 1000,
etc., are called ‘multiples’, smaller units,
obtained by multiplying by 0.1, etc. are
termed ‘sub-multiplies.
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International system of units (SI) (cont.)
• Multiplying factors:
Factor
Prefix
Symbol
1 000 000 000
[109]
giga
G
1 000 000
[106]
mega
M
1 000
[103]
kilo
k
100
[102]
hecto
h
10
[10]
deca
da
0.1
[10-1]
deci
d
0.01
[10-2]
centi
c
0.001
[10-3]
mili
m
0.000 001
[10-6]
micro
μ
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International system of units (SI) (cont.)
• Units outside the SI that accepted for use with the SI:
Derived quantity
Unit symbol
Value
Minute
min
1 min = 60 s
Hour
h
1 h = 60 min = 60 s
Day
day
1 day = 24 h = 86400 s
o
1o = (π/180) rad
Liter
l, (L)
1 L = 1 dm3 = 1000 cm3 = 0.001 m3
Metric ton (tonne)
t
1 t = 1000 kg
Degree angle
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International system of units (SI) (cont.)
• Other units outside the SI that are currently accepted for use
with the SI:
Derived quantity
Unit symbol
Value
Nautical mile
Nautical mile
1 nautical mile = 1852 m
Knot
Knot
1 knot = 1.852 km/h
Hectare
ha
1 ha = 1 hm2 = 104 m2
Bar
bar
1 bar = 0.1 MPa = 100 kPa = 105 Pa
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SI unit rules and style conventions
• Unit symbols are placed after the numerical value, leaving a
space between the value and symbol. e.g. 5 V not 5V.
• Only one prefix can be applied to a unit at a time. e.g. 1000
kilonewton must not express 1kilokilonewton but as 1
meganewton, (1000 kN ≠ 1 kkN = 1 MN).
• The correct use of upper and lower case letters (capital and
small letters) is important. i.e. m- meter; but M- mega; k- kilo;
K- kelvin.
• Symbols must not made plural by adding ‘s’ since ‘s’ is
symbol of second. e.g. 10 kg not 10 kgs.
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SI unit rules and style conventions (cont.)
• When a prefix is attached to a unit there should
be no space between the prefix and the unit; i.e.
mm- millimeter, kW- kilowatt… etc.
• When a complex unit is formed by multiplying
two units together, however, the symbol should
be separated by a space; e.g. N m- newton meter
(the unit of torque).
• Abbreviations such as sec, cc, or mps are avoided
and only standard unit symbols, prefix symbols,
unit names, and prefix names are used (s, cm3,
m/s).
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SI unit rules and style conventions (cont.)
• Unit symbols are generally written in lower
case letters, except when the name of the unit
is derived from a proper name. (Note that the
name of a unit which is derived from a proper
name is written out in full, such as ampere or
hertz, the name is not capitalized. The only
exception to this is Celsius. Note that "degree
Celsius" conforms to this rule because the "d"
is lowercase.
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Dimensional analysis
• Technique used in the physical and engineering to
reduce physical properties such as acceleration,
velocity, energy and others to their fundamental
dimensions of length(L), mass (M), and time (T).
This technique facilitate the study of
interrelationships of systems (or models of
systems) and their properties. Acceleration, for
example, is expressed as length per unit of time
squared (LT-2); whether the units of length in the
English or the metric system is immaterial.
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Physical quantities: Time
Time (t)
The fundamental unit of time suggested by SI system is
the second, since 1967 defined as the second of
international Atomic Time, based on the radiation
emitted by a Caesium-133 atom in the ground state.
Based on the second as base unit, the following units
are in use:
• minute (1 min) = 60 s
• hour (1h) = 60 min = 3.6 ks
• Julian day (1 day) = 24 h = 86.4 ks
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Physical quantities: Displacement, Area & Volume
Displacement and distance (L)
Displacement is measured as meters (m), or sometimes more
conveniently as kilometers, millimeters or centimeters. Distance
(scalar) is the magnitude of the displacement (vector).
Area (A)
Any flat, curved, or irregular expanse of a surface. It is measured
in meter square (m2).
Volume (V)
The volume of any solid, liquid, gas, plasma, or vacuum is how
much three-dimensional space it occupies, often quantified
numerically. It is measured in cubic meter (m3) or liter (l).
• 1 l = 1000 cm3 = 0.001 m3
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Physical quantities: Angle
Angle (θ)
• Angle is the figure formed by two rays sharing
a common endpoint, called the vertex of the
angle. The magnitude of the angle is the
"amount of rotation" that separates the two
rays, and can be measured by considering the
length of circular arc swept out when one ray
is rotated about the vertex to coincide with
the other.
• The degree and the radian are by far the most
common. The turn (or full circle, revolution,
rotation, or cycle) is one full circle.
• 1 turn = 360° = 2π (rad)
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Physical quantities: Linear & Angular Velocities
Velocity (v) and speed
Velocity is measured as meters per second (m/s), or sometimes more
conveniently as kilometers per hour (km/h).
Useful conversions are m/s = 3.6 km/h, and 0.278 m/s = 1 km/h). The
speed is the magnitude of the velocity vector.
Angular velocity (ω)
Angular velocity is a measure of the angular displacement per unit
time.
The angular velocity can be measured in revolution per minute (rpm).
ω = 2 π N/60
• Where:
N = revolution per minute (rpm)
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Physical quantities: Angular & Linear Velocity
Angular and linear velocity
The linear velocity of a particle is related to
angular velocity by :
v=ωr
v = (2 π N/60) r
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Physical quantities: Linear Acceleration
Acceleration (a)
Acceleration or deceleration is the rate of change of speed. It is measured as meters
per second per second or m/s2. If the speed increases from u m/s (initial velocity) to v
m/s (final velocity) during t seconds (time), then the average acceleration a m/s2 is
given by
a = (v-u)/t m/s2
Acceleration due to gravity (g)
In physics, gravitational acceleration is the acceleration on an object caused by
gravity, a conventional standard value of exactly 9.80665 m/s2 (g = 9.81 m/s2)
* Car acceleration and deceleration indication
Another way to indicate the car acceleration is the time taken by the car form 0
velocity to reach 100 km/h, or (0- 60 mph).
* A convenient way to measure braking action is to equate (compare) vehicle
deceleration to the gravity acceleration constant [g]. Example: declaration = 0.3 g.
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Physical quantities: Angular acceleration
Angular acceleration (α)
Angular acceleration is the rate of change of angular
velocity over time. In SI units, it is measured in radians
per second squared (rad/s2).
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Physical quantities: Mass & Weight
Mass (m) and weight (w)
A 'body' contains a certain amount of stuff or
matter called mass (m). The unit of mass is the
kilogram (kg).The pull of earth -the force of
gravity- acting on this mass is the weight (w)of
the body. The unit of weight is the newton (N).
w = mg
Where: g is the acceleration of falling body due
to gravity in meter per second square (m/s2).
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Physical quantities: Mass moment of inertia
Mass moment of inertia (I):
In classical mechanics, moment of inertia, also called
mass moment of inertia, rotational inertia, or the
angular mass, (SI units kg m2), is a measures of an
object’s resistance to changes to its rotation.
I = ∫ r2 dm
Where:
m is the mass,
r is the perpendicular distance to the axis of rotation.
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Physical quantities: Density
Density (ρ)
Density is the mass of a substance per unit volume (kg/m3).
The density of water is, for practical purposes, 1000 kg/m3
or 1 kg/l. (The litre (l) is 10-3 m3.)
• The density of solids and liquids are usually stated in g/cm3,
while gases are usually in kg/m3.
Relative density or specific gravity
• relative density of the substance = (mass of a substance /
mass of an equal volume of water)
• This ratio is called the relative density of the substance, and
represents how many times it is heavier or lighter than the
same volume of water. Note that relative density has no
units. Example of substances relative densities (oxygen =
0.0014, steel=8.0, lead =11.4, mercury = 13.6).
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Physical quantities: Force
Force (F)
The force is a measurable influence tending to cause
movement of body (its intensity). The unit of force is newton,
1 newton is the value of a force which if exerted upon a mass
(m) of one kilogram gives it an acceleration (a) of 1 m/s2.
F = m a,
1 N = (1 kg) (1 m/s2) = 1 kg m/s2
There are different types of forces; external force, internal
force, friction force, inertia force and reaction force.
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Physical quantities: Pressure
Pressure (p)
Pressure is the force per unit area; the unit is N/m2 or the Pascal (Pa). Larger practical
units are kN/m2 (kPa) and MN/m2 (MPa). Note that
1 MN/m2 (MPa) = 1N/mm2
A pressure of 7 MPa means that each mm2 subject to the pressure has a force of 7 N
acting on it, and the total force on the surface will be the product of the pressure and
the area.
Atmospheric pressure
Air has weight. The atmosphere above the earth produces a pressure at sea level of
approximately 1 bar, where 1 bar = 105 N/m2 or 105 Pa. Standard atmospheric
pressure (atm) is 1.01325 bar.
1 atm = 760 mm Hg (Torr) (mercury column) = 10333 mm H2O (water column)
Gauge and absolute pressure
The ordinary pressure gauge gives readings measured above atmospheric pressure. To
obtain the absolute pressure, that is the pressure measured above a perfect vacuum,
atmospheric pressure must be added to the gauge reading:
absolute pressure = gauge pressure + atmospheric pressure
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Physical quantities: Torque
Torque (T)
When a force (F) acts on a body
pivoted on a fixed axis, the product
of the force perpendicular to the
radius, and the radius at (r) which it
acts, is termed the turning moment
of the force or torque. Torque (T) is
measured in newton meters (N m).
T=Fr
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Physical quantities: Work & Power
Work (W)
Work is done when a force overcomes resistance and causes movement. Work is
measured by the product of the force (f) and the distance moved (s) in the direction of
the force, the unit being the joule (J):
W=Fs
If the force causes no movement, then no work is done, or if the force in the apposite
direction of the movement, then the work is negative.
Power (P)
Power is the rate of doing work. The unit, the watt, is a rate of working of 1 joule per
second (1 J/s)
power = work done per second = [W / t] {N m /s}, {J/s}, (W)
The relation between power and torque:
If a tangential force is applied to a shaft, then the work done per one revolution is:
W = F s = F (2 π r) = (2 π) T
Since the power is
P = W/t = (2 π / t) T, then: P = ωT, P = (2 π N/60) T
Using these formulae, the power can be calculated from the torque and speed of a
shaft.
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Physical quantities: Temperature
Temperature (t)
Temperature is a physical property of matter that
quantitatively expresses the common notions of hot
and cold. Quantitatively, temperature is measured
with thermometers.
The International System of Units (SI) defines a scale
and unit for the thermodynamic temperature by
using the kelvin temperature. The unit symbol of the
kelvin is K. While the Kelvin scale is the principal
temperature scale for use in science and engineering,
much of the world uses the Celsius scale (°C) for
most temperature measurements.
1 K = 1°C = 1.8 °F = 1.8 °R
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Physical quantities: Energy
Energy (E)
In all such energy transformation processes, the total energy
remains the same. Energy may not be created nor destroyed.
• Any form of energy can be transformed into another form.
When energy is in a form other than heat, it may be
transformed with good or even perfect efficiency, to any other
type of energy.
• Measurement of energy in the SI unit is the joule. In addition
to the joule, other units of energy include the kilowatt hour
(kW h) and the British thermal unit (Btu). These are both
larger units of energy. One kW h is equivalent to exactly 3.6
million joules, and one Btu is equivalent to about 1055 joules.
• There are different types of energies; kinetic, potential,
mechanical, thermal, chemical, electric and nuclear energy.
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