Reference Guide & Formula Sheet for Physics
|
|
- Beverly O’Brien’
- 6 years ago
- Views:
Transcription
1 D. Hoselto & M. Pice Page of 8 #0 Heatig a Solid, Liquid o Gas #3 Compoets of a Vecto Q = m c T if V = 34 m/sec 48 the V i = 34 m/sec (cos 48 ); ad V J = 34 m/sec (si 48 ) #4 Weight = m g g = 9.8m/sec² ea the suface of the Eath = m/sec² i Fot Woth, TX Desity = mass / volume m 3 ρ = ( uit : kg / m ) V #7 Ave speed = distace / time = v = d/t Ave velocity = displacemet / time = v = d/t Ave acceleatio = chage i velocity / time #8 Fictio Foce F F = µ F N If the object is ot movig, you ae dealig with static fictio ad it ca have ay value fom zeo up to µ s F N If the object is slidig, the you ae dealig with kietic fictio ad it will be costat ad equal to µ K F N (o phase chages!) Q = the heat added c = specific heat. T = tempeatue chage, K # Liea Mometum mometum = p = m v = mass velocity mometum is coseved i collisios #3 Cete of Mass poit masses o a lie x cm = Σ(mx) / M total #5 Agula Speed vs. Liea Speed Liea speed = v = ω = agula speed #6 Pessue ude Wate P = ρ g h h = depth of wate ρ = desity of wate #8 Uivesal Gavitatio mm F = G G = 6.67 E- N m² / kg² #9 Toque τ = F L si θ Whee θ is the agle betwee F ad L; uit: Nm # Newto's Secod Law F et = ΣF Ext = m a # Wok = F D cos θ Whee D is the distace moved ad θ is the agle betwee F ad the diectio of motio, uit : J #6 Powe = ate of wok doe Wok Powe = time uit : watt Efficiecy = Wok out / Eegy i Mechaical Advatage = foce out / foce i M.A. = F out / F i #9 Costat-Acceleatio Liea Motio v = v ο + a t x (x-x ο ) = v ο t + ½ a t² v v ² = v ο ² + a (x - x ο ) t (x-x ο ) = ½ ( v ο + v) t a (x-x ο ) = v t - ½ a t² v ο #9 Mechaical Eegy PE Gav = P = m g h KE Liea = K = ½ m v² #30 Impulse = Chage i Mometum F t = (m v) #3 Sell's Law si θ = si θ Idex of Refactio = c / v c = speed of light = 3 E+8 m/s #3 Ideal Gas Law P V = R T = # of moles of gas R = gas law costat = 8.3 J / K mole. #34 Peiodic Waves v = f λ f = / T T = peiod of wave #35 Costat-Acceleatio Cicula Motio ω = ω ο + α t θ θ θ ο = ω ο t + ½ α t² ω ω = ω ο + α (θ θο ) t θ θ ο = ½ (ω ο + ω) t α θ θ ο = ω t - ½ α t² ω ο Vesio 5//005
2 D. Hoselto & M. Pice Page of 8 #53 Resisto Combiatios #36 Buoyat Foce - Buoyacy SERIES F B = ρ V g = m Displaced fluid g = weight Displaced fluid R eq = R + R + R ρ = desity of the fluid PARALLEL V = volume of fluid displaced = + + K + = #37 Ohm's Law V = I R V = voltage applied I = cuet R = esistace Resistace of a Wie R = ρ L / A x ρ = esistivity of wie mateial L = legth of the wie A x = coss-sectioal aea of the wie #39 Heat of a Phase Chage Q = m L L = Latet Heat of phase chage #4 Hooke's Law F = k x Potetial Eegy of a spig W = ½ k x² = Wok doe o spig #4 Electic Powe P = I² R = V ² / R = I V #44 Speed of a Wave o a Stig mv T = L T = tesio i stig m = mass of stig L = legth of stig #45 Pojectile Motio Hoizotal: x-x ο = v ο t + 0 Vetical: y-y ο = v ο t + ½ a t² R eq R R R i = #54 Newto's Secod Law ad Rotatioal Ietia τ = toque = I α I = momet of ietia = m ² (fo a poit mass) (See table i Lesso 58 fo I of 3D shapes.) #55 Cicula Ubaked Tacks mv = µ mg #56 Cotiuity of Fluid Flow A i v i = A out v out #58 Momet of Ietia - I cylidical hoop m solid cylide o disk ½ m solid sphee / 5 m hollow sphee ⅔ m thi od (cete) / m L thi od (ed) ⅓ m L R i A= Aea v = velocity #59 Capacitos Q = C V Q = chage o the capacito C = capacitace of the capacito V = voltage applied to the capacito RC Cicuits (Dischagig) V c = V o e t/rc V c I R = 0 #60 Themal Expasio Liea: L = L o α T Volume: V = V o β T #46 Cetipetal Foce mv F = = mω #47 Kichhoff s Laws Loop Rule: Σ Aoud ay loop V i = 0 Node Rule: Σ at ay ode I i = 0 #5 Miimum Speed at the top of a Vetical Cicula Loop v = g #6 Beoulli's Equatio P + ρ g h + ½ ρ v ² = costat Q Volume Flow Rate = A v = A v = costat #6 Rotatioal Kietic Eegy (See LEM, pg 8) KE otatioal = ½ I ω = ½ I (v / ) KE ollig w/o slippig = ½ m v + ½ I ω Agula Mometum = L = I ω = m v si θ Agula Impulse equals CHANGE IN Agula Mometum L = τ oque t = (I ω) Vesio 5//005
3 D. Hoselto & M. Pice Page 3 of 8 #75 Thi Les Equatio #63 Peiod of Simple Hamoic Motio T = π m k whee k = spig costat f = / T = / peiod #64 Baked Cicula Tacks v = g ta θ = f D o + D i = + o i Magificatio M = D i / D o = i / o = H i / H o f = focal legth i = image distace o = object distace #66 Fist Law of Themodyamics U = Q Net + W Net Chage i Iteal Eegy of a system = +Net Heat added to the system +Net Wok doe o the system Flow of Heat though a Solid Q / t = k A T / L k = themal coductivity A = aea of solid L = thickess of solid #68 Potetial Eegy stoed i a Capacito P = ½ C V² RC Cicuit fomula (Chagig) V c = V cell ( e t / RC ) R C = τ = time costat V cell - V capacito I R = 0 #7 Simple Pedulum L T = π ad f = / T g #7 Siusoidal motio x = A cos(ω t) = A cos( π f t) ω = agula fequecy f = fequecy #73 Dopple Effect Towad 343 ± Away v o f = f Towad 343 m Away v s v o = velocity of obseve: v s = velocity of souce #74 d Law of Themodyamics The chage i iteal eegy of a system is U = Q Added + W Doe O Q lost W Doe By Maximum Efficiecy of a Heat Egie (Caot Cycle) (Tempeatues i Kelvi) Tc % Eff = ( ) 00% T h Helpful emides fo mios ad leses Focal Legth of: positive egative mio cocave covex les covegig divegig Object distace = o all objects Object height = H o all objects Image distace = i eal vitual Image height = H i vitual, upight eal, iveted Magificatio vitual, upight eal, iveted #76 Coulomb's Law qq F = k N m k = = 9E9 4 πε o C #77 Capacito Combiatios PARALLEL C eq = C + C + C 3 + SERIES = + + K + C eq C C C i = #78 Wok doe o a gas o by a gas W = P V = C #80 Electic Field aoud a poit chage q E = k N m k = = 9E 9 4 πε o C #8 Magetic Field aoud a wie µ o I B = π Magetic Flux Φ = B A cos θ Foce caused by a magetic field o a movig chage F = q v B si θ #83 Etopy chage at costat T S = Q / T (Phase chages oly: meltig, boilig, feezig, etc) i Vesio 5//005
4 D. Hoselto & M. Pice Page 4 of 8 #95 Relativistic Time Dilatio t = t o / β #84 Capacitace of a Capacito C = κ ε o A / d κ = dielectic costat A = aea of plates d = distace betwee plates ε o = 8.85 E(-) F/m #85 Iduced Voltage N = # of loops Φ Emf = N t Lez s Law iduced cuet flows to ceate a B-field opposig the chage i magetic flux. #96 Relativistic Legth Cotactio x = β x o Relativistic Mass Icease m = m o / β #97 Eegy of a Photo o a Paticle E = h f = m c h = Plack's costat = 6.63 E(-34) J sec f = fequecy of the photo #86 Iductos duig a icease i cuet t / (L / R) V L = V cell e I = (V cell /R) [ - e t / (L / R) ] L / R = τ = time costat #88 Tasfomes N / N = V / V I V = I V #89 Decibel Scale B (Decibel level of soud) = 0 log ( I / I o ) I = itesity of soud I o = itesity of softest audible soud #9 Poiseuille's Law P = 8 η L Q/(π 4 ) η = coefficiet of viscosity L = legth of pipe = adius of pipe Q = flow ate of fluid Stess ad Stai Y o S o B = stess / stai stess = F/A Thee kids of stai: uit-less atios I. Liea: stai = L / L II. Shea: stai = x / L III. Volume: stai = V / V #93 Postulates of Special Relativity. Absolute, uifom motio caot be detected.. No eegy o mass tasfe ca occu at speeds faste tha the speed of light. #94 Loetz Tasfomatio Facto β = c v #98 Radioactive Decay Rate Law A = A o e k t = (/ ) A 0 (afte half-lives) Whee k = (l ) / half-life #99 Blackbody Radiatio ad the Photoelectic Effect E= h f whee h = Plack's costat #00 Ealy Quatum Physics Ruthefod-Boh Hydoge-like Atoms f = R metes s o c = = cr Hz λ s R = Rydbeg's Costat = E7 m - s = seies itege ( = Balme) = a itege > s λ Mass-Eegy Equivalece m v = m o / β Total Eegy = KE + m o c = m o c / β Usually witte simply as E = m c de Boglie Matte Waves Fo light: E p = h f = h c / λ = p c Theefoe, mometum: p = h / λ Similaly fo paticles, p = m v = h / λ, so the matte wave's wavelegth must be λ = h / m v Eegy Released by Nuclea Fissio o Fusio Reactio E = m o c Vesio 5//005
5 D. Hoselto & M. Pice Page 5 of 8 MISCELLANEOUS FORMULAS Quadatic Fomula if a x²+ b x + c = 0 b ± x = the b 4ac a Tigoometic Defiitios si θ = opposite / hypoteuse cos θ = adjacet / hypoteuse ta θ = opposite / adjacet sec θ = / cos θ = hyp / adj csc θ = / si θ = hyp / opp cot θ = / ta θ = adj / opp Ivese Tigoometic Defiitios θ = si - (opp / hyp) θ = cos - (adj / hyp) θ = ta - (opp / adj) Law of Sies a / si A = b / si B = c / si C o si A / a = si B / b = si C / c Law of Cosies a = b + c - b c cos A b = c + a - c a cos B c² = a² + b² - a b cos C T-Pots Fo the fuctioal fom = + A B C You may use "The Poduct ove the Sum" ule. B C A = B + C Fo the Alteate Fuctioal fom = A B C You may substitute T-Pot-d B C B C A = = C B B C Fudametal SI Uits Uit Base Uit Symbol. Legth mete m Mass kilogam kg Time secod s Electic Cuet ampee A Themodyamic Tempeatue kelvi K Lumious Itesity cadela cd Quatity of Substace moles mol Plae Agle adia ad Solid Agle steadia s o st Some Deived SI Uits Symbol/Uit Quatity Base Uits. C coulomb Electic Chage A s F faad Capacitace A s4/(kg m ) H hey Iductace kg m /(A s ) Hz hetz Fequecy s - J joule Eegy & Wok kg m /s = N m N ewto Foce kg m/s Ω ohm Elec Resistace kg m /(A s ) Pa pascal Pessue kg/(m s ) T tesla Magetic Field kg/(a s ) V volt Elec Potetial kg m /(A s 3 ) W watt Powe kg m /s 3 No-SI Uits o C degees Celsius ev electo-volt Tempeatue Eegy, Wok Vesio 5//005
6 D. Hoselto & M. Pice Page 6 of 8 Αα Alpha agula acceleatio, coefficiet of liea expasio, Ββ Beta coefficiet of volume expasio, Loetz tasfomatio facto, Χχ Chi Aa acceleatio, Aea, A x =Coss-sectioal Aea, Ampees, Amplitude of a Wave, Agle, Bb Magetic Field, Decibel Level of Soud, Agle, Cc specific heat, speed of light, Capacitace, Agle, Coulombs, o Celsius, Celsius Degees, cadela, Dd displacemet, diffeetial chage i a vaiable, Distace, Distace Moved, distace, Ee base of the atual logaithms, chage o the electo, Eegy, Ff Foce, fequecy of a wave o peiodic motio, Faads, Gg Uivesal Gavitatioal Costat, acceleatio due to gavity, Gauss, gams, Giga-, Hh depth of a fluid, height, vetical distace, Heys, Hz=Hetz, Ii Cuet, Momet of Ietia, image distace, Itesity of Soud, Jj Joules, Kk K o KE = Kietic Eegy, foce costat of a spig, themal coductivity, coulomb's law costat, kg=kilogams, Kelvis, kilo-, ate costat fo Radioactive decay =/τ=l / half-life, Ll Legth, Legth of a wie, Latet Heat of Fusio o Vapoizatio, Agula Mometum, Thickess, Iductace, Mm mass, Total Mass, metes, milli-, Mega-, m o =est mass, mol=moles, N idex of efactio, moles of a gas, Newtos, Numbe of Loops, ao-, Oo Pp Powe, Pessue of a Gas o Fluid, Potetial Eegy, mometum, Powe, Pa=Pascal, Qq Heat gaied o lost, Maximum Chage o a Capacito, object distace, Flow Rate, R adius, Ideal Gas Law Costat, Resistace, magitude o legth of a vecto, ad=adias Ss speed, secods, Etopy, legth alog a ac, Tt time, Tempeatue, Peiod of a Wave, Tesio, Teslas, t / =half-life, Uu Potetial Eegy, Iteal Eegy, Vv velocity, Velocity, Volume of a Gas, velocity of wave, Volume of Fluid Displaced, Voltage, Volts, Ww weight, Wok, Watts, Wb=Webe, Xx distace, hoizotal distace, x-coodiate east-ad-west coodiate, Yy vetical distace, y-coodiate, oth-ad-south coodiate, Zz z-coodiate, up-ad-dow coodiate, δ Delta =chage i a vaiable, Εε Epsilo ε ο = pemittivity of fee space, Φφ Phi Magetic Flux, agle, Γγ Gamma suface tesio = F / L, / γ = Loetz tasfomatio facto, Ηη Eta Ιι Iota ϑϕ Theta ad Phi lowe case alteates. Κκ Kappa dielectic costat, Λλ Lambda wavelegth of a wave, ate costat fo Radioactive decay =/τ=l/half-life, Μµ Mu fictio, µ o = pemeability of fee space, mico-, Νν Nu alteate symbol fo fequecy, Οο Omico Ππ Pi , Θθ Theta agle betwee two vectos, Ρρ Rho desity of a solid o liquid, esistivity, Σσ Sigma Summatio, stadad deviatio, Ττ Tau toque, time costat fo a expoetial pocesses; eg τ=rc o τ=l/r o τ=/k=/λ, Υυ Upsilo ςϖ Zeta ad Omega lowe case alteates Ωω Omega agula speed o agula velocity, Ohms Ξξ Xi Ψψ Psi Ζζ Zeta Vesio 5//005
7 D. Hoselto & M. Pice Page 7 of 8 Values of Tigoometic Fuctios fo st Quadat Agles Pefixes (simple mostly-atioal appoximatios) θ si θ cos θ ta θ Facto Pefix Symbol Example 0 o o /6 65/66 / exa- E 38 Es (Age of 5 o /4 8/9 9/08 the Uivese 0 o i Secods) /3 6/7 7/47 9 o 5 / /8 7/8 5 / 0 5 peta- P /7 30 o / 3 / / /3 / 37 o 0 tea- T 0.3 TW (Peak 3/5 4/5 3/4 4 o powe of a /3 3/4 8/9 ps pulse 45 o / / / / fom a typical 49 o 3/4 /3 9/8 Nd-glass lase) 53 o 4/5 3/5 4/ / / / 3 / 0 9 giga- G G$ (Size of 6 o 7/8 5 / /8 7/5 / Bill & Melissa 70 o 6/7 /3 47/7 Gates Tust) 75 o 8/9 /4 08/9 80 o 65/66 /6 65/ 0 6 mega- M 6.37 Mm (The 90 o 0 adius of the Eath) (Memoize the Bold ows fo futue efeece.) 0 3 kilo- k kg (SI uit Deivatives of Polyomials of mass) Fo polyomials, with idividual tems of the fom Ax, we defie the deivative of each tem as ( ) d Ax = Ax dx To fid the deivative of the polyomial, simply add the deivatives fo the idividual tems: ( ) 6 d 3x + 6x 3 = 6x + dx Itegals of Polyomials Fo polyomials, with idividual tems of the fom Ax, we defie the idefiite itegal of each tem as + ( ) Ax dx = Ax + To fid the idefiite itegal of the polyomial, simply add the itegals fo the idividual tems ad the costat of itegatio, C. ( 6x + 6) dx = [ 3x + 6x C] deci- d 0 cm 0 - ceti- c.54 cm (= i) 0-3 milli- m mm (The smallest divisio o a mete stick) 0-6 mico- µ 0-9 ao- 50 m (Wavelegth of gee light) 0 - pico- p pg (Typical mass of a DNA sample used i geome studies) 0-5 femto- f 0-8 atto- a 600 as (Time duatio of the shotest lase pulses) Vesio 5//005
8 D. Hoselto & M. Pice Page 8 of 8 Liea Equivalet Mass Rotatig systems ca be hadled usig the liea foms of the equatios of motio. To do so, howeve, you must use a mass equivalet to the mass of a o-otatig object. We call this the Liea Equivalet Mass (LEM). (See Example I) Fo objects that ae both otatig ad movig liealy, you must iclude them twice; oce as a liealy movig object (usig m) ad oce moe as a otatig object (usig LEM). (See Example II) The LEM of a otatig mass is easily defied i tems of its momet of ietia, I. LEM = I/ Fo example, usig a stadad table of Momets of Ietia, we ca calculate the LEM of simple objects otatig o axes though thei cetes of mass: I LEM Cylidical hoop m m Solid disk ½m ½m Hollow sphee 5 m 5 m Solid sphee ⅔m ⅔m Example I A flywheel, M = 4.80 kg ad = 0.44 m, is wapped with a stig. A hagig mass, m, is attached to the ed of the stig. Whe the hagig mass is eleased, it acceleates dowwad at.00 m/s. Fid the hagig mass. To hadle this poblem usig the liea fom of Newto s Secod Law of Motio, all we have to do is use the LEM of the flywheel. We will assume, hee, that it ca be teated as a uifom solid disk. The oly exteal foce o this system is the weight of the hagig mass. The mass of the system cosists of the hagig mass plus the liea equivalet mass of the fly-wheel. Fom Newto s d Law we have F = ma, theefoe, If a = g/ = m/s, If a = ¾g = m/s, mg = [m + (LEM=½M)]a mg = [m + ½M] a (mg ma) = ½M a m(g a) = ½Ma m = ½ M a / (g a) m = ½ / (9.8 ) m = 0.7 kg m =.4 kg m = 7. kg Note, too, that we do ot eed to kow the adius uless the agula acceleatio of the fly-wheel is equested. If you eed α, ad you have, the α = a/. Example II Fid the kietic eegy of a disk, m = 6.7 kg, that is movig at 3. m/s while ollig without slippig alog a flat, hoizotal suface. (I DISK = ½m ; LEM = ½m) The total kietic eegy cosists of the liea kietic eegy, K L = ½mv, plus the otatioal kietic eegy, K R = ½(I)(ω) = ½(I)(v/) = ½(I/ )v = ½(LEM)v. Fial Note: KE = ½mv + ½ (LEM=½m) v KE = ½ ½ (½ 6.7) 3. KE = = 5 J This method of icopoatig otatig objects ito the liea equatios of motio woks i evey situatio I ve tied; eve vey complex poblems. Wok you poblem the classic way ad this way to compae the two. Oce you ve veified that the LEM method woks fo a paticula type of poblem, you ca cofidetly use it fo solvig ay othe poblem of the same type. Vesio 5//005
Ground Rules. PC1221 Fundamentals of Physics I. Uniform Circular Motion, cont. Uniform Circular Motion (on Horizon Plane) Lectures 11 and 12
PC11 Fudametals of Physics I Lectues 11 ad 1 Cicula Motio ad Othe Applicatios of Newto s Laws D Tay Seg Chua 1 Goud Rules Switch off you hadphoe ad page Switch off you laptop compute ad keep it No talkig
More informationROTATIONAL MOTION PR 1
Eistei Classes, Uit No.,, Vadhma Rig Road Plaza, Vikas Pui Ext., Oute Rig Road New Delhi 8, Ph. : 969, 87 PR ROTATIONAL MOTION Syllabus : Cete of mass of a two-paticles system, Cete of mass of a igid body;
More informationJEE(MAIN) 2018 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. 64. The density of a material in the shape of a cube ALLEN
6. The agula width of the cetal maximum i a sigle slit diffactio patte is 60. The width of the slit is mm. The slit is illumiated by moochomatic plae waves. If aothe slit of same width is made ea it, Youg
More informationAdvanced Higher Formula List
Advaced Highe Fomula List Note: o fomulae give i eam emembe eveythig! Uit Biomial Theoem Factoial! ( ) ( ) Biomial Coefficiet C!! ( )! Symmety Idetity Khayyam-Pascal Idetity Biomial Theoem ( y) C y 0 0
More informationPhysics Equations Course Comparison
Physics Equatios Couse Compaiso Ietify you couse. You may use ay of the equatios beeath a to the left of you couse. Math A A PeCalculus Calculus AB o BC A to B is OR A:B is (Cocuet) (Cocuet) B B Algeba
More informationANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)
AIITS-HT-VII-PM-JEE(Mai)-Sol./7 I JEE Advaced 06, FIITJEE Studets bag 6 i Top 00 AIR, 7 i Top 00 AIR, 8 i Top 00 AIR. Studets fom Log Tem lassoom/ Itegated School Pogam & Studets fom All Pogams have qualified
More informationAdvanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet
Advanced Subsidiay GCE (H57) Advanced GCE (H557) Physics B (Advancing Physics) Data, Fomulae and Relationships Booklet The infomation in this booklet is fo the use of candidates following the Advanced
More informationPhys 1215, First Test. September 20, minutes Name:
Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo
More informationFormulae and Tables for use in the State Examinations
Fomulae ad Tables fo use i the State Examiatios Page Daft fo cosultatio Obsevatios ae ivited o this daft booklet of Fomulae ad Tables, which is iteded to eplace the Mathematics Tables fo use i the state
More informationKCET PHYSICS 2018 VERSION CODE: G. A plane wavefront of wavelength is incident on a single slit of width a. The angular width of principal maximum is
KCET PHYSICS 08 ESION CODE: G. A plae wavefot of wavelegth is icidet o a sigle slit of width a. The agula width of picipal maximum is (A) a (B) a (C) a (D) a Width of the slit a Wavelegth Agula width of
More informationphysicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jauay 2009 2 a 7. Give that X = 1 1, whee a is a costat, ad a 2, blak (a) fid X 1 i tems of a. Give that X + X 1 = I, whee I is the 2 2 idetity matix, (b)
More informationKEY. Math 334 Midterm II Fall 2007 section 004 Instructor: Scott Glasgow
KEY Math 334 Midtem II Fall 7 sectio 4 Istucto: Scott Glasgow Please do NOT wite o this exam. No cedit will be give fo such wok. Rathe wite i a blue book, o o you ow pape, pefeably egieeig pape. Wite you
More informationPhys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
More informationPhysics C: Electricity and Magnetism
Physics C: Electicity an Magnetism TABLE OF INFORMATION FOR CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u =. 66 7 kg = 93 MeV/ c Poton mass, m p = 67. 7 kg Neuton mass, m n = 67. 7 kg Electon
More informationCHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method
CHAPTER 5 : SERIES 5.1 Seies 5. The Sum of a Seies 5..1 Sum of Powe of Positive Iteges 5.. Sum of Seies of Patial Factio 5..3 Diffeece Method 5.3 Test of covegece 5.3.1 Divegece Test 5.3. Itegal Test 5.3.3
More information2012 GCE A Level H2 Maths Solution Paper Let x,
GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs
More informationTechnical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
More information17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other
Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system
More informationELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.
ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic
More information$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer
Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =
More informationAdvanced Physical Geodesy
Supplemetal Notes Review of g Tems i Moitz s Aalytic Cotiuatio Method. Advaced hysical Geodesy GS887 Chistophe Jekeli Geodetic Sciece The Ohio State Uivesity 5 South Oval Mall Columbus, OH 4 7 The followig
More informationMATH Midterm Solutions
MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca
More informationGRAVITATIONAL FORCE IN HYDROGEN ATOM
Fudametal Joual of Mode Physics Vol. 8, Issue, 015, Pages 141-145 Published olie at http://www.fdit.com/ GRAVITATIONAL FORCE IN HYDROGEN ATOM Uiesitas Pedidika Idoesia Jl DR Setyabudhi No. 9 Badug Idoesia
More informationAlgebra-based Physics II
lgebabased Physics II Chapte 19 Electic potential enegy & The Electic potential Why enegy is stoed in an electic field? How to descibe an field fom enegetic point of view? Class Website: Natual way of
More informationGeneral Physics. Prefixes. Aims: The Greek Alphabet Units. Provided Data
General Physics Aims: The Greek Alphabet Units Prefixes Provided Data Name Upper Case Lower Case The Greek Alphabet When writing equations and defining terms, letters from the Greek alphabet are often
More information11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.
Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings
More informationCurrent, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
More informationa) The average (mean) of the two fractions is halfway between them: b) The answer is yes. Assume without loss of generality that p < r.
Solutios to MAML Olympiad Level 00. Factioated a) The aveage (mea) of the two factios is halfway betwee them: p ps+ q ps+ q + q s qs qs b) The aswe is yes. Assume without loss of geeality that p
More informationT m / A. Table C2 Submicroscopic Masses [2] Symbol Meaning Best Value Approximate Value
APPENDIX C USEFUL INFORMATION 1247 C USEFUL INFORMATION This appendix is broken into several tables. Table C1, Important Constants Table C2, Submicroscopic Masses Table C3, Solar System Data Table C4,
More informationADDITIONAL INTEGRAL TRANSFORMS
Chapte IX he Itegal asfom Methods IX.7 Additioal Itegal asfoms August 5 7 897 IX.7 ADDIIONAL INEGRAL RANSFORMS 6.7. Solutio of 3-D Heat Equatio i Cylidical Coodiates 6.7. Melli asfom 6.7.3 Legede asfom
More information18.1 Origin of Electricity 18.2 Charged Objects and Electric Force
1 18.1 Oigin of lecticity 18. Chaged Objects and lectic Foce Thee ae two kinds of electic chage: positive and negative. The SI unit of electic chage is the coulomb (C). The magnitude of the chage on an
More informationA moving charged particle creates a magnetic field vector at every point in space except at its position.
1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units
More informationANNEXE C Modèle mathématique du robot lego NXT
ANNEXE C Modèe athéatique du oot ego NX tié de a otice NXay-GS Mode-Based Desig - Coto of sef-aacig to-heeed oot uit ith LEGO Midstos NX, Yoihisa Yaaoto. 3 NXay-GS Modeig his chapte descies atheatica ode
More information06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )
06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and
More informationObjectives: After finishing this unit you should be able to:
lectic Field 7 Objectives: Afte finishing this unit you should be able to: Define the electic field and explain what detemines its magnitude and diection. Wite and apply fomulas fo the electic field intensity
More informationr r q Coulomb s law: F =. Electric field created by a charge q: E = = enclosed Gauss s law (electric flux through a closed surface): E ds σ ε0
Q E ds = enclosed ε S 0 08 Fomulae Sheet 1 q 1q q Coulomb s law: F =. Electic field ceated by a chage q: E = 4πε 4πε Pemittivity of fee space: 0 1 = 9 10 4πε 0 9 Newton mete / coulomb = 9 10 9 0 N m Q
More informationThe Discrete Fourier Transform
(7) The Discete Fouie Tasfom The Discete Fouie Tasfom hat is Discete Fouie Tasfom (DFT)? (ote: It s ot DTFT discete-time Fouie tasfom) A liea tasfomatio (mati) Samples of the Fouie tasfom (DTFT) of a apeiodic
More informationMultivector Functions
I: J. Math. Aal. ad Appl., ol. 24, No. 3, c Academic Pess (968) 467 473. Multivecto Fuctios David Hestees I a pevious pape [], the fudametals of diffeetial ad itegal calculus o Euclidea -space wee expessed
More informationCircular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.
Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement
More informationLecture 24: Observability and Constructibility
ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio
More informationProf. Dr. I. Nasser atomic and molecular physics -551 (T-112) February 20, 2012 Spin_orbit.doc. The Fine Structure of the Hydrogen Atom
Pof. D. I. Nasse atomic ad molecula physics -55 (T-) Febuay 0, 0 Spi_obit.doc The Fie Stuctue of the Hydoge Atom Whilst the pedictios of the quatum model of hydoge ae a vey good appoximatio to eality,
More informationECEN 5014, Spring 2013 Special Topics: Active Microwave Circuits and MMICs Zoya Popovic, University of Colorado, Boulder
ECEN 5014, Spig 013 Special Topics: Active Micowave Cicuits ad MMICs Zoya Popovic, Uivesity of Coloado, Boulde LECTURE 7 THERMAL NOISE L7.1. INTRODUCTION Electical oise is a adom voltage o cuet which is
More informationTUTORIAL 9. Static magnetic field
TUTOIAL 9 Static magnetic field Vecto magnetic potential Null Identity % & %$ A # Fist postulation # " B such that: Vecto magnetic potential Vecto Poisson s equation The solution is: " Substitute it into
More informationphysicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jue 005 5x 3 3. (a) Expess i patial factios. (x 3)( x ) (3) (b) Hece fid the exact value of logaithm. 6 5x 3 dx, givig you aswe as a sigle (x 3)( x ) (5) blak
More informationATOMIC STRUCTURE EXERCISE # 1
ATOMIC STRUCTURE EXERCISE #. A N A N 5 A N (5 ) 5 A 5 N. R R A /. (6) / cm 5. (6) / cm fm 5 m 5 fm. C 8. d m m A 6.75 m.59 A Fo atom.59 5. E.6 E ().6.6 e E (e + ).6.6 e E (Li + ).6 E (Be + ).6 As B 6.
More informationphysicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jue 005. A cuve has equatio blak x + xy 3y + 16 = 0. dy Fid the coodiates of the poits o the cuve whee 0. dx = (7) Q (Total 7 maks) *N03B034* 3 Tu ove physicsadmathstuto.com
More information15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.
Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)
More informationMapping Radius of Regular Function and Center of Convex Region. Duan Wenxi
d Iteatioal Cofeece o Electical Compute Egieeig ad Electoics (ICECEE 5 Mappig adius of egula Fuctio ad Cete of Covex egio Dua Wexi School of Applied Mathematics Beijig Nomal Uivesity Zhuhai Chia 363463@qqcom
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationChapter 8 Complex Numbers
Chapte 8 Complex Numbes Motivatio: The ae used i a umbe of diffeet scietific aeas icludig: sigal aalsis, quatum mechaics, elativit, fluid damics, civil egieeig, ad chaos theo (factals. 8.1 Cocepts - Defiitio
More informationCalculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m
MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3
More information2. Characteristics of Synchrotron Radiation
. Chaacteistics of Schoto Radiatio. Itoductio The adiatio i geeal is chaacteized b the followig tems: spectal age, photo flu, photo flu desit, billiace, ad the polaizatio. The photo flu is the oveall flu
More informationTHE LAPLACE EQUATION. The Laplace (or potential) equation is the equation. u = 0. = 2 x 2. x y 2 in R 2
THE LAPLACE EQUATION The Laplace (o potential) equation is the equation whee is the Laplace opeato = 2 x 2 u = 0. in R = 2 x 2 + 2 y 2 in R 2 = 2 x 2 + 2 y 2 + 2 z 2 in R 3 The solutions u of the Laplace
More informationm1 m2 M 2 = M -1 L 3 T -2
GAVITATION Newton s Univesal law of gavitation. Evey paticle of matte in this univese attacts evey othe paticle with a foce which vaies diectly as the poduct of thei masses and invesely as the squae of
More informationLecture 2: Stress. 1. Forces Surface Forces and Body Forces
Lectue : Stess Geophysicists study pheomea such as seismicity, plate tectoics, ad the slow flow of ocks ad mieals called ceep. Oe way they study these pheomea is by ivestigatig the defomatio ad flow of
More informationImportant Equations in Physics (A2) θ = s s is the arc length in meters in radians
Impotant Equations in Physics (A2) Unit 1: Non-unifom Acceleation (Topic 7 and 14) 1 Base units Length metes Mass Kilogams Time seconds 2 Multiples of units Tea T 10 12 Giga G 10 9 Mega M 10 6 3 Radian
More informationOn composite conformal mapping of an annulus to a plane with two holes
O composite cofomal mappig of a aulus to a plae with two holes Mila Batista (July 07) Abstact I the aticle we coside the composite cofomal map which maps aulus to ifiite egio with symmetic hole ad ealy
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More informationFAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK
The 4 th Wold Cofeece o Eathquake Egieeig Octobe -7, 8, Beijig, Chia FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK HogLiag Li,GuoHui Wu, Associate Pofesso, Depatmet of Egieeig Mechaics,
More informationEM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1)
EM- Coulomb s law, electic field, potential field, supeposition q ' Electic field of a point chage ( ') E( ) kq, whee k / 4 () ' Foce of q on a test chage e at position is ee( ) Electic potential O kq
More informationb) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block?
Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 13, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with
More information? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B.
PHY 249 Lectue Notes Chapte 32: Page 1 of 12 What we have leaned so fa a a F q a a in motion F q v a a d/ Ae thee othe "static" chages that can make -field? this lectue d/? next lectue da dl Cuve Cuve
More informationL8b - Laplacians in a circle
L8b - Laplacias i a cicle Rev //04 `Give you evidece,' the Kig epeated agily, `o I'll have you executed, whethe you'e evous o ot.' `I'm a poo ma, you Majesty,' the Hatte bega, i a temblig voice, `--ad
More informationSection 26 The Laws of Rotational Motion
Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to
More informationElectrostatics. 3) positive object: lack of electrons negative object: excess of electrons
Electostatics IB 12 1) electic chage: 2 types of electic chage: positive and negative 2) chaging by fiction: tansfe of electons fom one object to anothe 3) positive object: lack of electons negative object:
More informationPHYS 1114, Lecture 21, March 6 Contents:
PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam
More informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More informationPhysics NYB problem set 5 solution
Physics NY poblem set 5 solutions 1 Physics NY poblem set 5 solution Hello eveybody, this is ED. Hi ED! ED is useful fo dawing the ight hand ule when you don t know how to daw. When you have a coss poduct
More informationElectrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase?
Electostatics 1. Show does the foce between two point chages change if the dielectic constant of the medium in which they ae kept incease? 2. A chaged od P attacts od R whee as P epels anothe chaged od
More informationPhysics 107 TUTORIAL ASSIGNMENT #8
Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type
More informationF = net force on the system (newton) F,F and F. = different forces working. E = Electric field strength (volt / meter)
All the Impotant Fomulae that a student should know fom. XII Physics Unit : CHAPTER - ELECTRIC CHARGES AND FIELD CHAPTER ELECTROSTATIC POTENTIAL AND CAPACITANCE S. Fomula No.. Quantization of chage Q =
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More information1 2 U CV. K dq I dt J nqv d J V IR P VI
o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C
More informationPHYS 1444 Lecture #5
Shot eview Chapte 24 PHYS 1444 Lectue #5 Tuesday June 19, 212 D. Andew Bandt Capacitos and Capacitance 1 Coulom s Law The Fomula QQ Q Q F 1 2 1 2 Fomula 2 2 F k A vecto quantity. Newtons Diection of electic
More informationPhys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations
Phys-7 Lectue 17 Motional Electomotive Foce (emf) Induced Electic Fields Displacement Cuents Maxwell s Equations Fom Faaday's Law to Displacement Cuent AC geneato Magnetic Levitation Tain Review of Souces
More informationAP Physics - Coulomb's Law
AP Physics - oulomb's Law We ve leaned that electons have a minus one chage and potons have a positive one chage. This plus and minus one business doesn t wok vey well when we go in and ty to do the old
More informationev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e
. A paallel-plate capacito has sepaation d. The potential diffeence between the plates is V. If an electon with chage e and mass m e is eleased fom est fom the negative plate, its speed when it eaches
More informationBINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a
BINOMIAL THEOREM hapte 8 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4 5y, etc., ae all biomial epessios. 8.. Biomial theoem If
More informationChemical Engineering 412
Chemical Engineeing 41 Intoductoy Nuclea Engineeing Lectue 16 Nuclea eacto Theoy III Neuton Tanspot 1 One-goup eacto Equation Mono-enegetic neutons (Neuton Balance) DD φφ aa φφ + ss 1 vv vv is neuton speed
More informationAuchmuty High School Mathematics Department Sequences & Series Notes Teacher Version
equeces ad eies Auchmuty High chool Mathematics Depatmet equeces & eies Notes Teache Vesio A sequece takes the fom,,7,0,, while 7 0 is a seies. Thee ae two types of sequece/seies aithmetic ad geometic.
More informationRAO IIT ACADEMY / NSEP Physics / Code : P 152 / Solutions NATIONAL STANDARD EXAMINATION IN PHYSICS SOLUTIONS
RAO ACADEMY / NSEP Physics / Code : P 5 / Solutions NAONAL SANDARD EXAMNAON N PHYSCS - 5 SOLUONS RAO ACADEMY / NSEP Physics / Code : P 5 / Solutions NSEP SOLUONS (PHYSCS) CODE - P 5 ANSWER KEY & SOLUONS.
More informationCh 13 Universal Gravitation
Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)
More informationBINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a
8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4, etc., ae all biomial 5y epessios. 8.. Biomial theoem BINOMIAL THEOREM If a ad b ae
More informationNegative Exponent a n = 1 a n, where a 0. Power of a Power Property ( a m ) n = a mn. Rational Exponents =
Refeece Popetie Popetie of Expoet Let a ad b be eal umbe ad let m ad be atioal umbe. Zeo Expoet a 0 = 1, wee a 0 Quotiet of Powe Popety a m a = am, wee a 0 Powe of a Quotiet Popety ( a b m, wee b 0 b)
More informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity
More informationb) (5) What average force magnitude was applied by the students working together?
Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults
More informationc) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed?
Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 10, 2012 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with
More information16.1 Permanent magnets
Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and
More informationAnnouncements: The Rydberg formula describes. A Hydrogen-like ion is an ion that
Q: A Hydogelike io is a io that The Boh odel A) is cheically vey siila to Hydoge ios B) has the sae optical spectu as Hydoge C) has the sae ube of potos as Hydoge ) has the sae ube of electos as a Hydoge
More informationPhysics 4A Chapter 8: Dynamics II Motion in a Plane
Physics 4A Chapte 8: Dynamics II Motion in a Plane Conceptual Questions and Example Poblems fom Chapte 8 Conceptual Question 8.5 The figue below shows two balls of equal mass moving in vetical cicles.
More informationAP Physics Electric Potential Energy
AP Physics lectic Potential negy Review of some vital peviously coveed mateial. The impotance of the ealie concepts will be made clea as we poceed. Wok takes place when a foce acts ove a distance. W F
More informationConditional Convergence of Infinite Products
Coditioal Covegece of Ifiite Poducts William F. Tech Ameica Mathematical Mothly 106 1999), 646-651 I this aticle we evisit the classical subject of ifiite poducts. Fo stadad defiitios ad theoems o this
More informationExam 3, vers Physics Spring, 2003
1 of 9 Exam 3, ves. 0001 - Physics 1120 - Sping, 2003 NAME Signatue Student ID # TA s Name(Cicle one): Michael Scheffestein, Chis Kelle, Paisa Seelungsawat Stating time of you Tues ecitation (wite time
More informationChapter 4. Newton s Laws of Motion
Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto
More informationClassical Mechanics Qualifying Exam Solutions Problem 1.
Jauary 4, Uiversity of Illiois at Chicago Departmet of Physics Classical Mechaics Qualifyig Exam Solutios Prolem. A cylider of a o-uiform radial desity with mass M, legth l ad radius R rolls without slippig
More informationPhysics 1114: Unit 5 Hand-out Homework (Answers)
Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),
More informationExtra notes for circular motion: Circular motion : v keeps changing, maybe both speed and
Exta notes fo cicula motion: Cicula motion : v keeps changing, maybe both speed and diection ae changing. At least v diection is changing. Hence a 0. Acceleation NEEDED to stay on cicula obit: a cp v /,
More informationReview for Midterm-1
Review fo Midtem-1 Midtem-1! Wednesday Sept. 24th at 6pm Section 1 (the 4:10pm class) exam in BCC N130 (Business College) Section 2 (the 6:00pm class) exam in NR 158 (Natual Resouces) Allowed one sheet
More informationJEE(MAIN) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. Ans. (4) Sol. l. Þ k n = ALLEN. Þ k g k n = hc L.
6. Te agula widt of te cetal maximum i a sigle slit diffactio patte is 60. Te widt of te slit is mm. Te slit is illumiated by moocomatic plae waves. If aote slit of same widt is made ea it, Youg s figes
More information