.,, T = N N f = T rad/s. : dφ. ω =. dt

-,.. -. ( ). -.,,.. ( ),. t, t T = N N f = t. s s - /s Hz.,. f = T,, ( ) π ω = = πf T rad/s.... : dφ ω =. dt. 8

-3 ).......,...,. x x = Aηµ ωt (. ).,,. 9

.. -. -... υ = υ συν ωt (.) max a = a ωt (.3) maxηµ max max,. ( x = 0 ) ( x = A x = A )...3,. υ max = ωa a = ω A max..4. ( ) ( ),,.,...3.,. (. ), (.) (.3),., (..5), d. 0

..5. t=0. (. ), (.) (.3) : x = Aηµ ( ωt + ϕ) υ = υ συν ( ωt + ϕ) max a = a ηµ ( ωt + ϕ) max (.4) (.4). t = 0 x = d d (.4) d = Aηµϕ ηµϕ = A.. t +. ( ) ) m,,. F = ma (.5) (.5) (.3) F = mamax ηµωt F = mω Aηµωt (.6) x = Aηµωt (.6) F = mω x (.7)..,. D m ω (.7) F = Dx. F ( ) D...6,...7 ( ) ( ),,.

-,. π D = mω = m T m T = π (.8) D m... : m T = π (.8), D,.. l (..8. ). F=w (.9). x : F =w-f, (.9), F =F-F (. 0) Hooke F=Kl F =K(l+x), (. 0) F =-Kx (. )..8 (. ).. (.8) T = π m K ).,, K = mυ = mυ max ωt = mω A συν ωt (. )

, :,, x, F F.,, F = Dx...9 F F =f(x), (.. 0) W = Dx. To F, U = Dx (. 3) D = mω x = Aηµωt, (. 3) U = mω A ηµ ωt (. 4) (. ) (. 4) (.. )... 0 x, F =Dx. x. E = K + U (. ) (. 4) E = mω A ( συν ωt + ηµ ωt) = mω A.. o,,. DA E DA mω A = mυ E = = = max. 3

... LC. -4 C (.. ) L.. (.. ) Q (.. 3 )..,, ( ) (.. 3 ).,,..,. Q (.. 3 )... 3, Q,..., (.. 3 - )... q = Qσυν ωt (. 5) 4

, i = I ηµ ωt (. 6),., Q U E = C U B = Li., U E = LI.,,.., q U E = C (. 7) U Li B = (. 8), Q E = = C (. 7) (. 5) Q U E = συν ωt = E συν ωt (. 9) C (. 8) (. 6) U B = LI ηµ ωt = E ηµ ωt (.0) (. 9) (.0),.. 5 U E U B. U E U B..,, LI.. 4 O -, LC... 5, - -. 5

..,.,,. T = π LC (. )... 6., m.. 6,,., /. x = Aηµ ( ωt + π / ) = Aσυνωt = max ( t + / ) = max t., KA, - -. LC, Q E = - - C,. q = Q t i = Q t i = I t. - -. (. 6). 6

. LC L=mH, C=5 F. V=0V. ). ). : ) T = π LC f = / T f = π LC = 6 0 Hz ), Q = CV = 6 4 ( 5 0 F ) ( 0V ) = 0 C 4 ω = πf = 0 rad / s 4 4 q = Q συνω t = 0 0 t (S.I.),, Q Q = LI I A C = LC 4 i = I ω t = ηµ 0 t (S.I.) = 7

.. 7.. -5.. 7.,,.,,..,.. ( )..,...4.,.. F = bυ.. 8 ( ) F ( )... 9.. To b. b. b : (.. 9),. b., - (..0 ). b. : 8

), b, (..0 ). b (..0 ). ),,,, (..0 )...0 ( ) -. ( ).. ( ) -, -. ( ) -. ),.. -. A A ο A = A A = A 3 =... = σταθ. A K A e Λt = O KT t = K = 0,,,.... 9

. - -,,., b.,.,,,..... LC (..),..,,.,.,.,..,...3 ( ). ( ) ( ). ( ). 0

-6..4., f = π. f ) ( )....5,,,... ( ) -. K m ( o..4 -....5 -...5 Fundy.., f f,. f., f., f f o, f f o.. o..6 ' - -. - -.

( ), f=f 0,...6 - -, -. ( ). ( )...7,,....7 -, -..7,..8,.,,,. b ( -5).,., - - -

., f...,.. T LC (.. ). ( ) f 0 =. LC π LC..,. - (..9). - i,, - LC - i, i. f i,..8 (b <b <b 3 )...9 LC - -. i, (..30). f = fo....30 - LC - -. 3

....8,. (..3 ), (..3 ).,, (..3 ). (..3 ),,, f., f (..3 ). f ( ),,. o fo..3. ( )..3., ( )..3.,. 4

,,...3 -.. 850. 6.,,..,... LC,... LC. ( ). LC,. ( ),.,,,,...33 LC,. -7 5

.34,.. ( ). - -..34 - ( ),...,,.,,....,. x = A t (.) (..35 ) x = A ( t + ϕ) (.3) (..35 )..35 - ( ) ( ). - - - ( )., (..35 ), x = x + x (.4) (.) (.3) (.4) x = A ηµω t + A ηµ ( ωt + ϕ) (.5) 6

(.7) x = Aηµ ( ωt + ϑ) (.6) A = A + + A A Aσυν ϕ (.8) εϕ ϑ = A ηµ ϕ A + A συν ϕ..36 ( ), 3. ( ) - 80 3. (.6),.. =0 (..36 ), (.7) (.8) A = A + A ϑ = 0,. = 80, (.7) (.8), A = A A o ϑ = 0 ϑ = 80 (..36 ),..,,. x = A t (.9) (..35 ) = A t (.30) (..35 ) x, x = x + x (.3 ) (..35 ) (.9) (.30) x = Aηµω t + Aηµω t (.3) 7

α β α + β ηµα + ηµβ = συν ηµ (.3) ω ω ω + ω x = Aσυν t ηµ t (.33).. ω ω A = Aσυν t (.34) (.33) ω + ω ηµ t, ω ω ω. ω ω ω. (.33) x = A ηµ ωt (.35) (.35).,,. (..37). ( - ) ( ) -...37 ( ) ( ). 8

9 0 = t ω ω συν. ( ) π ω ω + = K t = 0,,,.. t t (..37) π ω ω = t ω ω π = t 3 π ω ω = t 3 ω ω π = t t t. 3 ω ω π ω ω π ω ω π δ = = = t t T f f T = δ f f f = δ f f f = δ

x = Aηµ ωt υ = υ max συνωt a = amaxσυν ωt υ max = ωa α max = ω A F = Dx. F = Dx. m T = π D. E = DA = mυ max., q = Qσυν ωt i = I ηµ ωt Q E = = LI C.. b.......,,.,,.,,. f = f f δ 30

.... ( ).. ( )....., ;...38..,. ( )... ( ).. 3

; 3...39..39..,........,., ) ) max ) max ) ) ;.. ;.,, ;.3 F x ; ) F = 0x ) F = 00x ) F = 5x ) F = 50x.4.., : ) ; ) ;.5. 3

x U K 0 x 3 J J x 4 J A.6. t=0 (x=a). ) ; ) x = - A; ) ;.7.40,. ) ; ) 4, ; )..40 4 ;.8. m A m B (m A > m B ),. d,. ) ) ). )...9 3 0-6 s.. ) ; ) ; ) ; ) ;. 0. ; 33

.,. U E 80x 0-3 J 0x 0-3 J U B 50x 0-3 J 0x 0-3 J E 0x 0-3 J....4,. ) ),...4. 3 LC C = C L = L. ) C, ), ), ),.. 4. 5. 6 LC 00k z. L. L/4, : ) 5k z ) 50k z ) 00kHz ) 400k z. -,5V. -. - 3V. ) ) ) ) ) ) ) ) : 34

,....,... 7. 8. 9, ). ). ).., ). ). ). ).. t. t,, ) /; ) /4; ) 3 /4;..0.4,.. ;..4.. ; ). ). ). ).. ). ). ). ).. 35

.3.43,,3, 4. f. To.,3 4 ;..43.4 L L. C C. C L,C. L L,... L C L C ( ) 6 mh F 5 mh 3 F ( ) 4 mh 8 F mh 6 F ( ) 5 mh 6 F 4 mh 7 F ( ) 6 mh 4 F mh 8 F.5,.,, 5cm 3cm. =.. 80 =.6. f f. ; ). ). ). ). ) f - f. 36

..44.7.44. = 0N/m =80N/m. To, m=kg.,. [ : = 0, s ].8 m= kg,. =0,5 m. x =0,3 m = 4 m/s. ) D. ) x = 0,4 m. [ : ) D = 00 N/m ) = 3 m/s ].9. l=,5 cm.,. g= 0 m/s. [ : 0,3 4 s ].30 C=5 F L=4 0-3 H.,. 37

[ : 6 z ].3 K C=0 0-6 F L=5 0 - H., V=50 V. N,. [ : q= 0-3 000t i= 000t (SI) ] 38

...3 C =8 0-6 F L =3 0-3 H, (C ) L =4 0-3 H.. C.. [ : 6 0-6 F ].33, x = 4 ηµ 50t x = 4 ηµ (50t π ) (S.I.),. ; [ : 0 ].34, x = 0 ηµ 50t x = 4 ηµ 50t,. cm.,. [ : x = 0, 4 ηµ 50t (S.I.)].35, x = 8 ηµ50πt x = 6 ηµ (50πt π ). cm.,. [ : υ = 3, 4 συν 50πt (m/s), α = 493 ηµ 50πt (m/s ), T = 0, 04s ].36.,.. f =500 Hz f =500,5 Hz.,. ; [ : s ] 39

.37 m= kg =0, s. x=cm,, = 0, 3 m / s.,. 5π 5π [ : x = 4 0 ηµ 0t +, υ = 0,4συν 0t +, 6 6 5π a = 4ηµ 0t +, (SI) ] 6.38, = 00 /m,, m= kg. d=5 cm. : ). ). ) ). ). g= 0 m/s. [ : ) 5/ z ) / ) 0,5 m/s ) 5 m/s ) 5 ].39 =0 cm = 0 s.. ( ) x= 0cm. [ : 0/3 s].40 O =5 0 5 /m. ), = 000 kg., = 8 km/h. -. ) m=60 kg.,. :. [ : ) 0, m, / 00 s, ) 5 0 3 ].4 M= 00 g 40

=300 /m,. m=0 g, =30 m/s,. : ). ),. ).. [ : 5 m/s, 0, m, 3, 4 0 - s ].4 C=5 0-5 F L= 0-4 H. R=. E=0V.. ;,, R f =. π LC L :. [ : 4 0 - J].43 C=4 0-5 F V= 00 V. L=0,9 H. ) ; ) ; ),, ;. [ : ) 4 0-3 C ) 0-3 C ),5 0-3 s ] 4

.44 L= 6 mh C=4 0-5 F. q=0 C i= 5 3 ma. ; [ : 40 C ].45 m= kg. x = 0 ηµ50πt x = 5 ηµ (50πt π ). cm. ) D ; ) ; ) x=4 cm; π 0. [ : D=5 0 4 N/m, E=6,5 J, = 3, 5 m/s ]..45.46 m..,,., h.. h m [ : + π ] g ηµ φ K.47 = 00 /m. m = kg,. m h. l=0,m,. ) h. ) m,, ( ). ). g = 0 m / s, π 0. [ : 0, 5 m,,6 kg, 0,3 4 s] 4

.48 m= kg =00 /m.. F, =0 cm,,. : ) F. ),.. g= 0 m/s. [ : 4J, 8J].49 m =0,45 kg h= 5 m m =0,3 kg = /m. T. ),, ; ) ;, ; g= 0m/s. [ : ) 7,6 m/s, ),5 m/s, 0,4 s ].50.46 E=6 V,R=,L=0, 0-3, r=0.,.. ) ; ) 0V; [ : 8 F ]..46 43

x, x = Aηµωt H,, x, : υ = lim. t 0 t,, x t dx. dt dx υ = = [ Aηµωt] (.36) dt f(g(t)) [ f ( g( t))] = f ( g( t)) g ( t) u u η µ u = συν u συν u = ηµ u [ A ηµω t] = A ηµ ωt ( ωt) = Aω συνωt (.36) = Aω συνωt (.37),. υmax = Aω (.37) : υ = υ συνωt max,, υ : a = lim t 0 t dυ ( ). dt dυ a = = [ Aω συνωt] = Aω συν ωt ( ωt) = Aω ηµωt (.38) dt,. A ω = α (.38) max a = a max ηµωt 44

... -,, -., -. - ( ),,,..,. -., ( ) ( - ). -.,.. -. -.. -, -.... -... -. 44

t x, x υ = (. ) t. -. - 344 m/s,.. -,,, -. -,... -.. - -.. -.3. -. -.,.. -,,... - - ( ) ( - ).,,.,,....3..4. 45

..5 - ( f ). ( ) - ( ). - λ..6 t. ' - υ t. - ( ) - (..6 ). - λ...6 ( ) t - t. ( ) -.,. (. ) t - x λ λ υ = (.) T T =,, f υ = λ f (.3). 46

- t 0 = 0 y = Aηµ ωt. x t =. t, υ x t t = t, υ, x π x y = Aηµ ω t y = Aηµ t υ T υ t x y = Aηµ π T υt, υ T = λ, t x y = Aηµ π (.4) T λ..7 - x -. t x y = Aηµ π + T λ (.4) -.. t x π. - T λ x -. (.4) y, t x. (.4). -,. (.. ). 47

..8 -. B,,..9. ). (t = t ) (.4) x y = Aηµ π σταθ λ -. (..8), -. ). (x=x ), (.4) t y = Aηµ π σταθ T -. (..9). -3, - ; ;, - - -.. 0,, -., -...3 -... 0 48

.3 -.,.,. -.. ( - ). -,. -.,,, -. -. To.. - - -. -4.4.4. -. ( ) ( )..4 49

.. 0,,,... 3 0,,, -. ( ),.. -, (r = r ). -,,,,. /,. -.., r -r =.,.. (.. 3), - r r, /. -. -,,. /, -,...,, /. r r,, - ( r r = Nλ N = 0, ±, ±... ).. r r,, - ( /) ( r r = (N + ) λ / N = 0, ±, ±... )... -., r r. t -, t r y = Aηµ π (.5) T λ t r y = Aηµ π (.6) T λ 50

, t y = y + y (.5) (.6) t r t r y = A ηµ π + ηµ π (.7) T λ T λ α β α + β ηµα + ηµβ = συν ηµ (.7) r r t r + r y = Aσυν π ηµ π λ T λ r r A = Aσυν π λ (.8) t r + π r T λ (.8), ( = ) - r r συν π = ± λ r r π λ = Nπ, r r = Nλ N = 0,,... r r συν π = 0 λ r r π π = ( N + ) λ r r = λ N + N = 0,,... ( ) (.8) A = 0.. r r = σταθ.. -, -. :,, - ( ).,,. 5

..,.,, x=4 cm,.. =340 m/s. :,, r r = (N + ) λ / N = 0, ±, ±... =0 r r = λ / AM + x ( BM x) = λ / x = λ / λ = 4 x = 6cm υ f = = 5 Hz λ -5 - (.. 4).. 4 -... 5... - -.,... - (.. 5). - (. 6) -., 5

- - - -. -.. ( = ), -.. t x y = Aηµ π (.9) T λ x (. 4 )., (. 4 ), t x y = Aηµ π + (. 0) T λ, t, y = y + y (.9) (. 0) t x t x y = A ηµ π + ηµ π + (. ) T λ T λ α β α + β ηµα + ηµβ = συν ηµ (. ) x π y = Aσυν π ηµ t (. ) λ T x A = Aσυν π (. 3) λ x. (. ) y = A ηµ π t y = A ηµωt T.. [ (. 3)]... 6. 53

..5. -. x x A = Aσυν π = 0 λ x π 3π π π =,,...( K + ) λ λ 3λ λ x =,,...( K + ) 4 4 4 (. 4),.. x A = Aσυν π = ± A λ x π = 0, π,..., Kπ λ 0, x =,,.... (. 5), A.. (. 4) (. 5),., - ( x=0, ). -, (..5)., - ( ), (. ) -, x=0... 7. -, =0, -, U,. t=t/8,.. t=t/4, - (U=0), -. -...6., ( - )., -,.,, -,,. - 54

,.. t t y = 8 ηµ π 5x y = 8 ηµ π + 5x 0,3 0,3. T x y cm t s. ) ; ) x = 3,05 cm; : t x y = Aηµ π T λ - A = 8cm, T = 0, 3 s λ = 0, cm x π y = Aσυν π ηµ t λ T π y = 6συν 0πx ηµ t 0,3 x = 3,05 cm x π A = Aσυν π = 6συν 0πx = 6συν 30,5π = 6συν (30π + ) = 6 = 8 λ 4 cm -6 -. ( - ).,,. +Q Q -. -, +Q Q (.. 8, ).,. 8, -...... 8 ( ), ( ). -. ±Q. ( ) - -. - ±q -. -. 55

. 9 -. - (.. 9 ).. t=t/4,, /4, (.. 9 ).,.. - -, c (.. 9 ).. 3 /4,.... 9. -... (..0) -. /4.. T/, -.... - ( ) c.. - ( - ). 56

..0 -. - 8 c = 3 0 m / s.. 0. -. E c =. B - -. -.. - ( ). -. -. -.,, -. 90 ( ). -. 57

, x, t x E = Emax ηµ π T λ t x B = Bmax ηµ π T λ (. ).., x. -7 «-». -, ( ) ( )., - - - -. -...,,. -, ( ) (.. )... ( amplitude modulation ). : ) - -. -. ) -. 58

... ( ) ( ) ( ).. - FM (frequency modulation) (..3)...3 ( ) ( ).. -.. -.,,.. -., ( ) LC (..4). - - ( ). -. -,. (..4. 59

),., -,.,.,,, - LC. To LC,. - C.,,....5 ( ), LC ( ) ( ) -. -. - (..5 )., LC.. ( ).. (..5 ). -, (.5 ). -,, 60

. (..5 ),...4 -. -. -8. -, -.. -. -.6,. -, - -6. c, c = λf - -. - -.. 0 5 m. -, LC,.. 30cm mm.. -...,. -,,. 6

..6... mm 7 0-7 m. -. -,.. -. 400 nm 700 nm ( 400 0-9 m 700 0-9 m)... : 700 630 nm 630 590 nm 590 560 nm 560 480 nm 480 440 nm 440 400 nm -., 490 49 nm. -. «580 nm» - 580 nm.,,. -.. - 3,8 0-7 m 6 0-8 m. -.,. -. 6

, - ( - )., -. -.,, -. ( Röntgen) 0-8 m 0-3 m. -., - ( ),. - ' -.. -. 0-0 m 0-4 m. -. -9.,..7, ( - ).., (..7 )., -,...7 ( ) - ( ) 63

,,. -, -,,.,...7 -...8. (..8). - ( ),, ( r ), :..8. - r -. = r.., -,.. r,. θ r = θ a., -, -,,. (..9). 64

(c), ( ) c n = υ (n)..., -, -.., - ( ) ( b ). ηµθ a nb = na ηµθ a = nb ηµθ b (. 6) ηµθ b na Snell ( ). (. 6) b (n b > n ),,,. - (b) (n b < n ),.,, -., =0, =0 (. 6) b =0. -. - b -. -, (f ),, -., -. ( c = λf )...9...30 -.. 65

..3. - c = λ f. υ = λf c λο = υ λ ο λ n = ο λ λ λ = ο n -., -..3. -. ( ),.,,.,...3 - - -,. -. -.., ( ). -, -.,..,,. 66

..9. -, 0 = 589 nm. -,309,333,5,36 ( ),66,50,434,544,00093,4 9,00045.3 = 590 0-9 m,,5. =30. : ). ). ). ). 8 c = 3 0 m / s. : ) c. c 4 c = λo f f = = 5 0 Hz λ o. - 4, f = 5 0 Hz. 67

) c c 8 n = υ = =,973 0 m / s υ n ). 9 υ = λf λ = υ = 395 0 m f ) Snell n ηµθ = n ηµθ a a b ( ) n a =, b - n b = n. o ηµ 30 ηµθ a = n ηµθ b ηµθ b = = 0, 39, n b θ b = 9, o - 0.33, - n. b n b...33, -. n >n b n > n b. Snell, na ηµθ b = ηµθ α (. 7) nb n /n b, b, θ b > θ a. - 90 - Snell b = b =90. 3.33. - ( ) crit. crit,. 68

-. 4.33. 4.,,,. crit - Snell. (. 7) b =90 - nb ηµθ crit = (. 8) n (. 8) n > n b, crit >,., ( ) (b) n > n b. -. a.. 0 - -., - 4,.,. 4 - ( ).,.... -...34 ( ).,..34..34-90.34 80 ( ). ( ) (..34 ) -. 69

.4 ( ) -. -,33. : ηµθ crit n = n n =. 33 b, n =. a ηµθ = 0, 75 crit b a b θ. o crit = 49,,., - - (..35)...35,., -...36 M. : ( ) - ( ) () - ( ) (3) (4) - (5) (6). - -,, -., - -. -..36,. -,. -., ',.37.,,. 70

-. -... -. -.,. - -., - ( - ), (..39),...37 - -..38,,...39 Newton, -,,. Newton -.,,...40 ( ).. -. -. - -. ( ). 7

.40. -,,, -, -.. -,, - (.40 ).... -... υ = λf t x y = Aηµ π T λ, - -. -. -,,. 7

- ( /)... ( ), - ( ).. /.. c.,. E = c, B,... :,,,,,. :,,. r n, (c),. c n = υ,, -., ( ) ( b )... ',,. 73

.... ( ) - ( ). -.4. ( ) ( ). ( ). -,...4...4 -.... 3. 3 mm,,.,,....43 74

. ). ). ). )...,..44...44 ) ; ) ;.3.45 ),, ) ; ) ; ),,, ). ). )..4 (, ),.. ; ). ). ) -. ) -..5..45 75

. ( ) y = 0 - (t-4x) ( ) y = 5 0-3 (4t-x) ( ) y = 0 - (t-3x) SI.. ;. - ;.6.46,, - x x...46, - ) ) ;.7 ;.8 :........9 ( ) y = 5 4x 0t ( ) y = x 0t ( ) y = 8x 5t. x y cm t s. ), - ; ) - ;. 0 - =3cm., 76

:, d = 8cm d = 6cm., r = 9,5cm r = 6,cm l =0cm l = 5,5cm.. ) ; ) ;..47. ) - ; ) ; ) ; ) - - ;..47., - ). ) /. ). )... 3 8,5 min. 8 c = 3 0 m / s. ; ( ). 4 ; 8 (R =6400 km c = 3 0 m / s ).. 5 ). ). ). ), -... 6-6 0 6 Hz. ) 5 0 6 m, ) 0 m, ) 5 0m, ) 0 9 cm; 8 c = 3 0 m / s. ( ) 77

. 7 -, - -. 0 3 Hz 0 7 Hz X 0 8 Hz 0 0 Hz 0 5 Hz 0 9 Hz. 8 - ) ; ) ; ) ; ) ; ( - 8 c = 3 0 m / s. ) ( ). 9 H ). ). )...0 ; ) E = 00 (6 0 0 t - 0 x) ) E = 50 ( 0 t - 4 0 4 x) ) E = 00 (9 0 3 t - 3 0 6 x) 8 c = 3 0 m / s. SI. ( ). ; -...48,. - 30 ;..48.3 - ; 78

..49.4., -, ;.5.50 -. ;.6. -, ;.7 -. -. -.,, ;..50..5.8.5,., d. d - 3 0 4, 0 4. ) ; ), - d;..5 79

.9. 0, 5 s. ; =, m ; [ : 0/6 z, m/s ].30 y = 3 0 ηµ ( 30t 4x) (SI). : ) ( ). ). ). ) 0. [ :,57 m, 330 m/s, 39,6 m/s, 0,53 m ].3 = 0 cm f=0,5 z. - =3 m/s. : ) B, x = 60 m. ) B,, t =,5 s. [ : 0 s, 5 cm ].3 : x y = 0,5 40 t x y cm t s. 3 ). ) ; ) t = 9/8 s cm x = 0; ) ; x x [ : y = 0,5ηµ π 0t, y = 0,5ηµ π 0t +, 3cm, 6 6-3,4 cm/s,, m/s ] 80

.33, -. = s. ) 0,5 s s. ) x =,5 cm. [ : cm ]..53.34 340 z -., -,., 0,5 m,. ) ; ). 0, m. - ; [ : 340 m/s, 850 Hz ].35 x. : y = 5 (5t x) y = 5 (5t + x) y x cm t sec. ). ) -. ) ; [ : ) 5cm/s ) 0cm ].36, 60Hz,. 0m/s... [ : m ].37 00 Hz. ) ; ) max = 0-3 V/m. ; ) - LC, 8

L=5 mh, - ; 8 ( c = 3 0 m / s). π 0. [ : 3 m, 4 0 - T, 5 0-6 F].38. n=,5 8. ( c = 3 0 m / s) [ : 0 8 m/s ].39. - 30. -. n =,33 n =,5. o [ : θ 30, ηµ θ = 0, 4375] r = b.40.. - 60 0 -. n b =,5, -. [ : 3 ].4 f = 5, 0 4 Hz - =4,4 0-7 m. -. c=3 0 8 m/s. [ :,33 ].4 650nm. ) ; ),4; ) ; c=3 0 8 m/s. [ : ) 4,6 0 4 z ) 464nm ), 4 0 8 m/s ].43 To,9 0 8 m/s. - ; c=3 0 8 m/s. [ : n=,56 ] 8

.44 n=,4.54. -, -. o συνϕ =,7 4 ϕ 45 ] 0 max [ : ( ) max.45-60 (..55). - - ; ( ). [ :,3 ]..54..55.46, =3 mm = 0,4 s., - x = 6 m x = 5,5 m. - =5 m/s. ; [ :, A = 3 mm - 0,4 s ].47.,, ( ) - -. -, -,,,, - d. -. [ : 4( H ) 4 + a + d + a H ]..56.48 h, n.. h [ : ] n 83

..57.49 d. - n. ) -. ) -. [ : συνϕ l = dηµϕ ] n ηµ ϕ.50 9 cm. -,,., -. -. n=,33. [ : 5,8 cm ]..58.5.59 -. x.,5 khz. - ( ).. ( x). x 0 =0,408m, x ( x > 0,408m ) - ; =340 m/s. [ : 0,544 m ]..59.5 (R) m -. - f, - h=50 m - D= km. h - 84

-. - ; -. c=3 0 8 m/s. [ :,5 0 9 Hz ]..60 85

O Hertz,, 887, - Maxwell, -.. 900 o Popov Marconi -., -., ',,, -,,,.... -... 60 km 350 km...,,.. : 000 m 000 m. T -.. : 00 m 000 m. - -. 0 m 00 m. -, 80 km. M, -. -..,,,,, -,.. 86

VHF UHF. VHF - m 0 m ( 0 MHz 300 Hz) UHF 0 cm m ( 300 MHz 30000 MHz). - o. ',,. : 0, mm cm. -. ( ). - ( ).,, (bandwidth). -.,...6, - 87

( ),..,,.., - ( ),. -.,,. hand-off.,., -., -. AMPS [Advanced Mobile Phone System, ( )] 800MHz, NMT 450 900 (Nordic Mobile Telephone 450 900MHz) - TACS [Total Access Communication System, ( )] - AMPS. AMPS Chicago, 983. - 666 30kHz, 83. FM. GSM [(Global System for Mobile communications, ( - )], IS- 36 (Industry Standard 36) IS-95 (Industry Standard 95). GSM -. 900, 800 900MHz. - 900 800 MHz. 00 khz.. TDMA [Time Division Multiple Access, ( - )], 8., 7. 8 -,. -. -,. 88

3-, - -. - ( ).,,. -.. ( ), - -. -. 3-. 3. H... 3.. -... 3. h gh. h : ρ : p = ρ g h ( ) ( ). df : p = da S.I. Pa (Pascal). Pa = N / m. 90

Pascal ( ),.. ( Pascal), 3.3,. - F F ( ). A,. F F. A :, -. h p = pat + ρ g h, Pascal.. 3. Blaise Pascal ( 63-66).., - -, -.. 3.3 ( ). - ( ),. 3- - w = 8000 N. - 3.4 ; r = 4cm r = 0 cm. : Pascal -.. 3.4 p = p = p (3. ) p = F / A (3.) p = F / A (3.3) 9

(3.3) (3.) (3. ) F F = A A F = F A A F w, = ( N ) ( 4 0 m) ( 0 0 m) π F 8000 = 70 N π 3.. 3-3 ( ) ( )... -... -.,. -. 3.5. -. -, - (. 3.5).. 3.6 - -., - (. 3.6).... 9

t V. V Π = (3.4) t 3 m / s. t x, V = A x (3.5) (3.5) (3.4) A x Π = t x t Π = Aυ -.. 3.7 t, x 3-4 ' (. 3.8).. m t m -. m = m (3.6) ρ V = ρ V V V - m m. V = A x = A υ t V = A x = Aυ t υ υ. (3.6) Aυ t = A υ t (3.7). 3.8, -. A υ = Aυ (3.8)... 93

. 3.9. 3- Π = Aυ (3.8) Π = Π Π = σταϑερ (3.9) (3.9) :. (3.8),.. -.., -. (. 3.9). 3 0,00 m / s. ) 3 cm ; ),, ; : 3 V V ) = Aυ υ = υ = 0,00 m / s =,4 m / s t A t ( 3 0 m) π 4 A ) A υ = Aυ υ = υ υ = (,4 m / s) =,84 m / s A 3-5 BERNOULLI ( ) -,,.., ( ). m -.. 738 Daniel Bernoulli. 94

(. 3. 0).,,. y. p. To y, - p., p A -, p A, p A. t s,, s.. 3.3 Daniel Bernoulli ( 700-78). -,. -. Bernoulli. Bernoulli -. - t. W + WB = K (3. 0) W. p A ( - ) p A ( ) W = p A s p A s (3. ) A s = A s = V W = ( p p ) V W B = m g( y y ) = ρ V g( y y ) (3. ),, m y y. K = mυ mυ = ρ V ( υ υ ) (3. 3). 3. 0 -. s s.. 95

υ υ. (3. ), (3. ) (3. 3) (3. 0) ( p p ) V ρ Vg( y y ) = ρ V ( υ υ ) V p + ρυ + ρgy = p + ρυ + ρgy p + ρυ + ρgy = σταϑερ Bernoulli. Bernoulli p, ( ) ρυ ( gy) ( ) ρ. Bernoulli. Bernoulli p + ρυ = σταθερ ( ), -.. 3.. -.. 3. 3- ; (. 3. ),, υ υ υ3 3,, ' ( ). 3, Bernoulli.3. 96

3. H -. -,. 3- Torricelli ( ) 3. 3. Bernoulli ( ) ( ): p ρ υ + ρ g h = p + ρυ + 0 (3. 4) E + E Κ K, :. 3. 3 p = p Κ = (3. 5) E p at υ E = 0 (3. 6) (3. 5) (3. 6) (3. 4) υ Κ υ Κ = gh Torricelli ( ). h h. 3-3 ;, -, (. 3. 4).. -. -,,,, -.. 3. 4 -,... 97

3-3 Ventouri. 3. 5., - h, -. :. 3. 5 Bernoulli p + ρυ = p + ρυ (3. 7) A A υ = Aυ υ = υ (3. 8) A (3. 8) (3. 7) A A p + ρυ = p + ρ υ p = A p ρυ (3. 9) A p = pat + ρgh p = pat + ρgh (3.0) h h. (3.0) p p = ρ g( h h ) = ρgh (3. 9) (3. ) A ρ gh = ρυ υ = A gh ( A / A ) (3. ) 3-6,.,. 98

'. 3. 6. l.. F. ( ),.. -, 0. -,,.,, l. -. F υ F = ηa (3.) l η (3.), S.I., N s / m. poise ( ) P = dyn s / cm. ( ). ( C ) ( s/m ) 0 3,0 0 00 3 0,3 0 37 3,7 0 0 3 830 0 ( ) 30 3 50 0 (3.). -. (3.)...,,.. 3. 6 -,.. 3. 7 - R. 99

. -... ( Pascal). - p = p gh t +..... A υ = A υ ( )., -. p + ρυ + ρgy = σταϑερ ( Bernoulli) Bernoulli.. υ F = ηa l η. 00

. -,... ;.. 3. 8.. ; 3. -.. ; ;. 3. 8 4. (. 3. 9).. -. ; h;. ;. 3. 9 Pascal 3. :... 3. ; 3.3 3.0. ) ; ).. 3.0 0

. 3. 3.4 3. ( ). F. ) ) ) ). ) F ) F ) F ) F. 3) o F ) F ) F ) F.. 3.5 :. -.. 3.6 H.. 3.7 3. ( m 3 /s). ;. 3. 3.8.. - ;. 3.3 3.9 -. ) 8 cm 3. ) 8 cm 3 ) 6cm 3 ) 3 cm 3 ) 4 cm 3 ) cm 3. ) 0 cm/s. ),5 cm/s ) 5 cm/s ) 0 cm/s ) 0 cm/s ) 40 cm/s.. 0

3. 0. ; Bernoulli 3.,,. ; 3.,.. 3.4 3. 3 ; 3. 4 h. h : ) A < A ) A = A ) A > A.. 3. 5. -,, ). ). 3. 6 : Bernoulli,..... - -. Bernoulli..... 3. 7 ; -.... 3.5. 3.6 03

Pascal 3. 8 To 3 cm 00 cm. 0000 ; [ : 50 ] 3. 9 - h =, 5m, υ =,3 m / s. ' υ = 0,3 m / s ; [ : 6,5 m ] 3 3.0 0,0 m / s. - ', cm. ; [ : 3,6 m / s ] Bernoulli 3. A 8,86 m/s. M atm; 3 3 5 ρ = 0 kg / m atm =,033 0 Pa. [ : 6,76 m/s ] 3. 08 km/h. ;. = 00 m., kg/m 3. 3 [ : 540 Pa, 54 0 N ] 04

3.3 -. =, cm =0,4 cm h=4 cm.. g= 0m/s. 5 [A :, 0 0 m 3 /s ] 3.4, h =, 8 m, A = 0,5 cm. - L ; g = 0 m / s. [ : 3,33 s ] 3.5 (. 3.7). = 0 - m = /. = 0 - m 3 /s.. - = 0 3 kg/m 3. [ : 6000 Pa ] 3.6 (. 3.8) = 0 m/s. To 6 cm 0 cm,. ) m 3 ; ) ; = 0 3 kg/m 3. 0 5 Pa. [A : 57,6 m 3, 8 kpa ]. 3.7. 3.8 3.7 5m. 0 cm =0 m/s.. - = 0 3 kg/m 3 g = 0 m / s. [ : 5kW ] 3.8,, (. 3.9).,, = m/s.. h= 0 m. = 0 3 kg/m 3, g= 0 m/s 0 5 Pa. [ : 8 0 3 Pa ]. 3.9 05

3.9 (. 3.30). To -. cm 3 /s cm, h. g= 0 m/s. [ : 4, cm ]. 3.30 3.30 (. 3.3 ) h. (x), ; [ : x=h/ ]. 3.3 3.3. h = m. 0 cm. : ). ). ) -. ). g = 0 m / s. [ : m / s, 0,8 m, 0, m, 0, 5 m ] 06

4-1,..,,.,, -, ( ),,,. -,. -.... 4. -.. 4-,.. -. -.. 4...,. (.4. ).. 4. ( ) -.. ( ).. 108

. -. -,. -., υ = ω r, r. -. 4.3 t 1 1 t =t 1 +dt - = 1 +d. 4.3 ( ) d.. t,. d = dt d rad/s. : α ( - ) a....,., ( )... 4.4.,,, cm (. 4.4 ), (. 4.4 ). -, 109

. cm (. 4.4 ).. 4.4 ( ) ( ) ( ). - ( cm ) - ( )... 4.. -... -. 4....... 4. -. -.. (cm), -....,. 110

.,.,,.. 4.3.. H (. 4.5).., dt ds, ds, d. H cm ds υ cm = (4.1) dt ds d θ = ds = R dθ R dθ dθ (4.1) υ cm = R, = ω, dt dt υ cm = ω R (. 4.6).,.. cm, dυ d υ cm = ω R o cm ω = R dt dt. 4.5 ds,. a cm = α R a cm α. 4-3. 4.6 : a cm R = α 111

. 4.7 H -. F... ( ),.. ) z z. F. F, l ( ). τ =. m... Fl. 4.8 F -. F -, (. 4.9).,,. -.. 4.9 F F x l 11

4.10 F 1 F. T. = 1 + = F1l 1 Fl ) ', ( - ). -, - ( )..,. ( ) -... F. 4. 0 F 1 F. H -. τ =. - F F. -. d, (. 4.1) x 1 F x F, Fl. 4.. τ = F1 x1 + F x = F1 ( x1 + x ) = F1 d τ = F d 1.,. 4. F F.. 113

4.1 4.13, R 1 =4 cm R =3 cm, x x. x x., F 1 =6 N F =10.. :. 4. 3 F 1 τ 1 = F1 R1. F τ = F R. τ = τ 1 + τ = F1 R1 F R = 0, 06 N m. 4. 4.14. x 1 =5 cm x =8 cm. F 1 =50 N F =40 N. F = 30. ; :. 4. 4 F 1. τ = F x, 5Nm 1 1 1 = F F x F y F x =F 30 F y =F 30. F x ( F x ), F y τ = F 30 x = 1, 6Nm. τ = τ + τ 1 = 0,9Nm H,. 114

4-4..,,.,,. -...,,.,,., ( ). - ΣF = 0 ΣF x ΣF y = 0 = 0 Στ = 0 4.3 l= 4m w 1 =00N,. x= 1m w =600 N. ; : (w 1 ), - w - 1.. 4. 5 F=0 1 + -w 1 -w =0 (4.),... l Στ Α = 0, T l w1 w x = 0, w l w x T 1 + = = 50N l (4.) T1 = 550N 115

4.4, l w=400 N,.. - =30.. : 4-5. 4. 6. x = 30 y = 30 F x =0 30=F x (4.3) F y =0 30 + F y =w (4.4) Στ = 0 l T ηµ 30 l w = 0 (4.5) F F y T. x (4.5) x (4.3) (4.6) (4.4) F T ηµ 30 = w T = 400N (4.6) F x = 00 3N F y = 00N F = Fy 3 εφθ = = F 3 x ( Fx ) + ( Fy ) = 400N ο θ = 30 zz (.4.17). m 1, m.,. m 1, m, r 1, r. 4. 7 To.. I = m1 r1 + mr +... 1 kg m. 116

. -.. I cm I p p, d -,, Steiner ( ). I cm,, d o - d. I = I p cm + Md. 4. 8 - d 117

4.5 R,. :. 4. 9 m 1, m. m 1 + m + =M R, R. I = m1 r1 + m r +... = m1 R + m R +... = ( m1 + m +...) R I = MR 4.6, m 1 m, (m 1 = m =m),, l., - ) ) m 1 ; : ) ) l l l ml I = m1 + m = m = I = m1l + 0 = ml. 4.0 4.7, - R,,. :. 4. I cm = MR / d=r I = I MR 3MR + Md = + MR p cm = 118

4-6, Σ F = m.., '. ( ) ( ) Σ τ = Iα (4.7),, ( ).. 4.,, m. (4.7) -.,,,.., (4.7),,,..., -,. -,,. 119

4.8 =40 kg R=40 cm,., F=6 N.,,. ;. 4.3 1 I = MR. : τ = FR 1 τ = Iα FR = MR α α α F MR 6N 40kg 40 10 = = = 0,75 rad / m s 4.9, R,,,. m.,. :. m, mg.. 4.4 mg T = ma (4.8) cm ( ), F ( ) Mg. g F. - τ = Iα TR = Iα (4.9) 10

(4.8) T T = mg ma (4.9) mgr mracm = Iα (4.10) a a = αr acm a cm = αr (4.11) (4.10) mgr mr α = Iα mgr α = (4.1) I + mr (4.11) a mgr = cm I + (4.13) mr (4.1) (4.9) I I mgr I mg T = α = T = R R I + mr I + mr 4.10 To -,.,, xx.. 1 I = mr - g.. :. 4.5 mg T. : Σ F y = ma cm mg T = macm T = mg macm (4.14) xx Σ τ = Iα TR = Iα (4.15) (4.14) (4.15) mgr mracm = Iα 1 1 mgr mra mr cm = α g acm = R α (4.16) a cm = Rα a α = cm R 1 g (4.16) g a cm = acm a cm = 3 cm 11

. 4.6 m.. 4-7 H..,,,. ) m p - r (. 4.6). z z L = p r L = mυ r z z. kg m /s.. 4.7 m 1 m -. ) 4.7 - z z.. -,,., m 1, m.,., L 1 = m 1 1r1, L = m r,. -. L = m1 υ1 r1 + m υ r +... m 1, m 1, υ 1 = ω r1, υ = ω r... ( m r + m...) L = m ω r + m r +... = ω r 1 1 1 1 + r + I m 1 r1 + m... =. 4.8 - z z.,. L = Iω (4.17) -. 1

,7 10 40 kg m /s 5,8 10 33 kg m /s ( =90km/h) 10 kg m /s - (33 min) 6 10-3 kg m /s 1,05 10-35 kg m /s 0,53 10-34 kg m /s -,.,,. -, - 0,53 10-34 Js. 1, =1,05 10-34 J s ( ). ), - -. L, L,.., L L=L +L + 4.17 dt d, - dl = I dω dl d = I = I dt dt (4.7) dl Στ = (4.18) dt, Newton. 13

O. -,,,.. Newton ( - )... 4.18 dl Στ εξ = (4.19) dt τ L εξ. 4-8,.., dl dl Στ = = 0,, L = σταθ. dt dt., ( ),,,. - 4.. 4.9 -. ewton dl Στ εξ =. dt,.. 14

, ( ),,. : I ω = I 1 1 ω -. 4.4 -,.,, -., - -,, I ω.,, I ω,..,,,,.,. 4.30,,.. 4.4.. 4.30 -. 1,4,5, - pulsars.,,, 15-0 km. 15

- -. 3000., 5. 4.11 4.31, =4 kg., 1 =4 rad/s. ;,,, -. ( ) 3,5 kgm,5 kgm. 4.3. 1 m, 0, m.. : I 1,,. I1 = I1 + I1 = I1 + MR1 = 11,5kg m I,. I = I + I = I + MR =,8kg m,. : I1 I 1ω 1 = I ω ω = ω1 = 16rad / s I 4-9 16

. 4.3 4.3,, z z,., m 1, m... υ 1 = ω r 1, υ = ω r, (4.0), 1 1 = m1 υ1 + mυ + K..., (4.0) 1 1 1 K = m1 ω r1 + mω r +... = ( m1r1 + mr +...) ω m 1 r1 + mr +... = I 1 K = Iω. -., 4.33 -. 1 1 K = Mυ cm + Iω M υ cm.. 4.33 4-10 -... F R, (. 4.35). d θ 17

. 4.34 F d. - F ds=r d. dw = F ds ds = R dθ dw = F R dθ FR. dw = τ dθ (4.1) - dθ1, dθ...., 4.35, W = τ θ (4.1) dw dt dθ = τ dt dw / dt P d θ / dt ω, P = τω.,, - W = 1 1 Iω Iω 1. 18

4.1 L=0,3 m M,.. ; - g=10 m/s. 1 ML 3 :. 4.35... L Mg,. 1 ω I, I L 1 L 1 1 Mg = Iω Mg = ML ω 3 3g ω = = 10 rad / s L 19

4.13 R. h. H (g). 1 I = MR. :..,.,,.,. 4.36, Mgh., 1 M cm 1 I. 1 1 1 1 1 Mgh = Mυcm + Iω Mgh = Mυcm + MR ω 1 1 gh = υcm + R ω 4 (4.) cm υ = (4.3) (4.) (4.3) 1 gh = cm ωr 1 υcm υ cm + R 4 R 1 1 4 gh = υ cm + υcm υ cm= gh 4 3 AN I 130

x dx υ = dt d = dt F m ΣF = m p=m ewton dp ΣF = dt F =0 p= 1 K = mυ dθ ω = dt dω α = dt Στ = Iα L=I ewton dl Στ = dt =0 L= 1 K = Iω 131

dω o. α = dt F, τ = Fl l, -. 1 m. F τ = Fl l, 1 m,. ΣF = 0 ΣF x ΣF y = 0 = 0 Στ = 0 - I = m1 r1 + mr +... Στ = Iα - - L = pr L = mυ r. 1kg m /s. - -. L = Iω. dl Newton Στ = dt 1 K = Iω W = τθ P = τω To - 1 1 ΣW = Iω Iω1 13

... 4.37..,...... 4.38,.. ( ) - (. 4.38 )....... 4.38. Mgx mgd = 0 Mg α ηµθ mgα συνθ = 0 m = Mεφθ 133

, - m. 3.,..,. 4.39 :,.. ; 4.1. 4.40,,, ;. 4.40 4.. ; 4.3. 4.41 ; ) t 1 -t.. 4.4 134

) t 4 t 1. ) t 1 t 4. ) t 3 t 1. 135

4.4. -. ) ) ) ), ; 4.5,, - ; 4.6. - ;. 4.7 :,...... 4.8 -. ; 4.9 4.4. -. -.. 4.4. 4.43 4.10 4.43 -. F 1. F. ) F ; ) F 1 F. 136

4.11 4.44 -. F 1 F.. - F 1 /3. F ) F 1 / ) F 1 /3 ) F 1 /3 ) F 1 ) 3F 1 / ) 3F 1.. 4.44 4.1 4.45 m., ). ). ). ). 4.13,,. ;.. 4.45 4.14 4.46 z z.. z z.. 4.46 4.15. ; 4.16 1,, 3 4 1,, 3 4 (.4.47). 4.47 137

4.17 - ). ). ). ).. 4.18 4.48 -.. 1. -. - ; -.. 4.48 4.19 4.49. F. F 4.49. 4.49 ; ). ) t 1, F. ). ) F.. 4.50 4.0 (. 4.50).,. ). ). ). 138

- 4.1,. ; 4. 4.51.,,,. t.. 4.5 4.3 ). ). ). ).. 4.4. -. ; ). ) ). ). 4.5,. ;. 4.6...., ; -,, - -. ; 4.7 1 (. 4.5),. 3 1. - : ) ) ) 3 ) / ) /3.. 4.5 139

4.8... 1.... 4.9 - F : ) 1 rad/s 3 rad/s. ) 4 rad/s 6 rad/s. ) - rad/s 5 rad/s. ) -3 rad/s 4 rad/s. ; 4.30,. -.. - 10 J 40 J 0 J 80 J 4.31 : 1 SI rad/s rad/s L m 1. 140

4.3, 4.53. ; 0 rad/s; [ : 0,5 rad/s, 7 s ] 4.33 0 m/s. 40 cm.. [ : 50 rad/s ]. 4.53 4.34, r = 40cm, m/s. ; [ : 5 rad/s ] 4.35 8cm. 5 m/s. : ). ). [ : 10 m/s, 9,9 z ] 4.36 o, R=0 cm,, =8 m/s. x=0 m. ; [A : 8rad/s ] 4.37, 0cm. 00. ; ; [ : 40 m ] 4.38 4.54 R= 0,5 m -. F 1 =0N F =30N. - ; [ : 5 m ]. 4.54. 141

. 4.55 4.39 H 4.55 '. F 1 =0N, F =N F 3 =10N.. : x= m =30. [ : 16 m ] 4.40 R 1 =0 cm,, R =0,5 m., ( ) 150.. [ : 60 ]. 4.56. 4.57 4.41, l= m, - w 1 =00 w =300 N (. 4.56). ; [ : 1,m ] 4.4 4.57 l=4 m w 1 =150 N. H 1 m,. w =700 N. ; [ : 79 cm ] 4.43 l w 1 =100 N - (. 4.58).. =30. w =40 N.. [ : =180, F=163,7 N, =0,3 ]. 4.58. 4.59 4.44 (.4.59). 6m 100kg.. L, 1, I = ML 1 [ : 4800 kg m ] 14

4.45, = kg R=0,5 m, =100 rad/s F,. 5s. : ) ( ). ) F. 1 I = MR. [ : = 0 rad / s F = 10N ] 4.46, L=1 m, (.4.60).,,, ; 1 I = ML g=10 m/s. 3 [ : 15 rad/s ]. 4.60-4.47, m=100 g, 4.61. - =16 rad/s, z z.. l=0,8 m. [ : 5,1 kg m /s ] 4.48 = kg R=0,4 m, =10 rad/s.. [ : 3, kg m ]. 4.6 4.49 0 cm 1 kg Hz. 100gr, 10 cm.. 1 I = MR [ : 1,9 Hz ] 143

- 4.50 =3 kg L=40 cm =10 rad/s.. 1 I cm = ML. 1 [ : 8 J ] 4.51 =8 kg R. =5 m/s. -. 1 I = MR. [ : 150 J ] 4.5 4 m 50 z. ; [ : 400 W ] 4.53 m=40 kg R=0 cm, 5 z. ) ; ) 5s. 1 I = mr π 10. [ : 400J, 80W ]. 4.6. 4.63 4.54 H 4.6 L= m = 3kg,. F=10 N. F. : ) F,. ). ) ( ). 1 I = ML. 3 [ : W=40 J, =7,9 rad/s, P=158 W ] 4.55 H, l=30 cm, (. 4.63).. 144

,. ml I = g=10 m/s. 1 [ : 3 m/s ] 4.56 l w=100 N 4.64.. =60. [ : T = 50 3N, F = 50 7N, = 3 / 3 ] 4.57 4.65 h R w. F. h(r h) [ : F > w ] R h 4.58 400 (. 4.66) 30... [ : 3 / ] 4.59 R=0,33 m 1 kg. 100 -. 5 s. -, 0,69.. ( ). [ : 1 ] 4.60 4.67. L=1 m =0,6 kg. r=0, m m=0,1 kg,. f 1 =10 z.,,.. 1 I = ML. 1. 4.64. 4.65. 4.66. 4.67 145

[ : 5,8 z ] 4.61 5 m/s. 30...,, [ : 3,5 m ] mr. g=10 m/s. 5 4.6 30.,, I = mr 5 g=10 m/s.. [ : 5/7 m/s ]. 4.68 4.63 4.68 m= kg R. 1 m 1 =3 kg, m =1 kg.. 1 I = mr g=10m/s.. : -. [ : = 4 m/s ]. 4.69 4.64. 4.69 00 gr 30 cm 40 rad/s.. 15 cm; ( ). [ : 43, J ]. 4.70 4.65 O 4.70 0,18 kg m =5 rad/s... [ : 4,5 kg m /s ] 146

4.66, 0 cm, -. 0 -. f=4 Hz.. 1 I = mr. [ : 50 kg ] 4.67. ; 1 I = mr. [ : > εφϕ / 3 ] 4.68 m=10 g R=1,5 cm, (. 4.7).,. ), ) 30cm.. 1 I = mr. g=10 m/s. [ : ) 6 10-3 kg m /s ) m/s ] 4.69 m r,, 4.73., h ; R=0 cm. I = mr. 5 R. [ : 54cm ] 4.70 1, d. 1, 4.74.,.. 4.7. 4.7. 4.73. 4.74 147

[ : d π ] µ g 148

4.71 m= kg (. 4.75). -.. =8,4m/s.. =11,5 kgm R=1, m. [ : 1,75 rad/s ]. 4.74.. ( ), AB ηµφ C =. C., ( ) ( ),. C,. C :. 4.76 ( ), C. C, -. 149

x, A y, A z, - B x, B y, z,, i j k C = A B = i, j k x, y z,. To A B = B A A B F = r F (4.4) r F. r F.. 4.77 To τ = rf ηµφ (. 4.77 ) r ηµφ = d d, F, τ = Fd (4.5) - F r. (4.4) (4.5) -, (4.4)., L = r p = mr (4.6) r. 4-7. (4.6). 4.78.,,. -.. x x A B y y A B z z 150

(4.4) (4.6).,,. ( Lorentz) : F = q, -. -. -. ( ). -, -, ( ). -, -.. 4.79 -,, - (4000 /min), - 450 km/h. -.. -, -,, 1. 1. 151

.. - ( ) (. 4.80)., ( - )., 1 1 - R (. 4.80). 1 ( ) 1 1 ( R E1 ). - ω 1 R 1 = E 1 ω R Ε1 1. 4.80 1. 1 1 1 (. 4.81)., -.,, -.. ( τ = F l).. 15

.4.8 -., (. 4.80). R =. R E 1. /3, -. -.,, -,...,. - (. 4.80)..... 153

. 4.8 (. 4.8 ).., -. 154

5-1,,,. -., -, -.,, -. O,,., - ( ).,.,.,., -,.. 5.., - -.. Doppler,, -,,. 5-15

, - (. 5.1),. - -,. - -. ( He) ( ),,, -.. -,.,,,, -. (. 5.).. 5... 5.., -,., ( ) -., - ( ) (. 5.3).. 5.3., (. 5.4 ). 153

(. 5.4 ).. 5.4 ( ). ( ).. 5.. 5.3 -.,,.., -.,,., -,. p p, : p = p. -, -., - -. :. 154

.,. -.,... 5-3. 5.4 -. 1 m 1 m, 5.5.. - -.. 5.5 : m1υ 1 + mυ = m1υ 1 + mυ ( ) (5.1) 1 1 1 1 m 1 1 + m = m 1 1 + m ( ) (5.) (5.1) m υ υ = m υ (5.3) ( ) ( ) 1 1 1 υ (5.) m υ υ = m υ (5.4) ( ) ( ) 1 1 1 υ (5.4) (5.3) υ + υ = υ + (5.5) 1 1 υ (5.1) (5.5) 155

υ m υ m m υ 1 1 = + 1 (5.6) m1 + m m1 + m m1 m1 m υ = υ1 + υ (5.7) m + m m + m 1 1 : -. - 1. m 1 = m (5.6) (5.7) υ = = 1 1 υ. ( =0) (5.6) (5.7) m m = (5.8) 1 υ 1 υ1 m1 + m m1 υ = υ1 (5.9) m + m 1. 5.6 - -. 5-4 1 (5.8) (5.9) υ = 1 υ 1 υ = 0. -. (. 5.6). 156

, ( x ) - ( y ) (. 5.7). ( x = - x ). H, y ( y = y ). x y υ = υ + υ = υ + υ = υ x. y,, υ y υ y ηµ π = ηµα = υ υ υ y = υ y υ = υ ηµ π = ηµ α π = α.. 5.7 - -. 5.1 m=0,0 kg =00 m/s =0,98 kg. ), ), ). µ K = 0,5. : ) V.. 5.8 p p. p = p (. 5.8), :. m m υ = ( M + m) V V = = 4 m / s M + m 157

) K K 1 1 = m ( M + m) V = 39 J ) - K + W W WI ( M + m) V µ K ( M + m) gs = 0 V s = = 1,6 m g αρχ w + n + = K τελ 1 K 5. m 1 = kg m =3 kg 1 =10m/s =5 m/s. -. : V. p p p = p V V x x V y y (. 5.7).,, ι px = p m x 1υ 1 = ( m1 + m ) Vx p = p ι p = p m υ = ( m + m ) V y y m1υ 1 mυ V x = = 4m / s V y = = 3m / s m1 + m m1 + m V y 3 V = ( Vx ) + ( Vy ) = 5m / s εφθ = = V 4 1 y x. 5.7 5-5 -..,..,., -. 158

. 5.9 - -.,. -.,.,., ; -.,. -...,, Newton ( ). -, Newton.,,, -.. 5. 0 -... 159

ewton... 5. -,. - ewton. -. 5-6..,, +.. 5. -, - -.. 5. 3 - - x y.. - (x, y, z)...., ( ) -.,. 160

-, ( ),. - -. - u. - t=0 u Ox (. 5.14). t, x, y. - x, y.. 5. 4 x = x + ut y = y,. υ, υ (. 5.15). x y. 5. 5 -. x = x + ut ρα x x t = + u υ x = υ x + u t t t y = y ρα y y = υ y = υ y t t 161

u x, u u, u (.5.16). x y. 5.5 (1564-164).. -.. 5. 6 x = x + u t x y = y + u t y διανυσµατικ για την ταχ τητα υ = υ + u x υ = υ + u y x y = + u. x y = + u u = + t t t u u = 0 t (5.10) = t t = (5.10) F = m F = m F = F,, -, u.,.., -. 16

5.3 u. (.5.17). ; : - = + u. = + u. 5.4. 5. 7 - (.5.18). - ; : - = + u = u.. 5. 8 5.5 x'o'y' 5.19. : - = + u = υ u.. 5. 9 5-7, -... 163

; m, m.. x i, y i, z i - m i, - x cm m1x1 + mx +... + mnxn = m + m +... + m y cm 1 mi yi = M n mi xi = = m z cm = i m z M i i m x M i i.,, m x + mx m 1 1 x cm = m1 +. 5.0 x x ' x (.5.0). Newton dp F = M cm = dt Σ εξ. 5.6. F -,, cm p. -. ( F =0).,. 164

... 5.6 (1,0), (3,0) (,5) (. 5.1). m, m 4m. : x y mi xi mx / 1 + mx / + 4mx / 3 1+ 3 + 4 16 = = = m = m = m M m/ + m/ + 4m/ 8 8. 5. cm mi yi = M 0 + 0 + 4 5 0 = m = m =, 8 8 cm 5 (,,5). m 5.7 0. (.5. ). (.5. ). ; :. 5. -., 165

5.8 l = 0, 5 m. m1 = 0, 001kg m = 0, 00kg q q. m1. : - m 1 x (. 5.3). - m1 x 1 = 0 m x = l.. 5.3 m1 x1 + m x x cm = = 0, 33 m m1 + m.,., 0,33 m m 1. 5-8... - ( ).. 5.7 -. -. ( ) -, -. x. M + dm., 166

dt, - dm u. d - dm. d. (. 5.4).. 5.4 -. p = 0 = dm u + Mdυ πριν p µετ. Md υ = dmu dυ dm M = u dt dt dm Ma = u dt dm F = u dt dm. dt 5-9 DOPPLER, - ( ),, -,.. - -. - -.. Doppler. 167

-. 5.5 ( ) S f S. f S = υ λ. 5.5.. f A., f f = υ λ. A = S -. 5.6 - (. 5.6).. υ +υ Α. υ + υ A =. υ λ = f S υ +υ A f A = f S f A f A υ +υ = υ f υ ( )., - υ υ A f A = f S υ ( ). S A λ υ ±υ A f A = f S υ (+) (-). - 168

S - (. 5.7). -. - -.. - ( ). t t+t - υ.. - S T λ υ s T.. υ υ s υ υ s λα = λ υ s T λα = = f s f s f s υ υ f A = = λ υ υ Α s f υ f A = f S υ υ S. - S (. 5.8), υ. T s υ f A = fs υ + υs -. υ f A = f S υ υ S (-) (+). s. 5.7. 5.8 -. υ ± υ A f A = f S υ υ S. 5.8 169

. Doppler,. Doppler -.., Doppler,. Doppler -.,...,,. ( ) ( ). -. 5.9 50 m/s, 400 z,.. -. 343 m/s. :, υ f A = f S υ υ S υ f A = f S υ + υ S 343m / s f A = 400 Hz = 468 Hz 343m / s 50 m / s 343m / s f A = 400 Hz = 349 Hz 343m / s 50m / s + 170

5.10 140 km/h 500 z., 110 km/h, ) ) ; 343 m/s. : 140 km/h = 39,9 m/s 110 km/h = 30,6 m/s υ + υ A f A = f S υ υs 343m / s + 30,6 m / s f A = 500 Hz = 616, 3 Hz 343m / s 39,9 m / s υ υ A f A = fs υ + υs 343m / s 30,6 m / s f A = 500 Hz = 408 Hz 343m / s + 39,9 m / s.,... ewton.. ewton -. 171

-. u. H,,, : x = x + u xt υ x = υ x + ux = y y + u t υ =υ + u F = F = y y y y mi xi mi yi xcm = ycm = M M z cm = m z M i i.. -. dm F = u dt u. dm dt Doppler. - υ ± υ A f A = f S υ υ S -,. 17

. - ( ).,,., - 5.9. -. ;. 5.9. :, -, -,,,., -. -, 5.30..,.,... 5.30 3. Doppler :,.. -. ; -. ; ;. 5.9 Doppler! 173

5.1 ; ; 5. : m 1 = kg m =3 kg, -, - 1 =3 m/s =3 m/s...kg m/s.. kg m/s... kg m/s kg m/s. 5.3 ; ). ). ).. 5.4 ). ). ). ).. 5.5 ). ). ).. 5.6 υ 1 =10 m / s υ = 0 m / s. 1 υ1 =16 m / s ; ; 5.7,. ). ). ). ).. 5.8 ; 174

). ) -. ) -. ) -,. 5.9 m. -. : ) 0; ) m /; ) m ; ) m ; 5.10,. -. 5.11 ; ) ). ). ). 5.1 ). ). ). ) Newton.. 5.13. u,. ; 5.14 u. ( ),. ; 5.15,, m. - u, -, m. - : 175

) ; ) ; ) ; ) ; ) ; ) ; ) ; 5.16, - ;. 5.17 ;. 5.18 ). ). ). ).. Doppler 5.19 Doppler ). ). ).. 5.0 5.31... 5.3 5.1 -.. 176

) ; ). ;, ; ). ;, ; 5. m=0,4 kg 1 =400 m/s. M= kg, =300 m/s., 0,5. : ),. ). ). g=10 m/s. [ : 0 m/s, 13.600 J, 40 m ] 5.3 m =1 m/s -. -. [ : 6 m/s, 6m/s ] 5.4 m1 = 10 kg m = 0 kg υ 1 = 3 m / s υ = m / s,,. -. [ : 0,33 m / s, 98 % ] 5.5 (1) m1 = 1 kg υ1 (). (1) υ 1 = υ 1 / 3. m () ) υ 1 υ 1. ) υ 1 υ 1. [ : 0,5 kg, kg ] 177

5.6 m 1 = kg 1 =4 m/s - m =4 kg - =5 m/s.. [ : 8 m/s, 1 m/s ] 5.7 m 1 υ 1 m. m 1 m m ; [ : m 1 = m ] 5.8. ) - ( 1 1 H ), ) ( 1 H ) ) ( 4 He) ;. [ : 100%, 88,9%, 64% ] 5.9 m1 = 6 kg m = 4 kg, -, υ 1 = 8 m / s υ = 9 m / s,. : ). ). [ : 6 m/s, =3/4, -174 J] 5.30 =5 kg. m=50 g 1 =50 m/s =80 m/s. l= m. ; g=10 m/s.. [ : 60 ] 5.31 =0 km/h. 5 km/h., - 4 km ; [ :,56 h ] 5.3 O 400 m/s, 300 m/s. ; [ : 500 m/s, =4/3 ] 178

5.33, m= kg - x, =6 m/s - M=4 kg. ) -, -. ) x u= m/s,,. [ : m/s ] 5.34 0 kg, 0 kg, 30 kg ( 1, 1), (, ) ( 3, 1) xy. -. 15 9 [ :, ] 7 7 5.35.. - -. 4 30 mγ = 5,98 10 kg, mη = 1,99 10 kg, 8 RΗ = 6,96 10 m 11 d = 1,49 10 m. [ : 4,48 10 5 m ] 5.36 M=10 kg s=6 m m=60 kg. N -.. [ : m ] 5.37 dm / dt = 140 kg / s u = 1000 m / s. - M = 10 ton. [ : 140.000, 14 m/s ] 179

5.38 4000 kg,. - 1500 m / s. kg 15 m / s. [ : 40 kg / s ] Doppler 5.39 ; 340 m / s. [ : 34 m / s ] 5.40,,, f 1 =500 Hz., f =450 Hz. ; 340 m/s. [ : 17,9 m/s, 473,7 Hz ] 5.41.,.. 5.3 5.4 m=50 g =00 m/s =950 g (. 5.3). =10000 /m. : ) ). [ : 0,1m 95% ] 5.43 m=0 g =1 kg 1 m. =60. N. g=10 m/s. [ : 55 J ] 5.44 m 1 =0 kg =30. m =30 kg -, =10 m/s. 180

3 / 3.. - ; g=10 m/s. [ : 1,8 m, ] 5.45, s=4, m =30 - m=1 kg,. s 1 =1,6 m -. -. : ). ). g=10 m/s. [ : 5 3, 13 34 J ] 5.46 M ( ).. m.,. M, m. H. m [ : H ] m + M 5.47 m 1 m =m 1 x=1 m (. 5.33).,, -. =0,5. : ). ). g=10 m/s. [ : 10 m/s, 4 m ] 5.48 =00 /m, =30, 5.34 m =1 kg. l=4 m m m 1 =m /3. m 1 m. N m 1 m. g=10 m/s. [ : 1m, 5 10 1 m ]. 5.33. 5.34 181

. 5.35 5.49 5.35 m =4 kg. 1 m =950 g. 1, =0,5. 1, m B =50 g =100 m/s. 1. ) 1, ; ),, ; ) 1 ; ) 1 ; g=10 m/s. [ : 1 m/s, 48 J, 0,8 s, m] 5.50 1,. ; υ [ : εφ ϑ = ] υ1 5.51 d = 400 m 540 Hz. 603,5 Hz. -. 340 m / s. [ : m/s ] 5.5 8 km/h 400 z. 54km/h,.. 340 m/s. [ : 415 Hz ] 5.53 1000 m, 1500 m,. 360 Hz 340 z.,.. [ : 355 z ] 18

DOPPLER -. 0.000 Hz.. MHz.,. (.., -..) (.. ).. 5. 0 Doppler. ( ). RA=, LA=. Doppler.,,.. -, -. - - Doppler. 183

υ συν θ fδ = ft c f t,, c., Doppler., -, ( <0 )., -.,, -.,. -. Doppler - ( ).. 184

6-1 1905, Albert Einstein,. Brown ( )., 191, ( )... 6. H, -,. -., -.. -,..,,. -, Lorentz, Einstein,.,, -.. (, - ).. 6. 1915 Einstein -..,. Newton -.. Grossman ( ) - (,, - - ). 1919,. - -,. 186

6- MICHELSON MORLEY Einstein,,,.,,., +, - -., -,.. 6. - + - -. 1887,...,.. Michelson ( 185-1931) E.W. Morley ( 1838-193).., -,. Michelson Morley -..,,.. 6.3 Michelson (185-1931)..... 6. ( ) Michelson. ( ). ( ). 187

(. 6. ), ( ), - ( ) ( 1, ) - ( ). ( - ). (. 6.3), 1. : 1 -. 6.. 1.. 6.3 o Michelson., 1,, L.. -. 3 υ = 30 10 m / s. c + υ c υ. (. 6.4). 6.4 1,, (.6.4). c υ L L L L t1 = + + + c + υ c + υ c υ c υ 188

1 t L = + c + υ t = t 1 t L L + + c υ c υ L L = + c + υ c υ c L L c υ υ c L υ. 90... -,. Michelson Morley 1905 Einstein. 6-3 Einstein... -.. - -., -.. Michelson Morley..,.. -.. -, Michelson. 189

6-4...,.. -. -..,,,,. 6-5 u -. -,, - (. 6.5).. 6.5 ( ) -,. ( )., -, d t0 = (6.1) c -., - - s = u t., -. l u t l d. = + 190

. u t d + l t = = (6.) c c ; (6.1) (6.) t d : t0 t = (6.3) 1 u c t t0, -. ' '....,.,,... -,, -,,,. - -.,,. 6.1 u = 108 km / h = 30m / s.,,. t 0. ; : 1 (6.3) t = t0 0,99999999999999 t t0. -. 191

,. u = 0, 5c t = 1,155 t0 u = 0, 9c t =,94 t0 u = 0, 99c t = 7,089 t0.. 6.4 CERN - -. -,. - -.. 197, - 13 1 /10 s... 9 10 s (1 ns). -. ( ) - 6. τ 0 =, 10 s -. (0,99c)., - 600 m.. -. τ 0 6 τ = 16 10 s. 1 ( 0,99c) / c 0,99c 4800 m.,,,. 1976 ï (CERN),, 0,9994c. 30,. 19

6-6,, (. 6.5).. 6.6 ( ) -, -. ( )., - u t 1 (l). -.. l0 t0 = (6.4) c l 0.,, d = l + u t1 d = l u t l.. d = c t 1 d = c t l + u t1 = c t l u t = c t 1 193

l t 1 = c u t l = c + u - : t = t + t 1 l l = + c u c + u l t = (6.5) c ( 1 u / c ) (6.3), (6.4) (6.5) u l = l 0 1 (6.6) c. 6.7 ( ). ( ) u=0,8c. ( l) ( l 0 ). -. ( l0 ), -.. - (. 6.7).,.,. - -. 194

6. u = 108Km / h (30m / s). -,, 5 m. ; : (6.6) u l = l0 1 = (5m) 0,99999999999999 = 5m c, l = l0 -. - u = 0, 5c 5 m. ; u l1 = l0 1 = (5m) 0,866 = 1, 65m c u = 0, 9c l = l0 0,436 = 10, 9m u = 0, 99c l = l 0,141 3, 55m 3 0 = 6-7 LORENTZ, ( ) u ( ). " " -.,. x t=0 (.6.8). (x, y, z) (x, y, z ). x x = ut + x'. x,. 195

. 6.5 H. A. Lorentz (1853-198), -. Lorentz - 1890, Maxwell. Einstein - 1905. x. Σ x = ut + x'. Σ x Σ x Σ =. 1 c u x x (6.6) u x = ut + x 1 (6.7) c x ut x x = (6.8) u 1 c, y = y (6.9) z = z (6.10) y z. 6.8 - ( x, y, z, u, t). -. u - u. (6.7). - (6.7) - u -u, u x = ut + x 1 c x (6.8) t t ux / c t = (6.11) u 1 c (6.8), (6.9), (6.10) (6.11) Lorentz., ( ). 196

x = x ut u 1 c y = y z = z t ux / c t = u 1 c x + ut x = u 1 c y = y' z = z t + ux / c t = u 1 c u c Lorentz x = x ut, y = y, z = z, t = t,. x ' t t x... - ( x 1, y1, z1, t1 ) ( x, y, z, t ). - ; Lorentz ( ) 1 t 1 + ux 1 / c t1 = u 1 c t + ux / c t =. u 1 c - t + u x / c t = t t1 = (6.1) u 1 c t = 0, u x / c t = 0 u 1 c. 197

c t. 6.3 680 m/s ( ). 0 m. O,. ; : 16 u x / c 680 0 / 9 10 t = = = 0,00000000000015s u 680 1 1 16 c 9 10. 6-8 M LORENTZ ', x. t x. - t x.,, u x. x ut t ux / c x = t = u u 1 1 c c x u t x = u 1 c dx udt dx = u 1 c υ dx dx udt υ = = dt dt udx /c dx u υ = dt u dx 1 c dt t u x / c t = u 1 c dt udx / c dt = u 1 c 198

dx = υ dt., υ u υ = (6.13) 1 υ c u υ,, υ. υ + u, υ = (6.14) 1+ υ c u υ,. υ u c υ υ u υ υ + u., υ = c υ = c,, υ = c υ =c,.. 6.4 -, -, 0,8c 0,7c,,. (. 6.9). ; :. 6.9 0,8c + 0,7c = 1, 5c. - c. Lorentz. -, 6.13 υb u υ B = u 1 υ B c u = 0, 8c υb = 0, 7c υb u υ B = u 1 υ B c 0,7c 0,8c υ B = = 0, 96c 0,8c 1 ( 0,7c) c 199

6.5 0,6c 0,5c, (. 6.10). ; :. 6. 0, 0,6c + 0,5c = 1, 1c.. Lorentz. - 6.14. υ + u υ = 1+ υ c u υ = 0.5c + 0,6c = 0,85c 0,6c 1+ 0,5c c 6-9,,... 6. 00

x υ 1 π υ π (.6.10) -. υ 1 µ υ µ -. m m υ = m υ υ π, µ 1υ 1π π µ m1 1µ. ( ). u. - υ υ, υ, υ, - 1 π, π 1µ µ Lorentz (6.13).,,,. - -.,, - Lorentz. m : m p = (6.15) 1 υ / c ( ) 1... υ c p m.,,, -. 3.. 4. c. (. 6.1). 5. m.. 6.,,,.,,. - c. -.. 6. <<c. 01

6-10 m mc E = (6.16) 1 υ / c. - υ = 0 E = mc E = 0. mc -.., m mc. -. - ( mc ),,. -. - c. -, 0,1% -.,., 4,5.,.. -,,. 6.6... 193 C. D. Anderson. ( ), -. -.. -.. ( ). - -. 0

. 6.7 o Einstein. ( K ) ( E ) ( mc ). K = mc 1 υ / c mc (6.17) 1 (6.17) υ c K = mυ. (.14). (6.17) υ = 0 K = 0., υ c, K = f υ 6.13. ( ) 6.6. ( Η). 6. 3 <<c. 7 7 1,67309 10 kg 1,67538 10 kg - 7 1 3,34451 10 kg. - ; : m. m. 7 7 m = ( 1,67309 + 1,67538 3,34451) 10 kg = 0,00396 10 kg 7 8 11 E mc 0,00396 10 ( 3 10 ) J 0,03564 10 J = = = -.. 03

6.7 υ = 0,85 c. 31 ev. m = 9,1 10 kg. : 31 8 15 mc ( 9,1 10 kg) ( 3 10 m / s) 81,9 10 J 0, 511MeV = mc 0,511MeV E = = = 0, 97MeV υ 1 0,85c 1 c c K = E mc = 0,97Mev 0,511MeV = 0, 459MeV = = 6-11 - (6.15) c p = mc / c 1 υ / c c υ υ = p c p + m c 1 υ / c = p mc + m c (6.16) υ 1 / c E m c + p c 4 = (6.18) ( ) E = mc,.,, E = pc. 04

. p = m. m p = - 1 υ / c - 0,,. 0..,. 6-1 Lorentz -., ;,,. - F = Buq, -. -.,. - -. -. -. u, - x. F = Buq (. 6.14 ). 05

. -. υ, ',. - ( ),.. 6. 4 - u x. (. 6.14 ). O (6.13)..., υ u υ + = u υ =. υ + 1 υ c u υ. (6.6). -.,... -. 06

(. 6.15 ) xoz.,, l a. σ E =, σ ( - ). ε 0. 6. 5 x u. - ; u (. 6.14 ). l = l α = α u 1 c u A = l α = A 1 c Q Q σ = = A u A 1 c σ E E = = ε 0 u 1 c = σ u 1 c. Q.,,. 07

x E = E. x. E = E x x E = y ( E ub ) ( E + ub ) y u 1 c z E = z z u 1 c y B x = B x B y B = y u + E c u 1 c z u Bz E y c B z = u 1 c -.. 6-13.,,,,..,.. -.. -., Maxwell,,. Newton. Newton 08

. -... Mm F B = G r ( F = ma).. Einstein -.. : -.., (. 6.16 ).., (. 6.16 ). -.. -. -, -, (. 6.17 ).,... - ; - -, -.. 6. 6 09

. 6. 7 ( ). ( ). -. (. 6.17).,. -.,, - -.,... - -.., (. 6.18).. -,.. 6. 8, -, Einstein,,,.,,. -. 10

,,...,,. -. (. 6.19).. 6. 9...,.. -... -. (. 6.0).... Einstein -. 6.0 Viking -. -. 11

., -,. -. Michelson-Morley...... -.. - u, t 0, t0 t =.. 1 u c. u, u, l 0, l = l 0 1. - c. Lorentz (x, y, z, t) - Lorentz u. u x t=0, - Lorentz x ut x + ut x = x = u u 1 1 c c y = y y = y' z = z z = z t ux / c t + ux / c t = t = u u 1 1 c c u c Lorentz. 1

... Lorentz x, u, x υ u υ + u υ = υ = 1 υ 1+ υ c u c u υ u c. -. m p = 1 υ / c υ c p = m.. c,. m.. c.. mc. mc E = 1 υ / c mc K = mc 1 υ / c 1 υ c K = mυ υ c. 4 E = m c + ( ) : E = pc. p c E = mc.,.. 13

.. -.. -..... n ( 1+ x) - n( n 1) n( n 1)( n ) 3 ( 1+ x) n = 1+ nx + x + x +... 1 1 3 mc 1 K = mc υ c K = mυ. 1 υ / c 6.1 Michelson Morley, ; 6. :...... 6.3 c.,, c ; 6.4 t. H t, u, ) t; ) t; ) t;. 14

6.5. ;. 6.6.,.. ;, ; 6.7 : ). ). ; 6.8 - d.,,, : ) d. ) d. ) d. ) d. ) d.. 6.9-600 m, - - ; 6.10. -. ) ; ) ; 6.11. 15

6.1 u,. -. - x,,,.. 6. ; ). ). ) -. ) - -. ) -. 6.13. x x, y., ; 6.14 -. -. 6.15 ; ; - ; 6.16 ; 6.17 -. 16

), ) ) - ;. 6.18 13,6eV. : ). ). ). 6.19 10 m 0m -. - - ; [ : 0,87c ] 6.0 0,99c 5 min,., - ; [ : 35,5 min ] 6.1.. ; [ : 3 c ] 6. - 0,5c.., - ; [ : 15,5 %] 6.3 10 mg. ; c=3 10 8 m/s. [ : 9 10 11 J ] 17

6.4 1000 kg 0,5c. ; c=3 10 8 m/s. 19 [ : 1,4 10 J ] 6.5 ) 0,5c 0,9c. ) 0,9c 0,99c. 0,511 ev. [ : 0,58MeV,, 45MeV ] 6.6 - x=100km, y=10km, z=1km t=0,5ms. (x, y, z, t ) - 0,8 c x; ( t=0 ). [ : x =367 km, y =10 km, z =1 km, t =1,8 ms ] 6.7,, 100 m. 4 s. ; [ : 0,083 c ] 6.8 0. 1000 0,995 c. ; 1000 ;. [ : 64, 51 ] 6.9 0,8c 0,6c,,. ; [ : 0,946 c ] 18

6.30, m p =1,6761 10-7 kg, m n =1,6749 10-7 kg, m d =3,34357 10-7 kg. ; c=3 10 8 m/s, 1 ev =1,6 10-19 J. [ :, ev ] 6.31. 0ns., 7,5ns. ; c=3 10 8 m/s. [ :,78 10 8 m/s ] 19

EINSTEIN Albert Einstein 1879. -,,. - Einstein.. 1894,, Albert. -.,, 1900., 190, -. Einstein,., -. Einstein 1905., Annalen der Physik. - 191 Einstein ',,., 1910, -. 191-1914,, - Max Planck. -, (1914) Van' t Hoff "Kaiser Wilchelm". Einstein, -. 1905, : 1906 Brown 1907 -, -. -, Einstein, 0

. Einstein,, - : (1911), (1915),., (1916). Einstein.,. -, Newton. - Einstein. Einstein 30, -,.,. -, Einstein -,.,, -.,, (193), Einstein, - Princeton. 1936, ' -. 1940., -.. -. 1

Einstein. -, -.,. -. Einstein,, -. -. Einstein,, - -. Einstein. To 1914. -.. 1939.. Einstein. Roosevelt., (1945),. Princeton 1955.

,,... 30.. -.,... -.!. -.. ;. -.. -.,,.. -.. 3

7-. 7. Max Planck ( 858-947)., -. 9 8. -. -. axwell, - ( 864),., 886, Maxwell, - Heinrich Hertz -.., -,,.,.,,, ( Compton),. 900 Max Planck - ( ),,.. H.. -. -. Planck, -... -. 7-. ( )..,. -. -.,,. 6

', ( ).,... -, I S.I. J / m s W / m..,,., - '. ', " " ( λ max ),. 000, λ max ( ), (. 7. ) ( ) - ( λ ) max λ max T = σταθερ ( Wien).. -,,.. 900, Planck... ( - ). - E n = nhf n, f h 7. - (W/m ).. 7

- Planck. H h = 6,66 0 34 J s.,,,. 7. 7.. E = hf,. -. ( ),.,,. 7. m = 50 g K = 5 N / m A = 5 cm. ( ) : ), ) n. : ) K 5 N / m 5 f = = = s π m π 0,05kg π, Planck 34 5 34 E = hf = ( 6,66 0 J s) s = 0,55 0 J π. 3 ) E = KA = ( 5 N / m) ( 0,05 m) = 6,5 0 J 3 E 6,5 0 J 30 E = nhf. n = = = 6 0 34 hf 0,55 0 J.. 8

7-3. -,. ( - ). 7.3. ( 0 7 atm) -.,,, - ( Cs).. -.,. ( ) - (. 7.3).. 7.3..,. f. ( ) 0. -. 3.. 9

7.4 7.4 7.3. -, -..,, -. -.,,,. (V o ) -... φ..,,,, -. -,,. 905 Einstein, - Planck,, - E = hf, (7. ) 7.5 f h Planck. Einstein, hf -. hf,. φ -. K = hf φ Einstein (7.) 30

7.6. H Einstein -. hf φ 0 hf φ φ f h φ f 0 =. h - -. -, -. 6- - - - E = pc. E = hf. hf p =. c = λf c h p = (7.3) λ ( ). (.. ). (7.3) -. -,,,. Planck. 3

. 7. Wilchelm Röntgen ( 845-93).,, -.. 90. 7-4 COMPTON X To 895 o Wilchelm Röntgen ( ) o. Röntgen. -. 0,00 nm, nm. -. -. -. -.,...,.,, -. Compton ( ). 7.3 Arthur Holly Compton ( 89-96). 94 o Arthur Holly Compton. Compton ( ). Compton - ( ). - Compton - h λ λ = ( συν ϕ) mc λ, λ, m ϕ. - f -,,, f.,,,,. 3

,.. λ (. 7.7). -. - λ λ > λ... 7.7 E = hf = hc / λ E = hc / λ. hc hc = + K e λ λ K e. 6. 7 hc hc mc = + mc (7.4) λ λ υ / c p = E / c = h / λ p = h / λ. mυ (6. 5) p e =. υ / c p = p + p e p e = p p 7.8 p e = p + p pp συν ϕ m υ υ / c h h = + λ λ h συν ϕ λλ (7.5). 7.8 33

7. (7.4) (7.5), υ, h λ λ = ( συν ϕ) mc = 0, nm 0 0 m. 90. : ) H. ),. ). : λ ( ) 34 8 hc 6,66 0 J s 3 0 m / s 6 E = hf = = = 9,878 0 = 44 0 0 m ( ) ( ) ) J ev 34 h 6,66 0 J s 4 p = = = 6,66 0 kg m / s 0 λ 0 h mc ) λ λ = ( συν ϕ) hc E = = h mc λ = λ + ( συν ϕ) = 0 0 34 8 (,66 0 J s) ( 3 0 m / s),04 0 m m + 6 6 = 9,4 0 0 6,66 0 34 h 6,66 0 J s 4 p = = = 6,47 0 kg m / s 0 λ,04 0 m ) = E E = 9 ev K e 34 J s 3 8 ( 9, 0 kg) ( 3 0 m / s) J = 33 ev =,04 0 0 m. 7.4 Louis de Broglie ( 89-987). -. 99. 7-5 H KYMATIKH Einstein -,,, 94, Louis de Broglie ( o ) p h λ = p de Broglie. 97,, Davisson Germer 34

, -., -. -.. 7.5 ( ). ( ) 7.3 de Broglie ), kg, 3 m / s, ) 0 g 3 6 300 m / s, ) 9, 0 kg 7 0 m / s. :,,,. ) ) ) λ = p 34 6,66 0 J s = =, 0 h 34 ( kg) ( 3m / s) 34 h 6,66 0 J s 3 = =, m 3 p ( 0 0 kg) ( 3 0 m / s) 34 h 6,66 0 J s 0 = =,04 3 6 p3 ( 9, 0 kg) ( 7 0 m / s) λ = 0 λ = 0 3 m m. de roglie. 35

7-6. -,,., ( - ), -. -..,,.,. - ;,, :. p x. de h Broglie λ =, p λ. πx t = 0 ψ = Aηµ λ 7.9.. 7.9, x,. 7.6 Werner Heisemberg ( 90-976).. 93. +. ;. -. -. -.. ( ) (. 7. 0). - - - - h p =. λ 36

. 7. 0 ( ) -. ( ) ( )., ( ), x... Heisemberg 97 ( ) : p x x. x p x -. h h p y y, pz z. π π Heisemberg E t h π h π - '.,. -, -. -, hf,... 37

. -.. 0-8 s. h E t E = h f π h h f f π t π t t= 0-8 s 7 f,6 0 Hz 7,6 0 Hz. 7.4 5 3 0 m / s 0, %. - ; 45 g 0 m / s,, ; : x = eυ x = 9, 0 3 0 / = 7,33 0 / 3 5 6 ) p m ( kg) ( m s) kg m s 9 H px 0, % 7,33 0 kg m / s. H x 34 h 6,66 0 J / s 4 x = = = 0,38 0 m. 9 π px 6,8 7,33 0 kg m / s. -.. ), 7 x, 6 0 m.. -. 7-7 SCHRÖDINGER ( ), -,,.. - -. Ψ. 38

Ψ = Ψ( x, y. z, t)... Ψ -..., -. Max Born -., dv ( x y, z), Ψ dv dv. dv Ψ Ψ dv. Ψ dv =.. Born Ψ.. ; Erwin Schrödinger - Ψ. x, Schrödinger : h d Ψ( x) + U x Ψ x = E Ψ x (7.6) h m d Ψ x dx U ( x) E ( ) m dx ( ) ( ) ( ) ( h-bar), h, π x,... 7.7 ax Born. ( 88-970)... -. 933 - -. 954.. 7.8 Erwin Schrödinger ( 877-96 ). -. -.,,, -.. P.A.M. Dirac 933. 39

x Ψ dx = - x. 7-8., -. H 7. -.. 7. ( ) - ' L x. ( ). T L, U=0 L U 0. U 0. -. ) x ' 7.. 0 x L U = 0 x < 0 x > L. (7.6). 7. ( ) = 0 Ψ x x < 0 x >L nπx Ψ ( x) = Aηµ 0 x L n=,,3,.. L ( x) Ψ -. 40

L λ = (n =,,3,..) n h p = λ nh p = (7.7) L h. L. p. E = K = m e (7.7) E h = n (7.8) 8meL.., Born,. x. Ψ ( x).. 7. 3 ( ) Ψ ( x).( ) - Ψ ( x). ( x) Ψ - ' dx. ( )., - n. 4

.. 7. 4. 7. 5 - ' (. 7. 4)., [0-L] U=0, [0-L] U 0. - U 0., 7.6, 0 x L,. x <0 x > L,, Ψ( x ) = 0,, x. - 7. 5. ( ). Ψ ( x) x. ( x) Ψ x <0 x > L., -, '.. 7. 6 ( ) Ψ ( x). ( ). ( ) Ψ ( x). ( x) : Ψ - ' dx..., -... n=.. 3. ',. (n= ) ( ) 4

.. 4.. - ( ). -. 7-9 '. ', -,.. -..,, -,,.. - '., -.. (. 7. 7) υ A. E = K A = mυ A. h. U = mgh mgh. E U. E < U h,. -, -. (. 7. 8). (7.6) U = 0 x < 0 x > L U = U 0 0 x L, 7. 9.. 7. 7 < U.. 7. 8 U 0. <U 0. 43

. 7. 9 -.. '. - L. -, - ( U 0 )....,. ;., ( ). Coulomb., -. -. - Coulomb. -..,. 44

-. Planck - :. ( ). E n = nhf n f 34 h Planck ( h = 6,66 0 J s ).,,.. -. - φ. O Einstein,. E = hf K = hf φ ( Einstein) h Planck. h p = λ Compton.. h λ λ = ( συν ϕ) mc p, λ h λ = p,,. h x p x x π -. h E t π 45

Ψ -. H Schrödinger. T Ψ - ( ). Ψ dv = ( ) '. - U 0 U 0. -. -. - '. -. - '. 7. - ; 7. ;,. 7.3. ; 7.4. - ; 7.5 ; 7.6 ; ). 46

) -,. ). ) 7.7. ; ) (f > f ). ). ) (φ =, ev), (φ Cs =,4 ev). ) (φ =, ev), (φ Cs =,4 ev). ), - (f > f ). ). Compton 7.8 : Compton... -... 7.9 ( > ). ) ). 7. 0 - ) 0 ) 45 ) 90. 47

7.,. de Broglie; 7. -. de Broglie ) ; ) - ; ) ;. 7.0 7. 3 de Broglie. ) ) ; 7. 4. ; 7. 5 400nm 0,8eV. - 34 8 500nm; h = 6,66 0 J s, c = 3 0 m / s, 9 ev =,6 0 J. [ : 0, 8 ev] 7. 6 400 nm -. 5 8 0 m / s. - 34 8 ; h = 6,66 0 J s, c = 3 0 m / s, 3 9 m e = 9, 0 kg, ev =,6 0 J. [ :,3 ev] 48

7. 7 To,8 ev. 400 nm; - 34 8 9 h = 6,66 0 J s, c = 3 0 m / s, e =,6 0 C, 9 ev =,6 0 J. [ :,3 V] 7. 8 - (400-700 nm); (4, ev), (4,5eV), (,5 ev), (,3 ev).. 34 8 9 h = 6,66 0 J s, c = 3 0 m / s, ev =,6 0 J. [ : ] 7. 9 49 nm 0,7 V. -,,43 V. : ) 34. ). h = 6,66 0 J s, 8 9 9 c = 3 0 m / s, e =,6 0 C, ev =,6 0 J. [ :,8 ev, 38 nm ] 4 7.0 5,6 0 Hz. 4 34 9 8,6 0 Hz. h = 6,66 0 J s, ev =,6 0 J [ :, ev] 7. 00 W, 600 nm. - 0 m 0 mm. 0, s; -. c=3 0 8 m/s h=6,63 0-34 Js. [ : 6,03 0 3 ] 7. 0 5 m/s; : c=3 0 8 m/s h=6,63 0-34 J s m e =9, 0-3 kg. [ : 3,64 nm ] 7.3 =663 nm,. h=6,63 0-34 J s. [ : 5 0 6 /s ] 49

7.4 Ni, 5 ev, 00 nm. ; : c=3 0 8 m/s h=6,63 0-34 J s ev =,6 0-9 J. [A :,V ] 7.5 To,7 ev. - - ; : c=3 0 8 m/s h=6,63 0-34 Js, ev=,6 0-9 J. [ : 460 nm ] 7.6 =550nm V =0, 9V. : ). ) = 90nm. ). : c=3 0 8 m/s, h=6,63 0-34 Js, e=,6 0-9 C, ev =,6 0-9 J. [A :,07eV, 4,47V, 500 0 Hz ] Compton 7.7,4 pm. ) 30 ) 60. : 34 8 3 h = 6,66 0 J s, c = 3 0 m / s, m e = 9, 0 kg. [ :,7 pm, 3,6 pm ] 7.8 0 - m - 80. -. 34 8 h = 6,66 0 J s, c = 3 0 m / s, 3 m e = 9, 0 kg, ev =,6 0-9 J. [ : 4,4 kev] 7.9 0, ev. ) ; ) 90 ; ) 60 ; : c=3 0 8 m/s, h=6,63 0-34 Js, ev=,6 0-9 J, m e =9, 0-3 kg. [A : 6, 0 - m, 8,6 0 - m, 0, 68 ev ] 50

7.30 de Broglie ) (m e =9, 0-3 kg) 0 6 m/s. ) (m p =,67 0-7 kg). ) (m=0,kg). h=6,63 0-34 J s [A : 3,6 0-0 m, 0-3 m,,65 0-39 m ] 7.3 50 V. de Broglie. 34 9 3 h = 6,66 0 J s, e =,6 0 C, = 9, 0 kg. 0 [ : 0 m ] 7.3 ) nm; ) de Broglie nm; 34 : h = 6,66 0 J s, 3 = 9, 0 kg, 8 c = 3 0 m / s, ev=,6 0-9 J. [ : 4 ev,,5 ev ] m e m e 7.33 Planck 0,6 J s, 0,5 kg 0 m/s %; ; [ : x 0, 96 m] 7.34 - n= - n= 0-8 s. - ; - 34 h = 6,66 0 J s, ev =,6 0-9 J. 7 [ : 0,66 0 ev ] 7.35,. x de Broglie, - υ χ υ x. π 5