INTRODUCTORY PHYSICS: ELEMENTARY MECHANICS
CONTENTS I: GETTING READY TO LEARN PHYSICS PRELIMINARIES SEE, DO, TEACH OTHER CONDITIONS FOR LEARNING YOUR BRAIN AND LEARNING HOW TO DO YOUR HOMEWORK E?ECTIVELY THE METHOD OF THREE PASSES MATHEMATICS SUMMARY HOMEWORK FOR WEEK 0 II: ELEMENTARY MECHANICS WEEK 1: NEWTON’S LAWS 11: INTRODUCTION: A BIT OF HISTORY AND PHILOSOPHY 12: DYNAMICS 13: COORDINATES 14: NEWTON’S LAWS 15: FORCES 151: THE FORCES OF NATURE 152: FORCE RULES 16: FORCE BALANCE – STATIC EQUILIBRIUM EXAMPLE 161: SPRING AND MASS IN STATIC FORCE EQUILIBRIUM 17: SIMPLE MOTION IN ONE DIMENSION EXAMPLE 171: A MASS FALLING FROM HEIGHT H EXAMPLE 172: A CONSTANT FORCE IN ONE DIMENSION 171: SOLVING PROBLEMS WITH MORE THAN ONE OBJECT EXAMPLE 173: ATWOOD’S MACHINE EXAMPLE 174: BRAKING FOR BIKES, OR JUST BREAKING BIKES? 18: MOTION IN TWO DIMENSIONS 181: FREE FLIGHT TRAJECTORIES – PROJECTILE MOTION EXAMPLE 181: TRAJECTORY OF A CANNONBALL 182: THE INCLINED PLANE EXAMPLE 182: THE INCLINED PLANE 19: CIRCULAR MOTION 191: TANGENTIAL VELOCITY 192: CENTRIPETAL ACCELERATION EXAMPLE 191: BALL ON A STRING EXAMPLE 192: TETHER BALL/CONIC PENDULUM 193: TANGENTIAL ACCELERATION 110: CONCLUSION: RUBRIC FOR NEWTON’S SECOND LAW PROBLEMS HOMEWORK FOR WEEK 1 WEEK 2: NEWTON’S LAWS: CONTINUED 21: FRICTION EXAMPLE 211: INCLINED PLANE OF LENGTH L WITH FRICTION EXAMPLE 212: BLOCK HANGING O?OF A TABLE EXAMPLE 213: FIND THE MINIMUM NO-SKID BRAKING DISTANCE FOR A CAR EXAMPLE 214: CAR ROUNDING A BANKED CURVE WITH FRICTION 22: DRAG FORCES 221: STOKES, OR LAMINAR DRAG 222: RAYLEIGH, OR TURBULENT DRAG 223: TERMINAL VELOCITY EXAMPLE 221: FALLING FROM A PLANE AND SURVIVING EXAMPLE 222: SOLUTION TO EQUATIONS OF MOTION FOR STOKES’ DRAG 224: ADVANCED: SOLUTION TO EQUATIONS OF MOTION FOR TURBULENT DRAG EXAMPLE 223: DROPPING THE RAM 23: INERTIAL REFERENCE FRAMES – THE GALILEAN TRANSFORMATION 231: TIME 232: SPACE 24: NON-INERTIAL REFERENCE FRAMES – PSEUDOFORCES 241: IDENTIFYING INERTIAL FRAMES EXAMPLE 241: WEIGHT IN AN ELEVATOR EXAMPLE 242: PENDULUM IN A BOXCAR 242: ADVANCED: GENERAL RELATIVITY AND ACCELERATING FRAMES 25: JUST FOR FUN: HURRICANES HOMEWORK FOR WEEK 2 WEEK 3: WORK AND ENERGY 31: WORK AND KINETIC ENERGY 311: UNITS OF WORK AND ENERGY 312: KINETIC ENERGY 32: THE WORK-KINETIC ENERGY THEOREM 321: DERIVATION I: RECTANGLE APPROXIMATION SUMMATION 322: DERIVATION II: CALCULUS-Y (CHAIN RULE) DERIVATION EXAMPLE 321: PULLING A BLOCK EXAMPLE 322: RANGE OF A SPRING GUN 33: CONSERVATIVE FORCES: POTENTIAL ENERGY 331: FORCE FROM POTENTIAL ENERGY 332: POTENTIAL ENERGY FUNCTION FOR NEAR-EARTH GRAVITY 333: SPRINGS 34: CONSERVATION OF MECHANICAL ENERGY 341: FORCE, POTENTIAL ENERGY, AND TOTAL MECHANICAL ENERGY EXAMPLE 341: FALLING BALL REPRISE EXAMPLE 342: BLOCK SLIDING DOWN FRICTIONLESS INCLINE REPRISE EXAMPLE 343: A SIMPLE PENDULUM EXAMPLE 344: LOOPING THE LOOP 35: GENERALIZED WORK-MECHANICAL ENERGY THEOREM EXAMPLE 351: BLOCK SLIDING DOWN A ROUGH INCLINE EXAMPLE 352: A SPRING AND ROUGH INCLINE 351: HEAT AND CONSERVATION OF ENERGY 36: POWER EXAMPLE 361: ROCKET POWER 37: EQUILIBRIUM 371: ENERGY DIAGRAMS: TURNING POINTS AND FORBIDDEN REGIONS HOMEWORK FOR WEEK 3 WEEK 4: SYSTEMS OF PARTICLES, MOMENTUM AND COLLISIONS 41: SYSTEMS OF PARTICLES 411: NEWTON’S LAWS FOR A SYSTEM OF PARTICLES – CENTER OF MASS EXAMPLE 411: CENTER OF MASS OF A FEW DISCRETE PARTICLES 412: COARSE GRAINING: CONTINUOUS MASS DISTRIBUTIONS EXAMPLE 412: CENTER OF MASS OF A CONTINUOUS ROD EXAMPLE 413: CENTER OF MASS OF A CIRCULAR WEDGE EXAMPLE 414: BREAKUP OF PROJECTILE IN MID?IGHT 42: MOMENTUM 421: THE LAW OF CONSERVATION OF MOMENTUM 43: IMPULSE EXAMPLE 431: AVERAGE FORCE DRIVING A GOLF BALL EXAMPLE 432: FORCE, IMPULSE AND MOMENTUM FOR WINDSHIELD AND BUG 431: THE IMPULSE APPROXIMATION 432: IMPULSE, FLUIDS, AND PRESSURE 44: CENTER OF MASS REFERENCE FRAME 45: COLLISIONS 451: MOMENTUM CONSERVATION IN THE IMPULSE APPROXIMATION 452: ELASTIC COLLISIONS 453: FULLY INELASTIC COLLISIONS 454: PARTIALLY INELASTIC COLLISIONS 455: DIMENSION OF SCATTERING AND SU?CIENT INFORMATION 46: 1-D ELASTIC COLLISIONS 461: THE RELATIVE VELOCITY APPROACH 462: 1D ELASTIC COLLISION IN THE CENTER OF MASS FRAME 463: THE “BB/BB” OR “POOL BALL” LIMITS 47: ELASTIC COLLISIONS IN 2-3 DIMENSIONS 48: INELASTIC COLLISIONS EXAMPLE 481: ONE-DIMENSIONAL FULLY INELASTIC COLLISION (ONLY) EXAMPLE 482: BALLISTIC PENDULUM EXAMPLE 483: PARTIALLY INELASTIC COLLISION 49: KINETIC ENERGY IN THE CM FRAME HOMEWORK FOR WEEK 4 WEEK 5: TORQUE AND ROTATION IN ONE DIMENSION 51: ROTATIONAL COORDINATES IN ONE DIMENSION 52: NEWTON’S SECOND LAW FOR 1D ROTATIONS 521: THE R-DEPENDENCE OF TORQUE 522: SUMMING THE MOMENT OF INERTIA 53: THE MOMENT OF INERTIA EXAMPLE 531: THE MOMENT OF INERTIA OF A ROD PIVOTED AT ONE END 531: MOMENT OF INERTIA OF A GENERAL RIGID BODY EXAMPLE 532: MOMENT OF INERTIA OF A RING EXAMPLE 533: MOMENT OF INERTIA OF A DISK 532: TABLE OF USEFUL MOMENTS OF INERTIA 54: TORQUE AS A CROSS PRODUCT EXAMPLE 541: ROLLING THE SPOOL 55: TORQUE AND THE CENTER OF GRAVITY EXAMPLE 551: THE ANGULAR ACCELERATION OF A HANGING ROD 56: SOLVING NEWTON’S SECOND LAW PROBLEMS INVOLVING ROLLING EXAMPLE 561: A DISK ROLLING DOWN AN INCLINE EXAMPLE 562: ATWOOD’S MACHINE WITH A MASSIVE PULLEY 57: ROTATIONAL WORK AND ENERGY 571: WORK DONE ON A RIGID OBJECT 572: THE ROLLING CONSTRAINT AND WORK EXAMPLE 571: WORK AND ENERGY IN ATWOOD’S MACHINE EXAMPLE 572: UNROLLING SPOOL EXAMPLE 573: A ROLLING BALL LOOPS-THE-LOOP 58: THE PARALLEL AXIS THEOREM EXAMPLE 581: MOON AROUND EARTH, EARTH AROUND SUN EXAMPLE 582: MOMENT OF INERTIA OF A HOOP PIVOTED ON ONE SIDE 59: PERPENDICULAR AXIS THEOREM EXAMPLE 591: MOMENT OF INERTIA OF HOOP FOR PLANAR AXIS HOMEWORK FOR WEEK 5 WEEK 6: VECTOR TORQUE AND ANGULAR MOMENTUM 61: VECTOR TORQUE 62: TOTAL TORQUE 621: THE LAW OF CONSERVATION OF ANGULAR MOMENTUM 63: THE ANGULAR MOMENTUM OF A SYMMETRIC ROTATING RIGID OBJECT EXAMPLE 631: ANGULAR MOMENTUM OF A POINT MASS MOVING IN A CIRCLE EXAMPLE 633: ANGULAR MOMENTUM OF A ROTATING DISK EXAMPLE 634: ANGULAR MOMENTUM OF ROD SWEEPING OUT CONE 64: ANGULAR MOMENTUM CONSERVATION EXAMPLE 641: THE SPINNING PROFESSOR 641: RADIAL FORCES AND ANGULAR MOMENTUM CONSERVATION EXAMPLE 642: MASS ORBITS ON A STRING 65: COLLISIONS EXAMPLE 651: FULLY INELASTIC COLLISION OF BALL OF PUTTY WITH A FREE ROD EXAMPLE 652: FULLY INELASTIC COLLISION OF BALL OF PUTTY WITH PIVOTED ROD 651: MORE GENERAL COLLISIONS 66: ANGULAR MOMENTUM OF AN ASYMMETRIC ROTATING RIGID OBJECT EXAMPLE 661: ROTATING YOUR TIRES 67: PRECESSION OF A TOP EXAMPLE 671: FINDING ?P FROM ?L/?T (AVERAGE) EXAMPLE 672: FINDING ?P FROM ?L AND ?T SEPARATELY EXAMPLE 673: FINDING ?P FROM CALCULUS HOMEWORK FOR WEEK 6 WEEK 7: STATICS STATICS SUMMARY 71: CONDITIONS FOR STATIC EQUILIBRIUM 72: STATIC EQUILIBRIUM PROBLEMS EXAMPLE 721: BALANCING A SEE-SAW EXAMPLE 722: TWO SAW HORSES EXAMPLE 723: HANGING A TAVERN SIGN 721: EQUILIBRIUM WITH A VECTOR TORQUE EXAMPLE 724: BUILDING A DECK 73: TIPPING EXAMPLE 731: TIPPING VERSUS SLIPPING EXAMPLE 732: TIPPING WHILE PUSHING 74: FORCE COUPLES EXAMPLE 741: ROLLING THE CYLINDER OVER A STEP HOMEWORK FOR WEEK 7 III: APPLICATIONS OF MECHANICS WEEK 8: FLUIDS FLUIDS SUMMARY 81: GENERAL FLUID PROPERTIES 811: PRESSURE 812: DENSITY 813: COMPRESSIBILITY 814: VISCOSITY AND ?UID ?OW 815: PROPERTIES SUMMARY STATIC FLUIDS 816: PRESSURE AND CON?NEMENT OF STATIC FLUIDS 817: PRESSURE AND CON?NEMENT OF STATIC FLUIDS IN GRAVITY 818: VARIATION OF PRESSURE IN INCOMPRESSIBLE FLUIDS EXAMPLE 811: BAROMETERS EXAMPLE 812: VARIATION OF OCEANIC PRESSURE WITH DEPTH 819: VARIATION OF PRESSURE IN COMPRESSIBLE FLUIDS EXAMPLE 813: VARIATION OF ATMOSPHERIC PRESSURE WITH HEIGHT 82: PASCAL’S PRINCIPLE AND HYDRAULICS EXAMPLE 821: A HYDRAULIC LIFT 83: FLUID DISPLACEMENT AND BUOYANCY 831: ARCHIMEDES’ PRINCIPLE EXAMPLE 831: TESTING THE CROWN I EXAMPLE 832: TESTING THE CROWN II 84: FLUID FLOW 841: CONSERVATION OF FLOW 842: WORK-MECHANICAL ENERGY IN FLUIDS: BERNOULLI’S EQUATION EXAMPLE 841: EMPTYING THE ICED TEA EXAMPLE 842: FLOW BETWEEN TWO TANKS 843: FLUID VISCOSITY AND RESISTANCE 844: RESISTANCE OF A CIRCULAR PIPE: POISEUILLE’S EQUATION 845: TURBULENCE 85: THE HUMAN CIRCULATORY SYSTEM EXAMPLE 851: ATHEROSCLEROTIC PLAQUE PARTIALLY OCCLUDES A BLOOD VESSEL EXAMPLE 852: ANEURISMS EXAMPLE 853: THE GIRA?E HOMEWORK FOR WEEK 8 WEEK 9: OSCILLATIONS OSCILLATION SUMMARY 91: THE SIMPLE HARMONIC OSCILLATOR 911: THE ARCHETYPICAL SIMPLE HARMONIC OSCILLATOR: A MASS ON A SPRING 912: THE SIMPLE HARMONIC OSCILLATOR SOLUTION 913: PLOTTING THE SOLUTION: RELATIONS INVOLVING ? 914: THE ENERGY OF A MASS ON A SPRING 92: THE PENDULUM 921: THE PHYSICAL PENDULUM 93: DAMPED OSCILLATION 931: PROPERTIES OF THE DAMPED OSCILLATOR EXAMPLE 931: CAR SHOCK ABSORBERS 932: ENERGY DAMPING: Q-VALUE 94: DAMPED, DRIVEN OSCILLATION: RESONANCE 941: HARMONIC DRIVING FORCES 942: SOLUTION TO DAMPED, DRIVEN, SIMPLE HARMONIC OSCILLATOR 95: ELASTIC PROPERTIES OF MATERIALS 951: SIMPLE MODELS FOR MOLECULAR BONDS 952: THE FORCE CONSTANT 953: A MICROSCOPIC PICTURE OF A SOLID 954: SHEAR FORCES AND THE SHEAR MODULUS 955: DEFORMATION AND FRACTURE 96: HUMAN BONE EXAMPLE 961: SCALING OF BONES WITH ANIMAL SIZE HOMEWORK FOR WEEK 9 WEEK 10: THE WAVE EQUATION WAVE SUMMARY 101: WAVES 102: WAVES ON A STRING 103: SOLUTIONS TO THE WAVE EQUATION 1031: AN IMPORTANT PROPERTY OF WAVES: SUPERPOSITION 1032: ARBITRARY WAVEFORMS PROPAGATING TO THE LEFT OR RIGHT 1033: HARMONIC WAVEFORMS PROPAGATING TO THE LEFT OR RIGHT 1034: STATIONARY WAVES 104: RE?ECTION OF WAVES 105: ENERGY 1051: ENERGY IN TRAVELLING WAVES 1052: POWER TRANSMISSION BY A TRAVELLING WAVE 1053: ENERGY IN STANDING WAVES HOMEWORK FOR WEEK WEEK 11: SOUND SOUND SUMMARY 111: SOUND WAVES IN A FLUID 112: THE WAVE EQUATION FOR SOUND 113: SOUND WAVE SOLUTIONS 114: SOUND WAVE INTENSITY 1141: SOUND DISPLACEMENT AND INTENSITY IN TERMS OF PRESSURE 1142: SOUND PRESSURE AND DECIBELS 115: DOPPLER SHIFT 1151: MOVING SOURCE 1152: MOVING RECEIVER 1153: MOVING SOURCE AND MOVING RECEIVER 116: STANDING WAVES IN PIPES 1161: PIPE CLOSED AT BOTH ENDS 1162: PIPE CLOSED AT ONE END 1163: PIPE OPEN AT BOTH ENDS 117: BEATS 118: INTERFERENCE AND SOUND WAVES 119: THE EAR WEEK 12: GRAVITY GRAVITY SUMMARY 121: COSMOLOGICAL MODELS 122: KEPLER’S LAWS 1221: ELLIPSES AND CONIC SECTIONS 123: NEWTON’S LAW OF GRAVITATION 124: THE GRAVITATIONAL FIELD 1241: SPHERES, SHELLS, GENERAL MASS DISTRIBUTIONS 125: GRAVITATIONAL POTENTIAL ENERGY 126: ENERGY DIAGRAMS AND ORBITS 127: ESCAPE VELOCITY, ESCAPE ENERGY EXAMPLE 1271: HOW TO CAUSE AN EXTINCTION EVENT 128: BRIDGING THE GAP: COULOMB’S LAW AND ELECTROSTATICS