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Τ Τ Υ Υ Π Π Ο Ο Λ Λ Ο Ο Γ Γ Ι Ι Ο Ο Φ Φ Υ Υ Σ Σ Ι Ι Κ Κ Η Η Σ Σ Λ Λ Υ Υ Κ Κ Ε Ε Ι Ι Ο Ο Υ Υ
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ΤΥΠΟΛΟΓΙΟ ΦΥΣΙΚΗΣ

### Transcript of ΤΥΠΟΛΟΓΙΟ ΦΥΣΙΚΗΣ

• 2

2

• 3

3

(S.I.)

L meter m m Kilogram Kg t second sec i Amperes A

T Kelvin K mole mole I Candela cd radian rad steredian sr

deka da = 101 deci d = 10-1 hecto h = 102 centi c = 10-2 Kilo K = 103 milli m = 10-3 Mega M = 106 micro = 10-6 Giga G = 109 nano n = 10-9 Terra T = 1012 pico p = 10-12 Peta P = 1015 femto f = 10-15 Exa E = 1018 atto a = 10-18

: 12 cm = 12 10-2 m = 0,12 m 220 m = 22010-6 m 15 KW = 15103 W 200 nF = 20010-9 F m2 m3. :

cm = 10-2 m (cm)2 = (10-2 m)2 cm2 = 10-4 m2 mm = 10-3 m (mm)3 = (10-2 m)3 mm3 = 10-6 m3

: 1 L = 10-3 m3, 1 m3 = 103 L 1 L = 103 mL, 1 mL = 10-3 L

• 4

4

. x , . x(t) . x=x(t) .

. x y o - x y . x y , . (x(t), y(t)) t.

. x y z o x y z -. r(t )r

=(x(t),y(t),z(t)) - t.

x . 2 1r r r=

uur ur ur

r1 r2 - . x = x2-x1

S . .

u (Velocity)

. rut

=uurr

r . (

11)

x

y

z

A(xA,yA,zA

A

yA

xA

zA

x

y

O

A

xA

yA A(xA, yA)

(x) i + - O

• 5

5

xut

=uurr

2 12 1

x xut -t

= xut

= m/sec2

: t 0

rut

=uurr

r(t )uuur

:

Su ut

= =

: .

u = x = xo + u(t to) x = xo + ut x = ut ( xo=0)

xo ( to=0 sec)

( )

x-t -

... .

10

S (m)

t (sec) 0 2 4

20

U (m/sec)

t (sec)0

• 6

6

u

t 0

ut

=uurr

: ut

=uurr

2 12 1

u u -u= =t t -t

m/sec2

uuur

, :

- () ()

. a

r -

.

-

.... (uo 0)

x

t

x

t

U

t

16

0

8

4 7 9

t

5

0 -2

4 8

+x

Uo U

+x

Uo U

• 7

7

(>0) (0) (

• 8

8

(Force) -. Newton = Kgm/sec2

F=F2+F1

F=F2-F1

F = 2 21 2F F+ = 1

2

FF

F = 2 21 2 1 2F F 2F F + + = 1

2 1

FF F +

:

: () .

Hooke .

F=Kx, K : , x : .

Newton .

F

y

Fx = F

F y =

F

x

F1

F2

F

F1

F1

-

F1

F2

F

F1 F2

F

F1 F2 F

• 9

9

F = 0uuur r

. . . Newton

F =

m

uuurr F = m

uuur r

: pF =t

uuruuur( = )

x y : Fx=max Fy=may

: F = m

: .... ... Newton FAB , FBA. :

AB BAF =-Fr r

Newton:

1 22

m mF=Gr

G : G = 6,67310-11 m2Kgr-2 r :

: 0 ,max T,max=Fk

: : Fk : . 9 ()

< ,max 9 : T = Fk () 9 = Fk

(Momentum)

p=mur r

F1 F2

m2m1 r

• 10

10

( ) .

F=0 p=p ( . 43) - Newton ( ) :

p F t= uur uuur ur = Fuuur t puur= ur p p+ =r ur r

( )

(, ) .

• 11

11

:

f : sec f = N t

= , Hz=s-1

- : 1f=T

u

: Su=t

u = 2RT

u =2Rf

: m/sec

: = t

= 2T

= 2f

u .

! .

.

- : u = R

: . u, - , .

=2u

R

: . - :

F=m F=2mu

R

Newton :

FR=F =2mu

R

r xy, ( ) r:

drudt

=uurr

u

S

u R

uR

• 12

12

, - . :

(//u) u

( u) u

=2u

R R ( -

) F = m

r

R

ro

r

u

x

y

O

• 13

13

-

W=FS ( W=F Sur r ) :

F: S: : F S.

Joule ( J = Newtonm)

F=(x) F=(x) x. W = F=(x) .

:

( x1 x2) :

W = 12x12 -

12x22

T x1, x2 - . (...) ( )

(Energy) , . . , , . Joule, J = Newtonm m =mc2 (Einstein 1905). , . ( ) (.. - ).

. .

x2x1

F

F1

x x

F S

ST

W=TS180 W=-TS

=90

• 14

14

(Potential Energy) UAB -

U = - W

UB = mg(hh) UB = mgh

UE= 12x2

To x .

q1 q2 r

1 2q qU Kr

= (Kinetic Energy)

= 12

mu2

(Conservative) ,

. : , (Coulomb), ,

: , , ,

= + U

( - ) ,

= 1 + U1 = K2 + U2

-

E=WF- (= Q)

( , ....)

• 15

15

-

= WF

= WF1+WF2+

(To .... , )

:

P = Wt

= t

P = E/t () F : P = Fu() :

u F u

: Watt, W=Joule/sec HP =750 W (Horse Power = )

: ,

• 16

16

q Q (Electric Charge) ( ). : (+) (-)

: , . , () e = 1,6 10-19 C e. Q=Ne

: . .

: Coulomb C ( = Amperesec)

Coulomb ( ) q1 q2 :

1 2 2

q qF=Kr

: K=9109 m2/C2 r :

=

14

: (permittivity of free space) = 8,8510-12 C2N-1m-2 : ( )

(Electric Field) . . (Electric Intensity) q -, q

FE=

+q

urur ()

/C V/m.

2

QE = K

r

: Q : r : -

-

-q

F

F +q

• 17

17

V (Potential) V , - q , - q.

V = AW+q

()

V = Uq+

VA = A

QKr

(o o Q o )

UA :

WA

V = VA - VB = A BW

q

+ ()

V = VA - VB = ABU

q+

VAB = A B

1 1K Qr r

( ) (Field Lines)

-

-q

-

q . : - . ( ) . .

+ -

+

+q

• 18

18

. - . -.

(Capacitor) . :

C (Capacitance)

QC=V

= = :

SC = l

: : : S : :

1U= QV2

21 QU

2 C= 21U CV

2=

(permittivity) () Co - C>Co =Co/C. ( ).

C

• 19

19

(Direct Current)

, .

(Electric Current) : = q/t i = q/t Ampere, ()

(Electric Cell) , .

() (Electromotive Force)

= PI E = W

q

(E W) . Volt, V=J/C

(Resistance) :

R= VI

Ohm, = Volt/Ampere

S ( ) :

R=Sl

=(1+)

: : : 0 :

: R=R(1+)

, Ohm i V R,

= VR

: -.

Joule R i t :

Q=i2Rt

• 20

20

E = iVt E = i2Rt

E = 2V

Rt

P = iV P = i2R

P = 2V

R

: i

i1=i2=i3 V1+V2+V3=V R=R1+R2+R3

V1=V2=V3=V i1 + i2 + i3 = i

1 2 3

1 1 1 1R R R R

= + +

Kirchhoff (+) (-) . i = 0 ( )

Kirchhoff .

V = 0 ( )

Ohm , r, R -:

EiR r

= + E=i(R+r)

P = i

P = Vi ( = i2R )

P = i2r

R1

V

i R2 R3

V1 V2 V3

R1

R2

R3

V

i1

i2

i3

i

• 21

21

. r

V = E iR

()

- ( )

-.. V i -

. .

i=/r

. .

() . - .

i

V

i

V

i

i

V

• 22

22

(Magnetism) , Fe3O4 (Magnetic Field) . B

ur .

(Magnetic Induction) : Tesla, T=N/Am

B . :

( ) (North N) (South S)

Biot-Savart i r

= 4 2

irl

: : (-

) =1,2610-6 mKgC-2

B = 4

2ir

B = 2ir

: : 10-7 Wb/Am

K = 4

(

)

i

r B

r

i

• 23

23

- i :

B = 4

2ir

B = 2 ir

(): i .

-: - .

(Solenoid) - :

= 4nI B = nI

= NlI

:

: ( )

: :

- : - (

!)

(Permeability of medium) .

=/ :

(Ferromagnetic)

Fe, Ni, Co >>1

(Paramagnetic) Al , U,

>1

(Diamagnetic)

Cu, Bi, Hg, ,

• 24

24

Laplace , Laplace

FL=Bi B Laplace

FL=Bi - Laplace

Laplace , . FL : B . Laplace.

Lorentz q u - , -

FL = Buq

: LF q(B u)=

ur r

( ) :

LF q(E B u)= + ur ur r

T (B) u - . Laplace. i u. i u -, .

B

FL

u

B

FL

i V

• 25

25

(Electromagnetic Induction) - .

(Magnetic Flux) S ,

= BS = B Sur r :

: S : ( ) :

n S. - .

: Weber, Wb = Teslam.

=-t

=-t 0

t

=- ddt

Lenz

( Von Neumann) - .

Q=-R

(Self-Induction) . :

=-Li

t

L = Henry () ( = VsecA-1)

: L = 2/ : ( ) : : :

- -

R

L

n

S

• 26

26

:

i ( )

2B

1U Li2

= (Mutual Inductance) ( (1) (2)) (2) i (1) :

=-i

t

M :

- U - ( ( , u)

rl ) -

:

= U

Laplace (Lorenz) .

:

E = 12

A

U

u

• 27

27

(Alternating Current) V=Vot

Vo : R i i=Iot

: = oVR

(Effective value) -

= oI2

=0,707

.

V = oV

2

V=0,707 V

Ohm , :

i= VR

, Io= oVR

, I= VR

Z () (Impedance)

Z= oV

= V

.

(Capacitance)

ZC=1

C

(Inductance) L = L

(Resistance) R = R

VC /2 i

VL /2 i

VR i

• 28

28

RLC (, , ) :

2 2 L C RV (V V ) V= +

22 2

1V L ( R)

C = +

221L R

C = +

-:

= RZ

i=t v=V(t+) V .

RLC

(Power) P=iv

(Effective Power) P=V

: - .

RLC L=ZC VL=VC V=VR =0. . RLC :

f = 12 LC

( RLC )

VR VC

VL

VL-VC V

i

• 29

29

(Periodic Motions) (Simple harmonic motion) -

x=At x=0 t=0 :

u = umaxt umax= = -maxt max=2

...

F = - Dx :

D : x : ..

(angular frequency) D = m2

= Dm

(Period)

=2 mD

- = - 2x

-

u = 2 2A x

= 2 2maxu u

UT = 21 Dx

2

= 21 mu2

()

= 21 DA2

= 2max1 mu2

..

+ - x

• 30

30

+ UT = E

( F=-bu) - . :

b:

= e-t

: : t=0 : b t : t=NT

o

1

AA

= 12

AA

= 23

AA

=

(-). f - fo . (Resonance) - :

f = fo.

fo

LC -:

T= 2 LC . q=Q i=0 t=0:

q = Qt i = - It = Q

B. q=0 i=I t=0: q = Qt i = It

fo f

A

• 31

31

. q0 i0 t=0:

q = Q(t+) i = - I(t+)

(Capacitor)

UE = 21 q

2 C

(Inductance)

UB = 21 Li

2

E = UE+UB

E = 21 Q

2 C= 21 LI

2

i = 2 2Q q

VL = VC

B

q=0

i=I

+ + +

Q- - -

i=0

+ + +

Q - - -

i=0

B

q=0

i=I

+ + +

Q - - -

i=0 i

3T/4 T

T/2 T/4 t=0

• 32

32

x q

u i

m L

D 1/C

Q

i/t

U UE

UB

- .

x=x1+x2 . 1=2= . 1=2= 1 2

x1=A1t, x2=A2t

x = 2A 1 2 t2

1 2 t2+

B1. 1=2= 1 2

x1=A1t, x2=A2(t + )

x = A(t+) A = 2 21 2 1 2A A 2A A + +

= 21 2

+

x = A t :

= 2A 1 2 t2 =

1 2

2 +

(beats) :

= 1 2

1f f f = |f1 - f2|

• 33

33

(Waves) ( ) . :

() ()

: () :

( ) . .

() : . .

() : - , .

(Wave length) . : - . : 2

u =

y = A t x2T

x

y = A t x2T

+ x

() (Interference)

y = 1 2 1 2r r t r r2A 2 2 2 +

: |r1-r2|= : |r1-r2|=(2+1)/2

(Stationary Wave) . -.

y = y1+y2

y = 2 x2

t2

: x =2

, =0, 1, 2, ... : x=(2+1) 4 , =0, 1, 2, ... Doppler (Doppler effect) (Observer O) (Source S) :

• 34

34

fo=fs os

u uu u

m

: fo : fs : u : uo : us :

( ) .

- . , , , c. - .

= max t x2T

B = Bmax t x2T

- :

c= EB

c .

c c=3108 m/s

E

B

c

• 35

35

(Reflection)

-.

=

. . . .

(Refraction) n1 n2 - . -.

n (Refractive Index)

n= occ

: n > 1 c

• 36

36

() . .

n1 n2.

, n1>n2

, n1

• 37

37

n

()

: c .

()

400 nm

n

700 nm

1,54

1,51

• 38

38

(Center of Mass) Oxyz ( mi xi, yi, zi) :

i icm

i

m xxm

= , i icmi

m yym

= , i icmi

m zzm

=

: iicmi

m rrm

=rr

( )

ddt

=urr

d

(). .

cm

F

=urur

: F : : CM :

P ( ) ()

dpFdt

=rur

F = 0 dP/dt = 0 P =

(Moment of Force)

= r F ur =Fd

=Fd : d : F -

F

r

F

d

• 39

39

F d r :

- F - d . = Fd

:

x

y

z

F 0F 0 F 0

F 0

== = =

ur r

: r

=0

uCM

(Moment of Inertia) :

I = m1r12 + m2r22 + + miri2 I = miri2

:

= 2r dm

F

F

d

m2

m1

m3

mi

r2 r1

r3 ri

• 40

40

R mR2

L 21 ML

12

, 2 21 M( )

12+

R2

21 MR2

21 MR2

21 MR2

22 MR5

22 MR3

Steiner-Huygens ( ) -

= CM + Md2

:

: CM :

: d :

L (Angular Momentum) L m u r

L r p= ur r r L=mur

: p : p=mu

d

L

p

r L r p= ur r rL r p= ur r r

• 41

41

. .

L r p= ur r r L = mur L = mud

: d : ()

I

L I=ur ur (1)

L = I

1 2L L L ...= + +ur ur ur (1) . L - ( !). - zL I=ur ur , z Lz z. Newton . :

= uur ur = :

dLdt

=uruur

dL

dt=uruur

- :

dL

dt=uruur

= 0 L L =ur ur I1=2 ( =) 11=22

= 122

:

= 122 + 1

2 2cmu

r

p

L

d

m

L

• 42

42

F

W = dW = FRd = d d . :

W=

=

W = 12 22 -

12

I 21

- .

R - uCM

uCM = u = R -:

CM = R :

CM : :

:

= = + t

:

= = + t = + t + t2

d

dS

F R

u R

u

ucm

• 43

43

(Collisions) . () . , , (scattering) (central) (non central), - (elastic) (inelastic), - ( ) , , .

p p=r r

. .

p=p m2u2 m1u1 = (m1+m2)u

. ... . :

' 1 21 2 21

1 2

(m m )u 2m uum m

+= +r rr

' 2 12 1 12

1 2

(m m )u 2m uum m

+= +r rr

( ) - , . :

' 11 21

1 2

(m m )uum m

= +rr

' 112

1 2

2m uum m

= +rr

. . ... . ( ). ( ).

u1 u2

u

m2 m1

m1+m2 +

+

u1 u2

u1

m2 m1

+

+

u2

• 44

44

(Perfect Gases)

( Gay-Lussac)

( Charles)

P .T

= V .T

=

( Boyle-Marriote)

( Poisson)

PV=. PV =.

PV = nRT :

n : mole, n=m/MB, n=N/N : Avogadro 6,0231023 mol R : 8,3144 Jmol-1K-1

PV .T

=

( P, V, T) , . , , , - , , : i. ii. ( , ) iii. iv. v. , -

. vi. vii. viii. ix. :

2 21 1 NP du mu3 3 V

= = 2u :

d : : m :

(root mean square speed) 2

rmsr

3kT 3RTu u um M

= = = =

3 kT2

= :

• 45

45

k : Boltzmann, k = R/NA 1,3810-23 JK-1

=kT. f (degree of freedom)

f=3 f=5 f=7 f>6

:

fK kT2

=

Cp=CV + R Cp : CV :

: = Cp/Cv CV = R/(-1) CP = R/(-1) CV = fR/2 CP = (f/2+1)R

(Internal Energy) 1U Nf kT2

= U = n CVT

• 46

46

A

Q=U+W Q : (>0) (0) (1

V

2 1

P

2 1

V

V2

V1

V1

• 47

47

Q = nCPT, U = nCVT, W = PV

:

V2/T2=V1/T1 . Poisson

PV = P1V1 = P2V2 ( Poisson)

:

:

Q = 0, U = nCVT U = - W, W = 2 2 1 1P V P V

1

Poisson: T1V1-1 = 2V2-1 T1P11-/ = 2P21-/

. - . : 9 =0

U = nCV = 0. 9 : Q = W -

( ) 9 -

P-V .

P

P2

P1

P

V

1 2

P2

P1 A B

P1

• 48

48

() - . - P-V. , , ( ), . - , .

() , . Q1 - 1, - , Q2 21

Carnot : : 1 -

Q1 : :

Q2 (

• 49

49

: nc Carnot 1 2.

Carnot : 1

2

1

2

TT

QQ = :

Carnot

nc= 1 - 1

2

TT

Kelvin-Planck: - . n

• 50

50

(Galileo Galilei 1600 ..) t t - t .

- uoy - uox x : ux=uox x=xo + uoxt y : uy=uoy - gt y=yo + uoyt - 2

1 gt2

uoy - uox x : ux=uox x=xo + uoxt y : uy=uoy + gt y=yo + uoyt + 2

1 gt2

- uox=uo x : ux=uo x=xo + uot y : uy=gt y=h - 2

1 gt2

g : g = G

2rM , r>R. go = G 2R

M ,

V = - GrM

m - WA=m(VA-VB). :

:

1=2 2mu21 - G

rM m = 0 u=

RGM2 , :

u=

RGM2 M R . u = 11,2 Km/sec

uoy

uox

uo

g

x

h g

x ux y

• 51

51

h

u= hRGM2

+

. - ( h ) -

: u= hRGM

+

- . =

mF =

mqE =

lmqV

, V - - u . u=uo at x=xo + uot 2

1 at2

- - uox=uo x : ux=uo x=xo + uot y : uy=t y=yo + 2

1 t2

(+) (-) uoy uox x : ux=uox

u

uor

F

+ + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - u

uo

E F +q

+q

uox

uoy

+ + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - u

uo

E +q

+ + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - u

uo

E

• 52

52

x=xo + uoxt y : uy=uoy gt y=yo + uoyt 2

1 gt2

q : WA=q(VA-VB). .

Lorentz u . FL=F Buq=mu2/R R=

Bqmu ( )

T=qm2 ( )

: e ( !) . , u , u|| . R=

Bqmu

( xx ) x= u||t .

( ).

u||

u u

+q

x

y

B

xz ... y

B

-Q1

+Q2u1

u2

R2

FL

• 53

53

x= u||t t=T

• 54

54

(atomic mass unit, a.m.u. u) 1/12 C126 . 1u= 1.6605410-27 Kg. (=mc) - eV. eV 1 Volt. 1 eV = 1,610-19 Joule. 1u = 931.4 MeV/c2 , . (Plank) Quantum: (. quanta).

f =hf p= hfc

= h

(Planck 1900)

m u = hmu

( de Broglie)

: h = 6.6310-34 Js Planck

. (-) (). . ( , ) .

Bohr 1. , ,

. L

h2

L = n h2

, L = n,

n=1,2,3

= h2

( h bar)

2.

: hf = E - : n : n < n

:

n = - Eo

2n, n=1,2,3,

• 55

55

:

: , =4

e2 2

m e8 h

me, e : : h : Planck

: rn = ron2, n=1,2,3,

:

r : , r=2

2

e

h m e

me, e : : : =3,14 h : Planck

( decay) AZ X A 4Z 2Y +

= He42 ..

23892U 23490Th + He42

+ (+ decay) p n +e+ + e ( , ) AZ X AZ 1Y + e+ + e

e+ : (positron) : (neutrino)

.. 116C 115 B + e+ + e

- (- decay)

n p + e- + e ( , ) AZ X AZ 1Y+ + e- + e

e- :

e : ..

23490Th 23491Pa + e- + e

( decay) A *Z X AZ X +

: , A *Z X :

• 56

56

t = = e-t

:

N : t : 0, :

: t -0

, t

.

bequerel

(half time) .

1/2=ln 2

.

= mp + Nmn - M = mp + Nmn (M me) : mp, mn, me , ,

EB EB=c2. , .

/, , . - .

9

4He

56Fe

235U7

1

50 150100 200 250

• 57

57

(Nuclear reaction) + + m = + - - Q=c2 Q>0 . Q56. ..

23592 U +

10 n 9338 Sr + 14054 Xe +3 10 n +198,3 MeV

23592 U +

10 n 14156 Ba + 9236 Kr +3 10 n +208 MeV

(Nuclear fusion)

• 58

58

(hadron) (lepton) -. (hadrons) , . : (bary-ons) 3 quarks, p=uud, (mesons) quark, antiquark, . +=u d (leptons) , , . (force carriers) 4 . ( : 10) (quark) . e -. ( ) e. Gell-Mann James Joyce Finnegans wake - !

quark : , , , , , quark color ( ) . quark - (gluons). , W Z (vec-tor bosons) .

(spin 1) (gravity) (electroweak)

(strong)

(weak) (electromagnetic)

GeV/c

GeV/c (graviton)

-

W+ W- Z0

80,4 80,4 91,18

+1 -1 0

(photon)

0 0

(gluon)

0, 0

quark 3 . : 18 . 6 - . 24 . 48 . , standard model.

(Quarks) spin=1/2 (Leptons) spin=1/2 flavor

GeV/c

flavor

GeV/c

u up d down

0.003 0.006

2/3 -1/3

ve e

• 59

59

- . 4 , 4 . , (Grand Unified Theories) . -. (string superstring theories)

• 60

60

=

, =

=

, =

2+2 = 1 =

=1

(2k+)= (2k+)= (k+)= (k+)=

(-)= (-)=- (-)=- (-)=-

(+)=- (+)=- (+)= (+)=

/2 /2

( 2

-)=

( 2

-)=

( 2

-)=

( 2

-)=

( 2

+)=

( 2

+)=-

( 2

+)=-

( 2

+)=-

(-)=- (-)= (-)=- (-)=-

0

1

1-1

-1

• 61

61

0 30 45 60 90 180 270 360 0

6

4

3

2 3

2 2

0 12

22

32

1 0 -1 0

1 32

22

12

0 -1 0 1

0 33

1 3 + 0 - 0

+ 3 1 33

0 - 0 +

x=

x=2k+ x=2k+-

x= x=k+

x= x=2k x= x=k+

-1 x 1, -1 x 1, - x , - x ,

()= ()=m ()=

1 m

()= 1

m

2=2 2=2-2

=22-1 =1-22

2= 22

1-

2=2 -1

2

. 3=3-43 3=43-3

3=3

2

3 - 1 3

3=3

2

-33 -1

2= 1 22

2= 1 22

+

2= 1-21+2

2= 1+21-2

• 62

62

+=2 2+ -

2

-=2 2+ -

2

+=2 2+ -

2

-=2 2+ -

2

+= ( )

+

-= ( )

+= ( )

+

-= ( )

=

=

=2R

, , , , R

2=2+2-2 2=2+2-2 2= 2+ 2-2

-

(/2) ( Werner)

=2

221+2

=2

2

1-21+2

= 12

[(-)-(+)]

= 12

[(+)+(-)]

= 12

[(+)+(-)]

2

1

-1

23 2

x x

• 63

63

-

()2=22+ ()=3+3 ()=4+64+ : - . - Pascal :

(+)n=

0n n+

1n n-1+

2n n-22++

1nn n-1+

nn n

nk

=n!

k !(n k )! ( ) n!=123(n-1)n ( ) -=(-)(+) ( ) -=(-)(++) -=(-)(+++) -=(-)(++++) -=(-)(-1+-2+-3++-2+-1) -=(+)(-) -=(+)(-+-) 2-2=(+)(2-1-2-2+2-32-+2-2-2-1) +=(+)(-+) +=(+)(-+-+) 2+1+2+1=(+)(2-2-1+2-22--2-1+2) ( 2+2)

2

1

-1

23 2

x

x

2

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 . . . . . . . .

• 64

64

=

... 14243

=+

-

=

()=

=

-= 1

- =

( ) =

: x= x= , =1 , =

=

=

+ =

-

=

=

( ) = 12=

x= :

>0 0, 1, >0 loga1=0

logaa=1 alog a =

log()=log+log log(

)=log-log

log=log

log =1

log log=

log log

=1+(-1), =+1-

S= 1 +

2

=1-1, = 1 +

S=11-

1 , S=11

1 0

=0

• 65

65

x - Sx + P = 0

x+x+

>0 x1 x2

=0 x

• 66

66

(Scalar product)

r=(1, 2, 3)

r=(1, 2, 3) -

r r ( )

r r=, 0 r r=11+22+33 r r= 0 r r r r= r ||r (Vector product)

r=(1, 2, 3)

r=(1, 2, 3) -

r

r :

r

r

= nr n

r (n=1)

r

r -

r

,r n

r

( r

r n

r

- ) :

r

r

= 1 2 31 2 3

i j k

r r r

r

r

= (23-32) ir

+(13-31) jr

+( 12-21) kr

r

r

= - r

r

r

r

= 0r

r ||r r r=nr r r

n

• 67

67

u (a.m.u.) 1.6605410-27 Kg 931.434 MeV/c2 Avogadro NA 6.0221361023(g mol)-1 Bohr =

2

2em e kh 0,5291810-10 m

Boltzmann k=R/NA 1.380710-23 J/K me

9.1093910-31 Kg 5.48579910-4 u 0.51099906 MeV/c2

eV 1.60217710-19 J e 1.60217710-19 C R 8.314510 J/Kmol

G 6.6725910-11 Nm/Kg =

4e2 2

m e8 h

13,605698 eV

mn 1.67492810-27 Kg 1.008664904 u 939.56563 MeV/c2

410-7 /

= 2

1 c

8,8518781710-12 C/Nm

Planck h

h2

=h 6.62607510-34 Js

1.0545726610-34 Js

mp 1.67262310-27 Kg 1.007276470 u 938.2723 MeV/c2

c 2.99792458108 m/s

• 68

68

• 69

69

A , 46 Kirchhoff, 20 , 47 , 26 , 21 , 35

, 32 , 8 , 37 , 57 , 57 , 19 , 19

, 46 Carnot, 49 Avogadro, 44 , 15 , 14 , 43 , 41 , 50 , 25 , 49 Kirchhoff, 20 , 38 , 45 , 50 , 51 , 21 , 54 , 29 , 36 , 38 , 35 , 35 , 23 , 37 , 55 -, 55 +, 55 , 56 , 4 , 38 , 3 , 18 , 51 , 8 Laplace, 24 Lorentz, 24 , 29 , 17, 22 , 45 , 43 , 43 , 52 , 56 , 27

, 27 , 27 , 27

, 27 , 13 , 26 , 15 , 14 , 14 , 29 , 14 , 18 , 45 , 14 , 20 , 14 , 29 , 31 , 14 , 29

, 26 , 56 , 56 , 20 , 44 , 27 , 27 , 19 , 49 , 30 de Broglie, 54 , 33 , 26 , 6 , 12 , 12

, 54 , 13 , 13 , 13 , 13 , 42 , 15 , 13

, 6 - , 6 - , 6 - , 6

, 5 - , 5 - , 5

, 19 , 19 , 31 - , 31 - , 31

• 70

70

, 17 , 17 , 17 , 16 , 18

, 19 , 20 , 19 , 20 , 19

, 33 , 34 , 33 , 41 , 48 , 46 Steiner-Huygens, 40 , 14 , 42

, 45 , 40 , 44 , 47 , 46 , 39 , 46 , 15 , 28 , 20 , 28

, 11 Lenz, 25 , 23 , 23 , 44 , 54 , 38 , 50 , 52 , 43 , 44 , 41

, 44 , 43 , 11 , 11 , 11 , 11 Newton , 11 , 11 , 11 , 11

, 47 , 29

Carnot, 48 - , 57 RLC, 28 , 42 , 33

, 33 , 33

, 54 , 23 , 22 (), 25 , 25 , 22 , 22 , 23 , 23

, 22 , 22 , 4 , 38 , 48 , 3 , 33 , 33 , 14 , 14 , 14

, 3 Bohr, 54 , 44 , 44 , 44 , 44 , 44 , 44

Biot-Savart, 22 Coulomb, 16 Hooke, 8 Von Neumann, 25 (Faraday), 25 , 26 Newton, 9 , 56 Joule, 19 Ohm , 27 , 20

Snell, 36 , 19 Newton, 9 Newton, 9 Newton, 9 , 36 , 50 , 9 , 10 , 10

, 23 , 4 , 4 , 4 , 4

• 71

71

, 29 , 42 , 43 , 21 , 3 , 18 , 18 , 18

, 57 , 55 , 21 , 40 , 39 , 38 , 39 , 23 Boltzmann, 45 Planck, 54 , 33 , 38 , 38 , 40 , 41 , 33 , 20 , 20 , 20

, 32 , 27 , 8 , 48

, 25 , 14 , 30

RLC , 28 - , 29 , 29 , 30 - , 29 , 29 , 30 , 30 , 30

, 5 , 11 , 11

, 50 , 44 , 35 , 9 , 9

, 3 Doppler, 33 , 16 , 16

, 22 , 21 , 56 , 18

• 72

72

.......................................................................................................................................................................................... 1 .............................................................................................................................................................................................................. 3 (S.I.).......................................................................................................................................................................................... 3 ............................................................................................................................................................... 3

.......................................................................................................................................................................................................................... 4 . ............................................................................................................................................................................................. 4 . ............................................................................................................................................................................................................. 4 . ............................................................................................................................................................................................................. 4 x........................................................................................................................................................................................................ 4 S................................................................................................................................................................................................................ 4 u (Velocity) .......................................................................................................................................................................................... 4 ............................................................................................................................................................................ 5 ................................................................................................................................................................................................................ 6 ............................................................................................................................................ 6

................................................................................................................................................... 7 : ................................................................................................................................................... 8 Hooke .......................................................................................................................................................................................................... 8 Newton ............................................................................................................................................................................................ 8 Newton ............................................................................................................................................................................................ 9 Newton ............................................................................................................................................................................................. 9 Newton:............................................................................................................................................................. 9 : ........................................................................................................................................................................................................... 9 :.................................................................................................................................................................................................. 9 (Momentum) ............................................................................................................................................................................................. 9 ...............................................................................................................................................................10 ........................................................................................................................................................................................................11 :...............................................................................................................................................................................11 :.......................................................................................................................................................................................11 Newton : ............................................................................................................................................11 ....................................................................................................................................................................11

- ........................................................................................................................................................................................................13 ................................................................................................................................................................................13 F=(x)...............................................................................................................................................................13 :...........................................................................................................................................................................................................13 ( x1 x2) :................................................................................................................................................................13 (Energy) ................................................................................................................................................................................................13 ...................................................................................................................................................................13 (Potential Energy) ......................................................................................................................................................14 .....................................................................................................................................................................14 .......................................................................................................................................................................14 ........................................................................................................................................................................14 (Kinetic Energy) ..............................................................................................................................................................14 (Conservative) ....................................................................................................................................................14 ..............................................................................................................................................................................................14 ................................................................................................................................................14 .........................................................................................................................................................14 ........................................................................................................................................................................14 .........................................................................................................................................................................15 ...........................................................................................................................................................................................................................15 : .............................................................................................................................................................15

...............................................................................................................................................................................................................16 q Q (Electric Charge) ..................................................................................................................................................................16 : ...............................................................................................................................................................................................16 Coulomb..................................................................................................................................................................................................16 (Electric Field).....................................................................................................................................................................16 (Capacitor) .....................................................................................................................................................................................18

(Direct Current) ...................................................................................................................................................................19 ...................................................................................................................................................................................................19 (Electric Current) ................................................................................................................................19 (Electric Cell) .......................................................................................................................................................................19 () ....................................................................................................................................................19 (Resistance) ................................................................................................................................................................19 , Ohm..........................................................................................................................................................................................19

• 73

73

Joule ..................................................................................................................................................................................................19 ..........................................................................................................................................................................20 .......................................................................................................................................................................20 Kirchhoff ........................................................................................................................................................................................20 Kirchhoff .........................................................................................................................................................................................20 Ohm ....................................................................................................................................................20 ....................................................................................................................................................................20 ............................................................................................................................................................................................................21 .......................................................................................................................................................21 ....................................................................................................................................................................................21 .........................................................................................................................................................................................................21 .............................................................................................................................................................................................................21

(Magnetism) ..................................................................................................................................................................................22 ............................................................................................................................................................................................22 (Magnetic Field) .............................................................................................................................................................22 ..................................................................................................................................................22 Biot-Savart ...............................................................................................................................................................................................22 ................................................................................................................................................22 ...........................................................................................................................................................23 (Solenoid) ...........................................................................................................................................23 (Permeability of medium) .......................................................................................23 Laplace ..................................................................................................................................................................................................24 Lorentz ....................................................................................................................................................................................................24

(Electromagnetic Induction).................................................................................................................................25 (Magnetic Flux) .............................................................................................................................................................25 (Faraday).........................................................................................................................................................................25 Lenz ...............................................................................................................................................................................................25 ( Von Neumann)..........................................................................................................................................25 (Self-Induction) ........................................................................................................................................................................25 .............................................................................................................................................................................26 (Mutual Inductance) .............................................................................................................................26 ...................................................................................................................................................26 .........................................................................................................................................................................................26

(Alternating Current) ...........................................................................................................................................27 (Effective value)..................................................................................................................................................27 ............................................................................................................................................................................................27 Ohm ..................................................................................................................................27 Z () (Impedance) ................................................................................................................................27 (Capacitance).........................................................................................................................................................27 (Inductance) ..................................................................................................................................................................27 (Resistance) ..............................................................................................................................................................27 ........................................................................................................................................................................................27 ...............................................................................................................................................................................................27 ......................................................................................................................................................................................27 RLC (, , ).......................................................................................................................................28 (Power).................................................................................................................................................................28 (Effective Power).......................................................................................................................................................................28 RLC ...................................................................................................................................................................28

(Periodic Motions) ......................................................................................................................................................................29 (Simple harmonic motion).........................................................................................................29 .......................................................................................................................................................................................29 (angular frequency) ...........................................................................................................................................29 (Period).............................................................................................................................................................................................29 - ........................................................................................................................................................29 - .............................................................................................................................................................29 ...................................................................................................................................................................29 ..................................................................................................................................................................29 ......................................................................................................................................................................29 () ..................................................................................................................................................29 .....................................................................................................................................30 ......................................................................................................................................................................................30 ..........................................................................................................................................................................30 ........................................................................................................................................................................................30 .....................................................................................................................................................................................32

(Waves) ........................................................................................................................................................................................................33

• 74

74

(Wave length)...................................................................................................................................................................33 ..........................................................................................................................................................33 ................................................................................................................................................................................................33 () (Interference) .......................................................................................................................................33 (Stationary Wave) ................................................................................................................................................................33 Doppler .....................................................................................................................................................33 ...................................................................................................................................................................................34 (Reflection).....................................................................................................................................................................35 .......................................................................................................................................................35 (Refraction) .....................................................................................................................................................................35 n (Refractive Index) .................................................................................................................................................35 ................................................................................................................................................................................................36 Snell....................................................................................................................................................................................................36 (Total internal reflection) ..........................................................................................................................................36 (Dispersion)............................................................................................................................................................................36

...............................................................................................................................................................................................................38 (Center of Mass) ...........................................................................................................38 .......................................................................................................................................................................................38 ...............................................................................................................................................................38 ..........................................................................................................................................................38 .....................................................................................................................................38 (Moment of Force).........................................................................................................................................................38 ................................................................................................................................................................................39 ........................................................................................................................................................................39 (Moment of Inertia) ....................................................................................................................................................39 ...................................................................................................................................40 Steiner-Huygens.............................................................................................................................................................................40 L (Angular Momentum) .........................................................................................................................................................40 ......................................................................................................................................................................41 ..........................................................................................................................................41 ..........................................................................................................................................................41 ....................................................................................................................................................................41 .................................................................................................................................42 ....................................................................................................................42 .......................................................................................................................................................................................................42 .....................................................................................................................................42 .................................................................................................................................42

(Collisions) ............................................................................................................................................................................................43 . ......................................................................................................................................................43 . .......................................................................................................................................................43 . . ..................................................................................................................................................43

(Perfect Gases) ...........................................................................................................................................................................44 ........................................................................................................................................................................................................44 .........................................................................................................................................................................44 .........................................................................................................................................................45 ..............................................................................................................................................................................45 (Internal Energy) .......................................................................................................................................45

.........................................................................................................................................................................................................46 A ...................................................................................................................................................................46 (Reversible change) .......................................................................................................................................46 ..........................................................................................................................................................................................46 .............................................................................................................................................................................................46 ..........................................................................................................................................................................................47 .........................................................................................................................................................................................47 .................................................................................................................................................................................................47 ..............................................................................................................................................................................48 ..............................................................................................................................................................................................48 ...........................................................................................................................................48 Carnot ......................................................................................................................................................................................................48 Carnot ................................................................................................................................................................................49 ............................................................................................................................................................................49 ..................................................................................................................................................................................................................49 ......................................................................................................................49

.............................................................................................................................................................................50 (Galileo Galilei 1600 ..) ............................................................................................50

• 75

75

...........................................................................................................................................................50 ...........................................................................................................................................................51 ......................................................................................................................................................52

..........................................................................................................................................................................54 ........................................................................................................................................................................................................54 .................................................................................................................................................54 ....................................................................................................................................................................54 .............................................................................................................................................................................................54 Bohr ................................................................................................................................54 :......................................................................................................................................................................54 : ..........................................................................................................................................................................55 (Radioactivity) ..........................................................................................................................................................................55 ( decay) ....................................................................................................................................................................................55 + (+ decay) .................................................................................................................................................................................55 - (- decay) ...................................................................................................................................................................................55 ( decay)......................................................................................................................................................................................55 .............................................................................................................................................................56 .....................................................................................................................................................................................................56 .............................................................................................................................................................................................56 ..........................................................................................................................................................56 .....................................................................................................................................................................................57

...............................................................................................................................................................................................57 ................................................................................................................................................................................................................60 .......................................................................................................................................................................................60 ...............................................................................................................................................................................................................63 ...................................................................................................................................................................................................................64 ............................................................................................................................................................................................................................64 .............................................................................................................................................................................................................64 ....................................................................................................................................................................................................................64 ..................................................................................................................................................................................64

................................................................................................................................................................................................................66 .............................................................................................................................................................66 ..............................................................................................................................................................66

................................................................................................................................................................................................................67 .................................................................................................................................................................67 ...............................................................................................................................! .

: X. http://users.altecnet.gr/martheo/