General Physics I - Pgccphy
General Physics I:Classical MechanicsDavid G. SimpsonDept. of Natural Sciences, Prince George’s Community College, Largo, MarylandLarry L. SimpsonUnion Carbide Corporation (ret.), South Charleston, West VirginiaFall 2020Last updated: October 8, 2020
ContentsAcknowledgments111What is Physics?122Units2.12.22.32.42.52.62.72.8Systems of Units. . . . . . . . . . . .SI Units . . . . . . . . . . . . . . . .CGS Systems of Units . . . . . . . . .British Engineering Units . . . . . . .Units as an Error-Checking Technique .Unit Conversions . . . . . . . . . . .Currency Units. . . . . . . . . . . . .Odds and Ends . . . . . . . . . . . . .1414151919192022223Problem-Solving Strategies4Density264.1Specific Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2Density Trivia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Kinematics in One Dimension5.1Position . . . . . . . . .5.2Velocity . . . . . . . . .5.3Acceleration . . . . . . .5.4Higher Derivatives . . . .5.5Dot Notation . . . . . . .5.6Inverse Relations. . . . .5.7Constant Acceleration . .5.8Summary . . . . . . . .5.9Geometric Introduction . . . . . . . . . . . . . .6.2Vector Arithmetic: Graphical Methods.6.3Vector Arithmetic: Algebraic Methods.6.4The Zero Vector . . . . . . . . . . . .6.5Derivatives. . . . . . . . . . . . . . .37. 37. 38. 38. 43. 431
Prince George’s Community College6.66.778910Simpson & SimpsonIntegrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Other Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44The Dot Product7.1Definition . . . . .7.2Component Form .7.3Properties . . . . .7.4Matrix Formulation.45. 45. 45. 46. 48Kinematics in Two or Three Dimensions8.1Position . . . . . . . . . . . . . .8.2Velocity . . . . . . . . . . . . . .8.3Acceleration . . . . . . . . . . . .8.4Inverse Relations. . . . . . . . . .8.5Constant Acceleration . . . . . . .8.6Vertical vs. Horizontal Motion . . .8.7Summary . . . . . . . . . . . . .4949494950505152Projectile Motion9.1Range . . . . . . . . . . . . . . . .9.2Maximum Altitude. . . . . . . . . .9.3Shape of the Projectile Path . . . . .9.4Hitting a Target on the Ground. . . .9.5Hitting a Target on a Hill. . . . . . .9.6Exploding Projectiles . . . . . . . .9.7Other Considerations . . . . . . . .9.8The Monkey and the Hunter Problem9.9Summary . . . . . . . . . . . . . .54555657575960606062Newton’s Method10.1 Introduction . . . . . .10.2 The Method . . . . . .10.3 Example: Square Roots10.4 Projectile Problem . . .63. 63. 63. 63. 6511Mass12Force12.112.212.312.412.513General Physics I.66The Four Forces of Nature .Hooke’s Law. . . . . . . .Weight . . . . . . . . . . .Normal Force . . . . . . .Tension . . . . . . . . . .67. 67. 68. 68. 68. 69Newton’s Laws of Motion7013.1 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7013.2 Second Law of Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7013.3 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722
Prince George’s Community CollegeGeneral Physics ISimpson & Simpson14The Inclined Plane7315Atwood’s Machine7516Statics7916.1 Mass Suspended by Two Ropes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7916.2 The Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8216.3 The Catenary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8217Friction17.1 Introduction . . . . . . . .17.2 Static Friction . . . . . . .17.3 Kinetic Friction . . . . . .17.4 Rolling Friction . . . . . .17.5 The Coefficient of Friction.84. 84. 84. 85. 85. 8518Blocks and Pulleys8718.1 Horizontal Block and Vertical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8718.2 Inclined Block and Vertical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8819Resistive Forces in Fluids9119.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9119.2 Model I: F R / v. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9119.3 Model II: F R / v 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9320Circular Motion20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20.2 Centripetal Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20.3 Centrifugal Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20.4 Relations between Circular and Linear Motion. . . . . . . . . . . . . . . . . . . . . . . .20.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Work21.121.221.321.421.521.622Introduction . . . . . . . . . . . . . .Case I: Constant F k r . . . . . . . . .Case II: Constant F r . . . . . . . .Case III: Variable F k r . . . . . . . .Case IV (General Case): Variable F rSummary . . . . . . . . . . . . . . .Simple Machines22.1 Inclined Plane .22.2 Wheel and Axle22.3 Pulley . . . . .22.4 Lever . . . . .22.5 Wedge . . . . .22.6 Screw . . . . .22.7 Gears . . . . 61081081083
Prince George’s Community College23General Physics IEnergy23.1 Introduction . . . . . . . .23.2 Kinetic Energy . . . . . . .23.3 Potential Energy . . . . . .23.4 Other Forms of Energy. . .23.5 Conservation of Energy . .23.6 The Work-Energy Theorem23.7 The Virial Theorem . . . .Simpson & Simpson.11011011011111411411511524Conservative Forces25Power11825.1 Energy Conversion of a Falling Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11925.2 Rate of Change of Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12025.3 Vector Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12026Linear Momentum12126.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12126.2 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12126.3 Newton’s Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12127Impulse28Collisions28.1 Introduction . . . . . . . . . .28.2 The Coefficient of Restitution .28.3 Perfectly Inelastic Collisions. .28.4 Perfectly Elastic Collisions . .28.5 Newton’s Cradle . . . . . . . .28.6 Inelastic Collisions. . . . . . .28.7 Collisions in Two Dimensions .29The Ballistic Pendulum30Rockets30.1 Introduction . . . . .30.2 The Rocket Equation.30.3 Mass Fraction . . . .30.4 Staging . . . . . . 531Center of Mass31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31.2 Discrete Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31.3 Continuous Bodies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32The Cross Product14032.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14032.2 Component Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14132.3 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414136. 136. 136. 137
Prince George’s Community College32.432.5General Physics ISimpson & SimpsonMatrix Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14333Rotational Motion14533.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14533.2 Translational vs. Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14533.3 Example Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14734Moment of Inertia34.1 Introduction . . . . . .34.2 Radius of Gyration. . .34.3 Parallel Axis Theorem .34.4 Plane Figure Theorem .34.5 Routh’s Rule . . . . . .34.6 Lees’ Rule . . . . . . .14914915315415515515635Torque15735.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15735.2 Rotational Version of Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15835.3 Couples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15836Measuring the Moment of Inertia15936.1 Torque Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15936.2 Pendulum Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16037Newton’s Laws of Motion: Rotational Versions16237.1 First Law of Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16237.2 Second Law of Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16237.3 Third Law of Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16338The Pendulum38.1 Introduction . . . . . . . . .38.2 The Simple Plane Pendulum .38.3 The Spherical Pendulum . . .38.4 The Conical Pendulum. . . .38.5 The Torsional Pendulum . . .38.6 The Physical Pendulum . . .38.7 Other Pendulums . . . . . .164164164165165167167169Simple Harmonic Motion39.1 Energy . . . . . . . . . . . .39.2 Frequency and Period . . . .39.3 The Vertical Spring . . . . .39.4 Frequency and Period . . . .39.5 Mass on a Spring . . . . . .39.6 More on the Spring Constant.1701721741741741751753940Rocking Bodies17840.1 The Half-Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1785
Prince George’s Community College41Rolling Bodies41.1 Introduction . . . . . .41.2 Velocity . . . . . . . .41.3 Acceleration . . . . . .41.4 Kinetic Energy . . . . .41.5 The Wheel . . . . . . .41.6 Ball Rolling in a Bowl .General Physics I.Simpson & Simpson.18118118118218318418542Galileo’s Law18742.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18742.2 Modern Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18743The Coriolis Force18943.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18943.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19044Angular Momentum19144.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19144.2 Conservation of Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19145Conservation Laws46The Gyroscope19446.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19446.2 Precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19446.3 Nutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19547Elasticity47.1 Introduction . . . . . . . . . . . . . . .47.2 Longitudinal (Normal) Stress . . . . . .47.3 Transverse (Shear) Stress—Translational47.4 Transverse (Shear) Stress—Torsional . .47.5 Volume Stress . . . . . . . . . . . . . .47.6 Elastic Limit . . . . . . . . . . . . . . .47.7 Summary . . . . . . . . . . . . . . . .4849193.196196196197198198199199Fluid Statics48.1 Introduction . . . . . . . . . . . . . .48.2 Archimedes’ Principle . . . . . . . . .48.3 Floating Bodies . . . . . . . . . . . .48.4 Pressure . . . . . . . . . . . . . . . .48.5 Change in Fluid Pressure with Depth .48.6 Pascal’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200. 200. 200. 200. 201. 202. 203Fluid Dynamics49.1 The Continuity Equation.49.2 Bernoulli’s Equation . . .49.3 Torricelli’s Theorem . . .49.4 The Siphon . . . . . . .6.204205205206208
Prince George’s Community College49.549.649.749.849.949.10General Physics IViscosity. . . . . . . . .The Reynolds Number . .Stokes’s Law. . . . . . .Fluid Flow through a PipeGases . . . . . . . . . .Superfluids. . . . . . . .Simpson & Simpson.20921121121221221450Hydraulics and Pneumatics21750.1 Hydraulics: The Hydraulic Press. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21750.2 Pneumatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21951Gravity51.1 Newton’s Law of Gravity .51.2 Gravitational Potential . . .51.3 The Cavendish Experiment51.4 Helmert’s Equation . . . .51.5 Earth Density Model. . . .51.6 Escape Velocity . . . . . .51.7 Gauss’s Formulation . . . .51.8 General Relativity . . . . .51.9 Black Holes . . . . . . . .220220220221221222224224228229Earth Rotation52.1 Introduction .52.2 Precession . .52.3 Nutation . . .52.4 Polar Motion.52.5 Rotation Rate.230230230230232232Geodesy53.1 Introduction . . . . . . . . . . . . . .53.2 Radius of the Earth . . . . . . . . . .53.3 The Cosine Formula . . . . . . . . . .53.4 Vincenty’s Formulæ: Introduction . . .53.5 Vincenty’s Formulæ: Direct Problem .53.6 Vincenty’s Formulæ: Inverse Problem .234234235235236236238525354.Celestial Mechanics24154.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24154.2 Kepler’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24154.3 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24254.4 Orbit Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24254.5 Orbital Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24354.6 Right Ascension and Declination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24454.7 Computing a Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24554.8 The Inverse Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24654.9 Corrections to the Two-Body Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 24654.10 Bound and Unbound Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24754.11 The Vis Viva Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2477
Prince George’s Community College54.1254.1354.1454.1554.1654.1755General Physics IBertrand’s Theorem . . . . . . .Differential Equation for an OrbitLagrange Points . . . . . . . . .The Rings of Saturn . . . . . . .Hyperbolic Orbits . . . . . . . .Parabolic Orbits . . . . . . . . .Simpson & Simpson.248248249250252253Astrodynamics55.1 Circular Orbits . . . . . . . . . . . .55.2 Geosynchronous Orbits . . . . . . .55.3 Elliptical Orbits . . . . . . . . . . .55.4 The Hohmann Transfer . .
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