Chapter 21 (Angle of Loll)

O@K\VNX ‟ 8; KJDIN BA IBII

O`kptnr ‟  8;  8; Kjdin ba ibii Nxnrogsn -;7

Kjswnr ; Dgvnj=; 8 VkjѸ 3

VkjѸ 3

∝

-8

∝

-8

*

-<.?<<

c

>.<<<

c

DC

HC *

-<.?<<

>.<<<

∝ 

VkjѸ 3

DC 3 HC 3

<.;8<

VkjѸ 3 

<.?61

Ѹ 3 

;7.;<4 ;7.;<4

¼

Kjdin ba ibii gs ;7.;<4¼

Kjswnr 8

Dgvnj=;

EH

kjdin ba ibii 3

3

?.?<7

;1

-

?.?<7

3

<.8

EH

3

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c

ECV (c)

3

0.;0<

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ECV (c)

3

0.;0<

<.<<<

0.;0< <.8

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3

x <.<<<

c \kdn ; ba 0

O@K\VNX ‟ 8; KJDIN BA IBII HC 3 EC ‟ EH HC 3 0.;0 ‟ ?.?<7

HC 3 6.04;c

VkjѸ 3

Vkj

;1

<.804

3

3

∝

-8

∝

-8

∝

-8

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DC

HC *

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6.04; *

DC

6.04;

_qukrgjd hbt` sgfns, wn dnt <.<08

3

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c

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c

Kjswnr ?

Dgvnj=;. Kjdin ba ibii 3 ;8¼ 8. Frkat 3 1.0c ?. Qnrtgoki fgstkjon 3 ;
HC 3 6.6>1c

VkjѸ 3

∝

-8

*

DC

HC \kdn 8 ba 0

O@K\VNX ‟ 8; KJDIN BA IBII

Vkj

;8

<.8;?

3

3

∝

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-8

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6.6>1 *

DC

6.6>1

_qukrgjd hbt` sgfns, wn dnt <.<6>

3

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6.6>1

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c

3

DC

Fgspikoncnjt kt 1.0c 3 ;?76?t O`kjdn gj Onjtrn ba drkvgty rnqugrnf 3 <.;<;c DD‗ 3

w*f T

<.;<; 3 w * ;< ;?76? ;6<.0t 3 w

Tngd`t tb s`gat vnrtgokiiy fbwjwkrfs gs ;6<.0t

Kjswnr 6 Dgvnj=;. Fgcnjsgbjs ba t`n vnssni 3 ;<< * ;8 * 0 8. Kjdin ba ibii 3 ;0¼ ?. Cnkj frkat 3 6c EH ba hbx s`kpnf vnssni 3 frkat 8 EH ba hbx s`kpnf vnssni 3 6 8

EH ba hbx s`kpnf vnssni 3 8c 8

HC ba hbx s`kpnf vnssni 3 h ;8 * f

\kdn ? ba 0

O@K\VNX ‟ 8; KJDIN BA IBII 8

HC ba hbx s`kpnf vnssni 3 (;8) ;8 * 6

HC ba hbx s`kpnf vnssni 3 ?c EC 3 EH + HC EC 3 8c + ?c

EC 3 >c

VkjѸ 3

Vkj

;0

<.?8>

3

3

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-8

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HC *

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DC 3

c

3

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DC

c

EC 3 ED + DC >c 3 ED + (-<.;>0c) > + <.;>0c 3 ED

>.;>0c 3 ED

\kdn 6 ba 0

O@K\VNX ‟ 8; KJDIN BA IBII

Kjswnr > Dgvnj=;. XF ba ibd 3 <.10 Int fgcnjsgbjs ba ibd 3 x

_b frkat ba ibd 3 x * <.10 EH 3 frkat 8 EH 3 <.10x 8

EH 3 <.?6x 8

HC 3 h ;8 * f 8

HC 3 x ;8 * <.10x

HC 3 <.;8?x EC 3 EH + HC EC 3 <.?6x + <.;8?x

EC 3 <.61?x ED 3 `ngd`t 8 ED 3 x 8

ED 3 <.>x

EC 3 ED + DC

<.61?x 3 <.>x + DC -<.
< : DC _`gp wgii hn gj kjdin ba ibii \kdn > ba 0

O@K\VNX ‟ 8; KJDIN BA IBII

Vkj Ѹ 3

∝

-8 * DC HC

Vkj Ѹ 3

∝

-8 * -<.
∝

<.<46 <.;8?

Vkj Ѹ 3

Vkj Ѹ 3 <.441 -;

Ѹ 3

Vkj (<.441)

Ѹ 3

?4.0¼

Qnssni wgii hn kt kjdin ba ibii kt ?4.0¼

Kjswnr 1 Dgvnj=;. @bcbdnjbus ibd wgt` orbss snotgbj Int sgfn ba ibd 3 x Int XF ba ibd 3 XF ED 3 `ngd`t 8 ED 3 x 8

ED 3 <.>x EH 3 XF * `ngd`t 8 EH 3 XF * x 8

EH 3 <.>x * XF 8

HC 3 h ;8 * f 8

HC 3 x ;8 * x * XF

\kdn 1 ba 0

O@K\VNX ‟ 8; KJDIN BA IBII

HC 3 x ;8 * XF

HC 3 <.<0?x EC 3 EH + HC

EC 3 (<.>x * XF) + (<.<0?x) XF EC 3 ED + DC EC ‟ ED 3 DC

(<.>x * XF) + (<.<0?x) ‟  <.>x  <.>x 3 DC XF Abr s`gp tb `kvn pbsgtgvn stkhgigty DC ≮ < (<.>x * XF) + (<.<0?x) ‟ <.>x ≮ < XF <.>x (XF ‟ ;) + (<.<0?x) ≮ < XF 8

<.>x (XF

 ‟ XF)

+ <.<0?x ≮ <

XF 8

<.>x (XF

 ‟ XF

+ <.;11) ≮ <

XF (XF

8

 ‟ XF

+ <.;11) ≮ < 8

XF; 3 -h + ∝h 8k

 ‟ 6ko

8

XF; 3 ; + ∝(;)

 ‟ 6

* ; * <.;11

8

XF; 3 <.407 8

XF8 3 -h - ∝h  ‟ 6ko 8k XF8 3 ; - ∝(;)

8

 ‟ 6

* ; * <.;11

8

XF8 3 <.8;< XF; : XF : XF 8

\kdn 4 ba 0

O@K\VNX ‟ 8; KJDIN BA IBII

<.407 : XF : <.8;< V`gs cnkjs, XF ba t`n hiboe s`buif hn cbrn t`kj <.407 Br XF ba t`n hiboe s`buif hn inss t`kj <.8;<

-b
\kdn 0 ba 0