Physics -I
Piri Reis University 2010-2011
Purpose of Course
Introductory Physics
o
o
o
o
o
Physics, Engineering, Materials Science are all closely connected.
Physical principles underlie many disciplines including engineering.
Good understanding of the physics can guide best technological practice.
Engineering is the application of physics to real situations.
Composite materials (new types of materials) rely in some cases on physics.
Of course there is much more to engineering than physics, but many
aspects of engineering benefit from a good understanding of principles.
Purpose of Course
At the end of the course students should have a basic knowledge of:
Mechanics; Fluid dynamics; Waves
There is a heavy emphasis on Mechanics, which will include
o Statics – balance of forces and torques
o Dynamics – mechanics of motion
o Energy, momentum, angular momentum
o Mass, moment of inertia,
o Newton’s Laws
Structure of Course
There are 14 weeks, each with 3 hours of theory and 2 hours
dedicated to laboratory exercises and problem solving
Students should:
o Attend the lectures and practical classes.
o Solve the set problems.
o Hand in homework when requested.
Lectures are more useful if you read ahead
o Lecture content by week is outlined [approximate]
o Read about subject before lecture [see reference list]
o Ask questions in class
Week
Structure of Course
1
Introduction
Basics: units, numbers, dimensional analysis, maths reminders
2
1-D Kinematics
Speed, velocity, acceleration, Reference frames
3
2-D Kinematics
Vectors, 2-D kinematics, projectile motion
4
Newton’s Laws
Newton’s Laws and Gravity.
5
Linear Dynamics
Mass, Weight, Force, Friction. Application of Newton’s Laws.
6
Linear Dynamics
Work, energy, power. Conservation Laws
7
Linear Dynamics
Momentum and motion of systems. Collisions.
8
Rotational Dynamics
Rotation and Angular Momentum
9
Equilibrium Mechanics
Static equilibrium of rigid bodies
10
Fluids
Density, Buoyancy force, Archimedes' Principle
11
Thermodynamics
Heat, temperature, the expansion of solids and gases, Gases, Heat transfer.
12
Materials
The physical phase changes. Vapours, cooling.
13
SHM & Waves
Simple harmonic motion and waves.
14
Travelling Waves
Sound, Light
Structure of Course
Examinations
o There will be two mid-term exams and
o One final examination.
o The examinations will be at the same level as the homework
problems
BASICS
Units
o There are two kinds
o Base units (there are seven of these in any system)
these cannot be defined in terms of anything else
o Derived units
 With a special name
 With a compound name
o Which are base and which derived is a choice - ‘common sense’
o In this course the base units mostly used are
o Time in seconds, s
o Mass in kilograms, kg
o Length in metres, m [but really this is derived from c]
o A numerical quantity without its unit is meaningless
BASICS
Some Derived Units
o Motion
o speed m/s
o acceleration m/s2
o Energy
o Energy is measured in Joules, J but [J] = [kg][m2]/[s2]
o Momentum has no separate name and is [kg][m]/[s]
o Angular speed is in [radians]/[s]
This is a special one as radians have no unit - why
o A numerical quantity without its unit is meaningless
Name
BASICS
m
length
kilogram
kg
mass
second
s
time
ampere
A
electric current
kelvin
K
thermodynamic temperature
candela
cd
luminous intensity
mol
amount of substance
mole
hertz
Hz
frequency
1/s
s-1
radian
rad
angle
m·m-1
dimensionless
steradian
sr
solid angle
m2·m-2
dimensionless
kg·m·s−2
newton
N
force, weight
kg·m/s2
pascal
Pa
pressure, stress
N/m2
m−1·kg·s−2
joule
J
energy, work, heat
N·m = C·V = W·s
m2·kg·s−2
watt
W
power, radiant flux
J/s = V·A
m2·kg·s−3
coulomb
C
electric charge
s·A
s·A
volt
V
voltage
W/A = J/C
m2·kg·s−3·A−1
farad
F
electric capacitance
C/V
m−2·kg−1·s4·A2
ohm
Ω
electric resistance
V/A
m2·kg·s−3·A−2
siemens
S
electrical conductance
1/Ω
m−2·kg−1·s3·A2
weber
Wb
magnetic flux
J/A
m2·kg·s−2·A−1
tesla
T
magnetic field strength
V·s/m2 = Wb/m2 = N/(A·m
)
kg·s−2·A−1
henry
H
inductance
V·s/A = Wb/A
m2·kg·s−2·A−2
Celsius
°C
temperature
K − 273.15
K − 273.15
cd·sr
lumen
lm
luminous flux
lux
lx
illuminance
lm/m2
m−2·cd·sr
becquerel
Bq
radioactivity
1/s
s−1
gray
Gy
absorbed dose
J/kg
m2·s−2
sievert
Sv
equivalent dose
J/kg
m2·s−2
−1
Quantity
metre
SI system of units – this is the usual choice
lx·m2
Unit symbol
Base units
Derived units
(with a special name)
Compound units derived from SI units
Expression in terms
Name
BASICS
Some of the
derived SI
units with no
special name
Symbol
Quantity
of SI base units
square metre
m2
area
m2
cubic metre
m3
volume
m3
metre per second
m/s
speed, velocity
m·s−1
cubic metre per second
m3/s
volumetric flow
m3·s−1
metre per second squared
m/s2
acceleration
m·s−2
metre per second cubed
m/s3
jerk, jolt
m·s−3
metre per quartic second
m/s4
snap, jounce
m·s−4
radian per second
rad/s
angular velocity
s−1
newton second
N·s
momentum, impulse
m·kg·s−1
newton metre second
N·m·s
angular momentum
m2·kg·s−1
newton metre
N·m = J/rad
torque, moment of force
m2·kg·s−2
newton per second
N/s
yank
m·kg·s−3
reciprocal metre
m−1
wavenumber
m−1
kilogram per square metre
kg/m2
area density
m−2·kg
kilogram per cubic metre
kg/m3
density, mass density
m−3·kg
cubic metre per kilogram
m3/kg
specific volume
m3·kg−1
mole per cubic metre
mol/m3
amount (-of-substance)
m−3·mol
cubic metre per mole
m3/mol
molar volume
m3·mol−1
joule second
J·s
action
m2·kg·s−1
joule per kelvin
J/K
heat capacity, entropy
m2·kg·s−2·K−1
joule per kelvin mole
J/(K·mol)
molar heat capacity
m2·kg·s−2·K−1·mol−1
joule per kilogram kelvin
J/(K·kg)
specific heat capacity
m2·s−2·K−1
joule per mole
J/mol
molar energy
m2·kg·s−2·mol−1
joule per kilogram
J/kg
specific energy
m2·s−2
joule per cubic metre
J/m3
energy density
m−1·kg·s−2
newton per metre
N/m = J/m2
surface tension
kg·s−2
watt per square metre
W/m2
heat flux density, irradiance
kg·s−3
watt per metre kelvin
W/(m·K)
thermal conductivity
m·kg·s−3·K−1
SI system is not the only unit system. There are several.
In nautical environment for example, the standard unit of
speed for sailing is knots.
1 international knot =
1 nautical mile per hour (by definition),
1.852 kilometres per hour (exactly),
0.514 metres per second,
1.151 miles per hour (approximately).
To convert 12mph to knots, divide by 1.151
12mph = 10.43 knots
BASICS
Writing Numbers
o There is more than one way to write an answer
o 0.000001 is equivalent to 1 x 10-6 which is also 1m
 In scientific notation write one figure before decimal point
 1.23 x 104 NOT 12.3 x 103
o Precision is a measure of repeatability, a number can be very precise but
the wrong answer. A precise measurement is one that always gives the
same answer.
o Accuracy is a measure of how close to the correct value the number is.
An accurate measurement is one which is close to the real value.
o The number of decimal places used in a number should reflect its
accuracy (usually). If not then the precision and the accuracy need to be
specified explicitly.
BASICS
Accuracy and Conversion
o Writing the answer to a computation as 1.76 implies that the
answer is accurate to 0.005 which would be quite accurate.
The answer is between 1.755 and 1.765
o Round answers to reflect the actual precision in a calculation.
o eg if you use g=9.81 m/s2 then answers are only accurate to
2 decimal places. So don’t list any extra useless decimal places.
o The overall accuracy of a calculation is limited by the least
accurate number in the calculation.
o It does no good to use a very accurate constant with an
inaccurate measurement. Round off numbers
eg don’t use p = 3.141592654 if you are using g=9.81
o Approximations – use approximate numbers when appropriate
BASICS
Prefix
Symbo
l
Decim
al
yotta
Y
1E+24
zetta
Z
1E+21
exa
E
1E+18
peta
P
1E+15
tera
T
1E+12
giga
G
1E+09
mega
M
100000
0
kilo
k
1000
hecto
h
100
deca
da
10
Prefixes and Suffixes
o Base units are defined to be ‘sensible’ for humans.
One kilogram of meat can be eaten.
One metre can be stepped over
One second can be counted
o But these are not always a useful size in physics
o The units are frequently used with letters
to indicate a change in size
Normally we only use these
1
deci
d
0.1
centi
c
0.01
milli
m
0.001
micro
μ
0.0000
01
nano
n
1E-09
pico
p
1E-12
femto
f
1E-15
atto
a
1E-18
zepto
z
1E-21
yocto
y
1E-24
BASICS
Prefixes and Suffixes
o
o
o
o
o
1000 m = 1 km
1000 byte = 1 kbyte
1000,000,000 = 1 Gbyte
1/1000 m = 1 mm
1/1000,000 m = 1 mm
o note well: m = milli 10-3 M = mega 106
despite newspapers getting it wrong!
o There is one other commonly used prefix, which is not SI
o The Angstrom, Å, 10-10 m (about the size of an atom)
BASICS
Dimensional Analysis
o It is critical to efficient problem solving that
dimensional analysis is used
 After ‘every’ step in a calculation
 Certainly at the end of a calculation
 To help figure out what the correct formulae is !
o It is not possible to equate apples and oranges.
o It makes no sense to write down a length in [kg]
o A formula must be dimensionally consistent on the two sides
o ie Units must match – apples and oranges cannot be equated
o Dimensional analysis is the business of matching units (dimensions)
+
=
2
BASICS
Dimensional Analysis
For example, suppose we want to know the formulae for the volume
of a sphere. It must depend on radius, but in what way?
o Volume, V, has dimensions [m3]
o There are no other variables in the problem except radius.
o Radius, R, has the dimensions [m]
o Therefore V = k R3 where k is a constant we don’t know. [its 4p/3]
o This was a ‘simple’ example, but it works for more complex cases
o [in fact its been used to discover ‘unknown’ equations!]
+
=
+
BASICS
Notation
Notation is key to communicating.
its important to use the same variables as everyone else.
o Symbol choice helps clarify equations
o A famous formula is V = I R where
V is voltage, I current and R resistance.
o It would be confusing to write R = V I where
R is voltage, V the current and I the resistance
[ but it is not actually wrong]
o Learn the conventional (standard) notation and use it.
o m – mass; v – velocity; a – acceleration; t – time;
I – moment of inertia; w – angular velocity;
o note that vector quantities are underlined often [see later]
o Some quantities, such as moment of inertia, need tensors, in this
course we will use simple scalars to describe them.
Angles and Angular Quantities
o Usually use Greek letters for angles
o a b c ….
Vector & Scalar Notation
o Vectors may be written as v or v or v
 It is usual to use an underline in hand written versions
 And bold in printed – The book by Giancoli uses v which is unusual
o Scalar quantities are simply written as s
Review of some Mathematics
Linear Algebra
Manipulation of linear equations
If
Then
A+B=C
B=C–A
If
Then
AB = C
B = C/A
If
Then
A(B+C) = D
AB + AC = D
AB = BC ;
A+B=B+A
Associative
Commutative
Distributive
Review of some Mathematics
Linear Algebra
Manipulation of linear equations
If
And
Ax + By = C
Dx - Ey = B
Then
x = DB/E + C – FB/E
y = EA/B + F – CA/B
Simultaneous equations
- DO not use these formulae!
Review of some Mathematics
Trigonometry
For a right angled triangle
C2 = B2 + A2
Pythagoras’
theorem
Sine(a) = A/C
Cosine(a) = B/C
Tangent(a) = A/B
Use sin(a) cos(a) & tan(α)
b
C
A
a
90º
B
Review of some Mathematics
(cosine,sine)
Sines &
Cosines
around a circle
In radians and
degrees
Review of some Mathematics
Trigonometry
There are many identities, these are particularly useful:
Review of some Mathematics
Calculus
o Differentiation –
•the rate of change
•the instantaneous slope
•the limit of Dy/Dx
As Dx –> 0
m=
m = positive
m = zero
m = negative
Review of some Mathematics
Calculus
o Differentiation –
o Some basic derivatives
o dyn/dx = yn-1
o dcos(a)/da = sin(a)
o dex/dx = ex
o tables of these exist
Review of some Mathematics
Calculus
o Integration –
•the opposite of differentiation
•the area under a curve
=
o Indefinite Integral
If
Then
= F(x)
= F(b) – F(a)
Review of some Mathematics
Calculus
o Integration –
o Some basic indefinite integrals