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Classical Mechanics

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Classical Mechanics ¨kyF®k yAkym Classical Mechanics (Introduction) Tdq 1 Tr Anh .As± Tr :An Xy ¨t Tywy Ty`ybW r¡w\ y bt ¨l§ Amy ¤AnF . , wk Tr ,r ªwqs ,Ty An¶Ak .Tr AbF rysf dh As³ Ah`R¤ ¨t A§r\nl ¨§CAt CwWt :As T`C Y Cwm @¡ ysq km§ §dq rO` Trtqm ryFAft LAnnF :(free fall) r ªwqs • §d yCA ¨lyA wlyA Am T§A Y (TyAwy ­CAS) . wk Tr TA` d` A Y TyÐAl wy wA ¨§CAt CwWt A`nF :(Newton's laws of motion) wyn Tr yw • , Az :¨ Tlmtm ¤ ,ywq £@¡ TAy} Ahyl dmt` ¨t y¡Afml .­wq ¤ ,Tr Tym ,TAW` ,rf T}A ºASf rJ ¤ }w Artqm lt xCdnF :(Astronomy) wk Tr • .TyÐAl wy wA LAnnF Ð d` . wk Tr y¡Afm {` Yl AnAmt¡ OnyF :(Beyond Newton) wy d` A • ,_Af³ yw : TykyF®k yAkym ¨ CwV ¨t TyFAF± .Tynq TKAn © AyA ¤ AyWF AnRr wkyF . wmk Anf`F - ¤AnF .(electromagnetism) TysVAn¤rhk w¡ rb± ¶A .wRwm @h ®A Cw PO -^ :¨¤rtk³ wm fO thm ¹CAql km§ https://plato.stanford.edu/contents.html .¨l§ Amy hn {`b rÐ tyF .ºAml` ¤ TfF®f {` Am Yl ®V² (Free Fall) r ªwqs 2 .TWs |C± Aqt³ Yl dmt` r ªwqsl Y¤± rysft A © Y At ¯¤ (natural) Ty`ybV Tr ¨¡ fF Y Yl ªwqsA ¨w |C± T§¤r C AA} d`§ ÐAs rysft @¡ k .rysf .(1) ®ym b A rq x As rq ¨w A®W ,Ð b |C± T§¤r TyAk §r³ TfF®f LA dq(1) .hnym z§z`t T ± {` wd ¤ , ®ym b 1 §dqt T`C± r}An` T§r\ Yl (Aristotle 384-322 BC) wWFC dmt dw ¨t As± w¡ @ d¶As Aqt³ A .r ªwqsl rysf ,(Air) ºwh ,(Water) ºAm :(3)r}An T`C §z ¨¡ (Earth) (2)|C± Yl TyFAF³ r}An` £@h wWFC YW .(Earth) Trt ¤ |C± ¤ ,(Fire) CAn :Tyr P¶AO Universe) wk zr £A ¨ AWqs§ Amhl` ºAm ¤ Trt T`ybV • .(Earth center) |C± zr ¢sf w¡ ©@ (center .(Heaven) ºAms w d`O§ Amhl` CAn ¤ ºwh T`ybV Aqm ¨ • sA .Ahbyr ¨ TyFAF± r}An` Tbsn As° Ty`ybW Tr l`t Hk` ¤ TbA ¨¡ Trt ¤ ºAm Tbs A |C± zr w Xqs§ AhE¤ FAnt As± ªwqF TrF wWFC dqt ,@¡ Y TAR .y} .Tfyf As± rF Xqs Tlyq As± :(weight) AJAqn \`m .r ªwqsl wWFC ­r\ HF ymlsm AAR Hm r@ .d` Amy Tsl Ah` An wkyF ¨t wk Tr w Cwmt A rq ¨w ,(Abu al-Fath Khazini) ¨EA tf w Am Aqm @¡ ¨ gravitational potential) TyÐAl TnAk TAW whf CwV y ,rK © A Am .A¡zr TAsm Aysk FAnt |C± TyÐA rt ¤ ,(energy .(weight) q ¤ (mass) Tltk y zyymt ¨ Abs A ¢ ryyt ¢Am ¤ (Galileo Galilei 1564-1642) ¨lyA wylyA CA\t Anyl A Ð y rk ¢yC dt ¨t ­CwWF± C .r ªwqs Ay An r\ TrF Ab³ (Leaning Tower of Piza) ¶Am zy r yflt yE¤ Yl` .Ð dt ¯ Twtkm ¢Am ¯ , EwA l`t ¯ r ªwqs w¤ Ab³ (thought experiment) Tylq` Trt wylyA m`tF ,Hk` r s r ªwqs xCd An y .¨ µA wWFC T§r\ ¨ {An Atyt An¡ .Tltk mh ySq ytVwr yflt yE¤ Ð y r :r ªwqsl wWFC T§r\ s Trt £@h Atnkm .rb± w¡ ¢E¤ ± ,¯¤ k s Xqs§ ,Th • .± ­rk ,q± ­rk Xqs ,«r Th • T}®A .T·VA Ahn AnqlW ¨t T§r\n Yl y Rw {Ant @¡ .« As± Ew l`t ¯ r ªwqs TrF » ¨¡ wylyA Tymt Am dtl Trt m`tF d wylyA A Ð A w wC¥m lt A ¢ dqt`§ ¨t (inclined surface) ¶Am ©wtsm Tr Anh .¢y }w r ªwqs TrF ryy ¶Am ©wtsm dtF ºC¤ dh A .Ah xAy ¯ r@t § . ªwqs ­d xAy `§ Am W Ahl` ¤ Yl ®V³ km§ Awl`m d§zm .TyA T Ð k @ z : Atk ¨ ¤± Of dn |C± CwOt Annkmy .T§wA ªAq ¨ Anwhf §r³ dn |C± whf lt§(2) .©w Ah® TyRC± ­rk Ah Yl §r³ .(Chemisty) ºAymyk Cw ¨ yOft º¨K T§r\n £@h w`nF(3) 2 http://www.arvindguptatoys.com/arvindgupta/ten-beautiful-experiments.pdf .r ªwqsl rysf Yl On wy Am r\tn Anyl y` k (Newton's Laws of Motion) Trl wy yw 3 rb TfF® ¤ yy¶A§zy ­d wh rA\ At ¨¡ Trl wy yw ¨ AFAbt³ lt ¤ TqyK TOq £@¡ w {` ¨ Qw b .§CAt Ansf r@ Aw ,A¡E¤A yy¶A§zyf Yl A ¨t Aw`O ¤ y¡Afm .§CAtl ArbF ¢yw dh Tr ¹ Abm (The Principles) ¹ Abm 1.3 ¤ ,¢tfyR¤ wA k .Trl yw T® (Newton 1642-1726) wy R¤ yqr ywq £@¡ QwO -¨l§ Amy- |r`nF .TlAkt Twm kK§ k .¢yn`§ A ¤ Ahn Tym¡ w Xys MAqn Ð (Principle of Inertia) TAW` wA 1.1.3 :T}A (frames) A` An r`§ ¢± TAW` wAq wyn ¤± wAq Yms§ .(Inertial frames) TyAW` A`m (Tm\tn Tyqts Tr ¤ wkF) ¢A Yl s © Yqb§ ,¨AW l` ¨» «.¨CA r¥ ¢yl r¥§ \In an inertial frame, an object either remains at rest or continues to move at a constant velocity −!v , unless acted upon by a force." ¤A Adn Annk .TyAW` A`m £@¡ ¨ kK Hf @ ºA§zyf ywq (time) zl A}A Awhf lWt Ah ^® TyAW` A`m £@¡ Ty¡A h ­r¡AZ © Xb r ¯ ¤ Ahsfn ­ ww TyAW` A`mA .(space) ºASf ¤ yqlW yAy Akm ¤ Az wy rbt ,A`m £@h CAV ºAW³ .Ty¶A§zy ¤ z whf CwW LAn Adn TWqn £@¡ Y w`nF .(absolute entities) .¨l§ Amy -(vacuum) rf T}A- ºASf perpetual) Tb¶d Tr w¡ ¤ ¯ r h whf Yl wAq @¡ ©wt§ Tr wn @¡ .Tm\tnm Tmyqtsm Tr ¨ Tlmtm ¤ (motion -d` Amy Ð «rnF Am- CwO` r Yl xAbt ¤ Amt¡ Rw A (The Second Law) ¨A wAq 2.1.3 .yAkyml ¨FAF± wAq ¨A dbm ¨W`§ 3 −! Tlt s Yl ­r¥m F TyCA «wq wm ©¤As§ ,¨AW l` ¨» «.−!a CAst rR m s @¡ −! \In an inertial frame, the vector sum of external forces \F " on an object is equal to the mass \m" of that object multiplied by its acceleration \−!a "". X −! d F = m · −!a = −!p : dt :¨¡ }± TAyO ¯ ¯¤d r± ¨¡ wAql TAyO £@¡ C −! Cdq s Yl ­r¥m F TyCA «wq wm ©¤As§ ,¨AW l` ¨» «.zl TbsnA s @¡ (momentum) Tr Tym ry k ,−!v ¢trF rR m s Tlt Ah Yl ­ A Tr Tym r` .yAkyml (Hamiltonian formulation) ¨wtlyAh }w m`ts§ ± §r`t ¤ ­wq :¨¡ wAq @¡ ¨ TyFAF± y¡Afm St§ TAyO £@¡ ® .Tr Tym wAq CAbt ,(mathematical formulas) TyRA§r TyO Y r\nA ,Annkm§ ¨FAF± bs A ­r\n £@¡ k .¨A wAq T}A TA ¤± ,r@ AnflF Am .(¤± wAq) }w @¡ ¢¶AW ¤ ¤± wAq TAyO .TyAW` A`ml §r` ºAW w¡ ¤± wAq dh (The Third Law) A wAq 3.1.3 .(equilibrium) Ew wA A wAq CAbt km§ « .£A ³ ¨ ¢sA`§ ¤ ­dK ¨ ¢§¤As§ ` C ` k » \When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in the direction on the first body." isolated) T¤z`m TykyAkym m TFC dn AyFAF C¤ wAq @¡ `l§ Yl r¥ ¯ ¨t m ¨¡ T¤z`m TykyAkym mA .(mechanical systems .{`b AhS` Yl r ¥ Ah Awk lt k ,¨CA XFw Ahyl r¥§ ¯ ¤ m ºAntF m £@¡ A§ km§ ¯ £® A wAq w¤ ¤db .(trivial systems) Tym¡± Tm§d` A` ¤ wslyf d§ Yl wAq @¡ TAyO ¯¤Am ¤ «d A «­ AS ­w ­r¥ ­w k » :A y .(Avempace 1095-1138) TA lsm d§ ¢nk .(\there is always a reaction force for every force exerted") .`fl A§¤As `f C A 4 (Force) ­wq 2.3 (Aristotle 384-322 BC) wWFC Y (external force) TyCA ­wq lWO w`§ :An} T® Y «wq s ©@ As± T`ybW l`t ¨t «wq ¨¡ ¤ :(Natural Forces) Ty`ybW «wq • T§¤Ams r± Tr ¤ (r ªwqs ­rq AV) r ªwqsA .(TysmK Twmm ­rq AV) (Heavenly Bodies) An¶Ak T`An «wq ¨¡ ¤ :(Spontaneous Forces) Ty¶Aqlt «wq • .(Living Orgamisms) Ty .«r± «wq ym ¨¡¤ :(External Forces) TyCA «wq • Ty¶Aqlt ¤ Ty`ybW «wq CAbt kmy .Tymst bF ysqt @¡ Ayl rh\§ .TyCA «wq Hk ,A º¨J T`A Ah± Tyl «w :(4)TyCA ­wq ryt ¨At }w wWFC YW −! Aysk ¤F TyCA ­wq ­dJ A§ rV TbFAtn −!v s TrF wk » .«ρ XFw TA ¤ m s E¤ \The speed \−!v " at which an object moves is proportional to the amount of −! force exerted on it \F " and inversly proportional to its weight \m" and the density of medium \ρ" through which it moves." :¨At kK Yl wWFC± Tr wA TAy} km§ −! m F = · −!v ρ :§r wAq TAy} ¨ Tbk rm ºAW± XC An`Fw ¤ ¨ Aqy z xAy k§ :(Time Measurement) z xAy • AV ,rytA ¢WC ©@ zl wWFC §r` Tl yW E A ¤ .wWFC .Awl`m d§zm zA T}A ­rqf As± Tr wWFC ^¯ :(Friction or Resistance) Akt³ • XC .s kJ @ ¤ ¢y rt ©@ (ºAm ¤ ºwh) XFwA l`t rysf d§ ¢nk ,(5)XFw TA ryt Y¤± T\®m wWFC CAq§ wWFC Cr ,­ry± TyAkJ³ Yl ltl .TyA T\®ml Yl rOt @¡ h km§ .¢sf kK Ð As Yl ­wq ry ­w w¤ ¨¡ T§d ­r\n .¢t`ybV ºz s kJ rbt wWFC .¢y rt§ ©@ XFw ¤ s y Akt .TyA`K r§ Aqm ¤d wAq @h wWFC TAy} wk km§(4) {` dqt`§ .Aqy Af§r` AhW`§ ¢ ¯ ¢nyw ¨ XFw TA m`tF wWFC C(5) .XFw (viscosity) T¤z dO ¢ yC¥m 5 ºAyJ±A A¡A§ yCAq ¢wA ¶At LAn ¤ wWFC PJ Pmqt Aw : wAq dqn TlyFw Tl·F rV Annkm§ .@ T¤r`m ?Tny` TynE ­dm ­wq r¥ Adn d§ ÐA - ?(vacuum) rf ¨ d§ ÐA - y AAm wt§ s -AnwA A®W- tnts hs ¶@q Tr TyAkJ dW} ¢nk wWFC w @¡ A .­wq ry wt§ |rt ,TyAkJ³ £@¡ .­wq ry ºAht C rmts ¨t (projectiles) xAmt³A r¥ ­wqA .ryt yWts ¨k XFw At ­wq wWFC (ºAm ¤) ºwh §rV Ahlq t§ ¤ ,A Ams s ¤ d Adn (contact) .Tf§@q TA ¨ £@¡ ¨ lO§ ¯ AnwA ± (dilemma) TlS` A ¨A ¥s An`S§ XF¤ w¤ Tyz As rt³ TyAkJ³ Hf AO .(ρ = 0) TA §@¡ rf Plt§ wWFC Cr .r¥ ­wq yWts ¨k £@h w`nF .(horror vacui) ®} ww ry ¢y TbsnA rfA .yAkJ³ .rf An§d dn TWqn Archimedes) xdymC A` Y TyCA ­wq TyRA§C TAy} ¤ w` @¡ wq§ .(Archimedes law of buoyancy) xdymC T` ¨¡¤ (287-212 BC .«zm ºAm q FAnt ­wq H§ ºAm ¨ Cwm s » wAq s ¤ z xAy ¯ TAn} dq wWFC wA wy rh\ d ¤ wm TA §r`t (yy¶Aymyk T}A) ºAml` Amt¡ Ð Yl E .Aht ry A l` Yf ©@ (Avempace 1095-1138) TA A` Anh .AhAs wA {qn (1080-1164) © db ¢l Tb¡ £r}A` A .XFw TAk ­wq Trs |w (acceleration) CAst FAnt ­wq A y wWFC dJC A .z Trs ry Cdq ¢ Yl CAst r ¤ .(speed) y HA`m £A ³ ¨ Tr wA Y r\nA (Averroes 1126-1198) TA ryyt E® m` Cdq Ah Yl Ahr y, ­wq x Ayq ¢lm`tF Anyl A ¢ ¯ wmlsm ºAml` ¢y ¡Ð A T} C ¤ .A s Tyr .¨A ¢wAq Tqyd TyRA§r TyO Tr`m wy CA\t Amh Awhf LAn Aw ,TAW`A Xb rm ¨At wRwm Y C¤rm b :¨At ¥sA ºd wyn ¨A wAq ¨ «?yAkym ¨ (£d ©@) (mass) Tltk y¡Af d » Tylq Tltk ¤ (inertial mass) TyAW` Tltk : Awhf w¡ ¢yl CA`tm w , wyn ¨A wAq ¨ rh\ ¨t ¨¡ TyAW` TltkA .(gravitational mass) wd §@ ¶¤± ºAml` ¤ .TyÐA ­wq rt ¨t ¨h Tylq Tltk A ªwqs TrF Am ¢nk .(Averroes 1126-1198) dJC TyAW` Tltk -Trl ¨A wAq Yl Amt- Q®tF Ankmy ,TltkA l`t ¯ r CAyt At§¤Ast Amhl` An`Fw ¤ .
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