Purpose of Course

Introductory Physics

o Physics, Engineering, Materials Science are all closely connected.o Physical principles underlie many disciplines including engineering.o Good understanding of the physics can guide best technological practice.o Engineering is the application of physics to real situations.o Composite materials (new types of materials) rely in some cases on physics.

Of course there is much more to engineering than physics, but manyaspects of engineering benefit from a good understanding of principles.

Physics -IPiri Reis University 2010-2011

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 includeo Statics – balance of forces and torqueso Dynamics – mechanics of motiono Energy, momentum, angular momentumo 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 aheado Lecture content by week is outlined [approximate]o Read about subject before lecture [see reference list]o Ask questions in class

Structure of Course

Week

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 kindso Base units (there are seven of these in any system) these cannot be defined in terms of anything elseo 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 areo Time in seconds, so Mass in kilograms, kgo 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 Motiono speed m/so acceleration m/s2

o Energyo 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

BASICS

SI system of units – this is the usual choice

hertz Hz frequency 1/s s-1

radian rad angle m·m-1 dimensionless

steradian sr solid angle m2·m-2 dimensionless

newton N force, weight kg·m/s2 kg·m·s−2

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 strengthV·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

lumen lm luminous flux lx·m2 cd·sr

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

katal kat catalytic activity mol/s s−1·mol

Name Unit symbol Quantity

metre m length

kilogram kg mass

second s time

ampere A electric current

kelvin K thermodynamic temperature

candela cd luminous intensity

mole mol amount of substance

Base units

Derived units (with a special name)

Compound units derived from SI units

Name Symbol QuantityExpression in terms

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

square metre per second m2/s kinematic viscosity m2·s−1

pascal second Pa·s = N·s/m2 dynamic viscosity m−1·kg·s−1

coulomb per square metre C/m2 electric displacement field m−2·s·A

coulomb per cubic metre C/m3 electric charge density m−3·s·A

ampere per square metre A/m2 electric current density A·m−2

siemens per metre S/m conductivity m−3·kg−1·s3·A2

siemens square metre per mole S·m2/mol molar conductivity kg-1·s3·mol−1·A2

farad per metre F/m permittivity m−3·kg−1·s4·A2

henry per metre H/m permeability m·kg·s−2·A−2

volt per metre V/m electric field strength m·kg·s−3·A−1

ampere per metre A/m magnetic field strength A·m−1

candela per square metre cd/m2 luminance cd·m−2

coulomb per kilogram C/kg exposure (X and gamma rays) kg−1·s·A

gray per second Gy/s absorbed dose rate m2·s−3

ohm metre Ω·m resistivity m3·kg·s−3·A−2

Some of thederived SIunits with no special name

BASICS

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 answero 0.000001 is equivalent to 1 x 10-6 which is also 1

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 1.765o 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 = 3.141592654 if you are using g=9.81

o Approximations – use approximate numbers when appropriate

BASICS

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 overOne second can be counted

o But these are not always a useful size in physicso The units are frequently used with letters to indicate a change in size

PrefixSymbo

lDecimal

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 M100000

0

kilo k 1000

hecto h 100

deca da 10

    1

deci d 0.1

centi c 0.01

milli m 0.001

micro μ0.0000

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

Normally we only use these

BASICS

Prefixes and Suffixes

o 1000 m = 1 kmo 1000 byte = 1 kbyteo 1000,000,000 = 1 Gbyteo 1/1000 m = 1 mmo 1/1000,000 m = 1 m

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 SIo 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 sideso 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 4/3]o This was a ‘simple’ example, but it works for more complex caseso [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 equationso 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; – 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.

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

Vector & Scalar Notation

Angles and Angular Quantities

o Usually use Greek letters for angleso ….

Review of some Mathematics

Linear Algebra

Manipulation of linear equations

If A + B = CThen B = C – A

If AB = CThen B = C/A

If A(B+C) = DThen AB + AC = D

AB = BC ; A + B = B + A

AssociativeCommutativeDistributive

Review of some Mathematics

Linear Algebra

Manipulation of linear equations

If Ax + By = CAnd Dx - Ey = B

Then x = DB/E + C – FB/Ey = 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

Sine() = A/CCosine() = B/CTangent() = A/B

Use sin() cos() & tan(α)

A

B

C

90º

Pythagoras’ theorem

Review of some Mathematics

Sines &Cosinesaround a circle

In radians anddegrees

(cosine,sine)

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 y/x

As x –> 0 m =m = positivem = zerom = negative

Review of some Mathematics

Calculus

o Differentiation –

o Some basic derivatives

o dyn/dx = yn-1

o dcos()/d = sin()

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

= F(x)

Then = F(b) – F(a)

If

Review of some Mathematics

Calculus

o Integration –

o Some basic indefinite integrals