1. Physics

- Part of science that describes (not "explains") the behavior of matter and its interactions at the most fundamental level. Physics is based on experimental observations.

Geology, chemistry, engineering, astronomy, biology, psychology and medicine all 'require' an understanding of the principles of physics.

classical physics

a) classical mechanics: the study of motion

b) thermodynamics: the study of energy transfer

c) electromagnetism: electricity, magnetism, optics

modern physics

a) relativity: a theory of the behavior of particles at high speeds

b) quantum mechanics: a theory of the submicroscopic world

Structure of physics

• Physics describes (!), in an approximate way, the natural phenomena taking place in the universe.

• An abstract model, using imaginable elements and mathematical relations is created to analyze the phenomena.

Example (mixing of liquids)

pepsi water

pepsi pepsi pepsi

water pepsi water

0 1

0 0 0

1 0 1

pepsi 0water 1

Because of their simplicity and accuracy, mathematical models are used to represent nature. The most common mathematical concepts used for this purpose are:

numbersvectorstensorsfunctionsoperators

55 km/h

120 kJ

[5,4,3] N

xx xy xz

yx yy yz

zx zy zz y(t) = A sin (t)

xp̂x

i

3. Measurement

The procedure, which assigns a mathematical quantity to a physical quantity is called a measurement. A measurement is based on a comparison of the given element of the quantity with a chosen element called a standard.

units

The most commonly used SI (metric) system is based on m, kg, s, mole. In some cases it is convenient to introduce other units by adding prefixes.

femto- 10-15

pico- 10-12

nano- 10-9

micro- 10-6

mili- 10-3

kilo- 103

mega- 106

giga- 109centi- 10-2

Conversion of units.

In principle the choice of units for a certain quantity is arbitrary. Different numbers can be assigned to a single quantity! Therefore, it is always necessary to indicate the units. The numbers are related by conversion factors.

4. Concepts, axioms, theorems...

a) A concept is an idea that is used to analyze natural phenomena. It can be either a primitive concept (undefined) or a concept defined in terms of other concepts.

b) An axiom is a relationship between concepts assumed to be valid (postulates, laws).

c) A theorem is a relationship between concepts, which can be derived from other relationships (laws, principles).

d) A model is a convenient representation of a system (a theory).

5. Scalars

The character of a physical quantity is determined by the rules of combination of that quantity.

A scalar quantity obeys the same rules of combination as numbers. Each scalar quantity can be represented by a number.

3 + 2 = 5

Time

- a scalar quantity associated with changes in the universe.

(The SI unit is one second defined as a time interval in which a specific spectral line of cesium-133 (Cs133) performs a defined number of oscillations.)

Example 1. Time-interval

(do not confuse with time‑instant)

A repetitive process is used as a time counter (a clock). The number of repetitions is the value assigned to the time‑interval.

Distance

- a scalar quantity associated with the relative arrangements of two points.

(The SI unit one meter defined as the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.)

s 0

Mass

- a scalar quantity assigned to the principal inertial property of a body, i.e. its 'resistance' to a change in motion.

(The SI unit is one kilogram defined as the mass of the platinum-iridium cylinder kept at the International Bureau of Weights and Measures.)

Length

- a scalar quantity associated with the size of objects and figures.

i

icurve 0s

s ds l limi

example: length (circumference) of a circle

x

y

22 xRy

R

R

22 dydx2l

R

R

2

dxdx

dy12

R

R

2

22dx

xR2

x212

R

R22

dxxR

R2

R

RR

xarcsinR2

dxdy

dl

22

R2 R2

example: area of a circle

x

y22 xRy

R

R

xR

xR

dxdy22

22

Adx

dy

R

R

xR

xRdxy

22

22

R

R

22 dxxR2

R

R

222

R

xarcsinRxRx

2

12

R

RarcsinRRRR

R

RarcsinRRRR 222222 2R

example: area of a circle

x

y

R

0

2

0

drrdA

rddr

R

0

2

0drr

R

0

rdr2

R

0

2

2

r2 2R

Density The (differential) mass dm of a

(differential) volume dV of a substance is proportional to the volume.

dm dV

The proportionality coefficient is called the density of the substance.

example: (non-uniform density)

rdr

= 0(1 – r2)

r

drrr4drr4r1dVdm 420

220

5

R

3

R4

5

r

3

r4

53

0

R

0

53

0

mass of a differential shell

total mass

R

0

420

object

drrr4dmM

example: (uniform density)

dVdm 0mass of a differential fragment

total mass

VdVdVM 0object

0object

0