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Part I – Mechanics Motion in One-Dimension I. Motion Terminology A. Distance B. Displacement C. Speed D. Velocity i. Average ii. Instantaneous E. Acceleration F. Vector G. Scalar II. Graphical Analysis of Motion A. Position (Displacement) vs. Time Graph B. Velocity vs. Time Graphs C. Acceleration vs. Time Graphs D. Moving between the Graphs III. Motion Under Constant Acceleration A. Galilean Equations B. Free Fall Problems Motion in Two Dimensions I. Adding Vectors a. Same Directions b. Opposite Directions c. Right Angles d. Non-Right Angles II. Projectile Motion a. Parabolic Motion b. Motion in X-Direction c. Motion in Y-Direction Forces I. Newton’s Laws of Motion a. 1st Law b. 2nd Law c. 3rd Law II. Static Equilibrium III. Non-Equilibrium IV. Frictional Forces V. Center of Mass (Gravity) VI. Torque VII. Rotational Equilibrium Work, Power, and Energy I. Work a. Work Formula b. Conditions for Work II. Power III. Energy a. Forms of Energy b. Kinetic Energy c. Potential Energy i. Gravitational Potential Energy ii. Elastic Potential Energy d. Conservation of Energy IV. Efficiency Momentum I. Momentum a. Formula b. Units II. Conservation of Momentum a. Types of Collisions i. Elastic ii. Inelastic iii. Perfectly Inelastic b. Conservation of Momentum Formula c. Conservation of Momentum Problem III. Impulse a. Definition of Impulse b. Impulse Momentum Theorem c. Impulse Momentum Problems ROTATIONAL MOTION/CIRCULAR MOTION I. Measuring Rotational Motion a. Definition of Rotational Motion b. Definition of Radian c. Arc Length d. Angular Displacement e. Angular Speed f. Angular Acceleration g. Rotational and Linear Kinematics Equations II. Tangential and Centripetal Acceleration a. Tangential Speed b. Tangential Acceleration c. Centripetal Acceleration d. Total Acceleration III. Centripetal Force a. Centripetal Force Definition b. Centripetal Force Formulas c. Inertia IV. Motion in Horizontal Circles a. Examples b. Force that holds car on track V. Motion in Vertical Circles a. Examples b. Motion at Top of Loop c. Motion at Bottom of Loop VI. Ball on a Rope a. Examples b. Motion at Top of Loop c. Motion at Bottom of Loop SIMPLE HARMONIC MOTION and PENDULUM I. Simple Harmonic Motion a. Definition b. Examples c. Hooke’s Law II. Pendulum a. Conditions for Simple Harmonic Motion b. Relationship between Potential and Kinetic Energy c. Period of a Pendulum d. Period of a Mass-Spring System Part II – ELECTRICITY AND MAGNETISM I. Properties of Charge a. Conservation of Charge b. Basic Law of Electrostatics c. Charged is Quantized i. Total Charge Formula ii. Robert Millikan’s Oil Drop Experiment II. Transfer of Charge a. Conductors b. Insulators c. Charge by Conduction i. Charging a Conductor ii. Charging an Insulator d. Charge by Induction i. Inducing a charge on a Conductor ii. Inducing a charge on an Insulator III. Electric Force a. Field Forces b. Coulomb’s Law c. Coulomb’s Constant d. Superposition Principle IV. Electric Field a. Test Charge b. Electric Field Strength (2 formulas) c. Electric Field Lines d. Rules for Drawing Electric Field Lines V. Conductors in Electrostatic Equilibrium a. Electric Field Inside b. Excess charge resides on outside c. Electric field is perpendicular to outside surface d. Charge tends to accumulate on sharp points e. Van de Graff Generator VI. Electric Potential Energy a. Electric Potential Energy Formulas b. Factors that affect Electric Potential Energy i. Charge ii. Electric field strength iii. Position of charge VII. Electric Potential or Potential Difference or Voltage a. Potential difference formulas b. Difference between electric potential energy and electric potential VIII. Capacitance a. Definition of capacitance b. Ratio of charge to potential difference c. Parallel plate capacitor d. Factors that produce high capacitance IX. Current and Resistance a. Current b. Conventional Current Direction c. Types of Current d. Resistance e. Resistors f. Ohm’s Law g. Superconductors h. Electric Power i. Kilowatt hours X. Electrical Circuits a. Schematics b. Light bulbs c. Series Circuits d. Parallel Circuits e. Kirchhoff’s Rule f. Complex Circuits XI. MAGNETISM a. Magnetic Fields b. Magnetic Field of a Current Carrying Wire c. Magnetic Field of a Current Carrying Soleniod d. Magnetic Domains e. Charged Particles in a Magnetic Field i. Magnitude of Magnetic Field ii. Right hand rule to find direction of magnetic force iii. Magnetic Force on a Current-Carrying Conductor f. Electromagnetic Induction i. Lenz’s Law- the magnetic field of the induced current opposes the change in the applied magnetic field ii. Faraday’s Law of Magnetic Induction PART III- Waves and Optics I. Wave Properties a. Mechanical Waves b. Longitudinal Waves c. Transverse Waves d. Crest e. Trough f. Wavelength g. Frequency h. Period i. Wave Speed II. Wave Interference a. Superposition b. Constructive Interference c. Destructive Interference d. Standing Waves e. Nodes f. Antinodes g. Wavelengths of standing waves i. 2L ii. L iii. 2/3 L III. The Dual Nature of Light a. Planck – Energy comes in discrete units b. Einstein – Extended Planck’s theory to all electromagnetic waves (including light), stating that they sometimes behave like particles c. Louis de Broglie – using the dual nature of light theory, he proposed that all matter has wavelike characteristics. i. Wavelength = constant/(mass x velocity) ii. Patterns of constructive and destructive interference can be detected by electron microscopes. IV. Sound Waves a. Longitudinal Waves b. Compression c. Rarefaction d. Frequency determines pitch e. Speed of sound depends upon medium f. Doppler Effect i. As a moving car is approaching a stationary individual the frequency appears to be greater due to relative motion. ii. Radar uses the idea of Doppler Effect g. Resonance – frequency of force applied matches natural frequency V. Light and Reflection a. Electromagnetic Spectrum i. Waves vary depending upon frequency and wavelength ii. Wave speed equation b. Reflection of Light i. Images in flat mirrors ii. Mirror Equation iii. Magnification Equation iv. Virtual Images 1. Always upright 2. Formed behind a mirror v. Real Images 1. Always inverted 2. Formed behind a mirror vi. Focal point vii. Concave Mirror 1. Outside Focal Length - images are inverted, real, and de-magnified or magnified 2. At Focal Point – image does not exist (at infinity) 3. Inside Focal Point – images are upright, virtual, and magnified viii. Convex Mirror 1. All images are upright, virtual, and de-magnified 2. Convenient Store Mirrors c. Refraction of Light i. Refraction ii. Index of Refraction iii. Snell’s Law iv. Virtual Images v. Real Images vi. Double Convex Lenses – Converging Lenses 1. Outside focal point – images are real, inverted and demagnified or magnified 2. At focal point – image is at infinity 3. Inside focal point – images ate virtual, upright, and demagnified vii. Double Concave Lenses – Diverging Lenses 1. All images upright, virtual, and demagnified viii. Thin-Lens Equation ix. Magnification Equation x. Total Internal Reflection 1. Moving from higher index of refraction to lower index of refraction 2. Critical Angle 3. Fiber Optics d. Physical Optics i. Dispersion – separating polychromatic light into component wavelengths ii. Interference 1. Coherence – two waves with identical wavelengths maintain a constant phase relationship. Laser light 2. Producing two coherent sources of visible light through two small slits 3. Fringes observed 4. Diffraction – the spreading of light into a region behind an obstacle 5. Diffraction patterns resemble interference patterns because they also result from constructive and destructive interference. In the case of interference, it is assumed that the slits behave as point sources of light. For diffraction, the actual width of the slit is considered. 6. Diffraction becomes more evident as the width of the slit is narrowed. The brightest spots appear in the middle. 7. Diffraction occurs around the edges of all objects. You must observe with a magnifying glass. iii. Polarization 1. Polarization – the alignment of electromagnetic waves in such a way that the vibrations of the electric fields in each of the waves are parallel to each other. 2. Polarized light is produced from transmission or reflection. iv. Color 1. Primary Additive Colors – red, blue green 2. Primary additive colors form to produce white light. PART IV – Heat and Thermodynamics I. Temperature a. Internal Energy b. Thermal Equilibrium c. Temp. Conversions i. Tf = 9/5 Tc + 32 ii. Tc = 5/9(Tf – 32) iii. Tk = Tc + 273 d. Heat e. Conservation of Energy Formula i. KE + PE + Change in Internal Energy = 0 ii. Total Energy is Conserved f. Specific Heat Capacity i. The amount of energy needed to raise the temp. of 1 kg of a substance by 1 degree Celsius at a constant pressure ii. c = Q / (m T) iii. Units - J / (kg C) iv. Calorimeter 1. Energy absorbed by water = Energy released by the substance 2. Q w = Q x g. Latent Heat i. Energy needed for temperature increase ii. Energy needed for phase change iii. Graph of Temp. vs. Heat for Phase changes of water iv. More energy needed to break bonds between particles in order for particle to break bonds v. Heat of fusion – energy per unit mass transferred in order to change a substance from a solid to liquid or liquid to a solid at constant temperature and pressure vi. Heat of Vaporization – energy per unit mass transferred in order to change a substance from a liquid to a vapor or from a vapor to a liquid at constant temperature and pressure. vii. Because gas molecules are so far apart it takes more energy to vaporize a mass than to melt it. Therefore, heat of vaporization is greater than heat of fusion. viii. Latent Heat (L)– the energy per unit mass that is transferred during a phase change of a substance J/kg 1. Q = m L II. Thermodynamics a. Heat and work are transfers of energy to or from a system b. Work done in terms of Volume change i. Cylinder of gas compressed ii. W = F x D => W = P x V iii. When volume is constant no work is done c. First Law of Thermodynamics i. Energy Conservation takes into account a system’s total internal energy + the energy transferred to or from the system to do work ii. Change in the system’s total internal energy = energy transferred to/from the system by heat – energy transferred to/from the system to do work d. Second Law of Thermodynamics i. Some energy must always be transferred by heat to surroundings ii. No system totally contains all energy e. Efficiency of an Engine i. Never 100 % due to 2nd Law of Thermodynamics ii. Eff = Net work done by engine / Energy added to engine f. Entropy i. Measure of disorder of a system ii. Increasing Entropy (disorder) reduces the amount of energy available to do work iii. Entropy of the Universe increases as a natural process iv. Second Law of Thermodynamics in terms of Entropy 1. Heat lost to surroundings because of entropy increase 2. As ice melts entropy increases Part V – Modern Physics I. Quantum Mechanics a. Birth of Quantum Mechanics i. Glow of objects at high temperatures ii. All objects emit E/M radiation. Infrared at low temp and visible light at high temp. Scientist couldn’t understand why different wavelengths at different temperatures. iii. Blackbody Radiation – electromagnetic radiation emitted by a blackbody, which absorbs all incoming radiation and then emits radiation based only on its temperature 1. As temperature increases radiation emitted increased (wavelength increased) 2. Max Plank developed formula for blackbody radiation that agreed with results 3. Particles resonate back and forth at different frequencies 4. Particle resonators can only absorb/emit energy at certain discrete amounts of energy. This is due to jumping from one quantum state to another. 5. Energy = Plank’s Constant x Frequency a. h = 6.63 x 10 –34 J s b. Energy for one quantum jump 6. no change in quantum state = no energy emitted 7. Quantum Mechanics – idea that energy is in discrete units b. Photoelectric Effect i. The emission of electrons from a surface that occurs when light of certain frequencies shines on the surface ii. Photoelectric Conflict 1. Classically – the energy of the wave increases when the intensity increases 2. Experimentally – the energy of the wave increases when the frequency increases 3. Albert Einstein resolves conflict (Noble Prize) by extending Planck’s concept of quantization to E/M waves. a. Photons – discrete unit of light energy b. Light of the same frequency has the same energy. II. Atomic Models a. J.J. Thompson’s Model – watermelon (electrons imbedded in positively charged sphere) b. Ernest Rutherford i. Alpha particles shot at atom to find a nucleus ii. Planetary model of the atom iii. Electrons revolving around nucleus iv. According to his model electrons radius would decrease c. Atomic Spectrum i. Not explained by Rutherford model ii. Each gas has an emission and absorption spectrum when voltage is supplied iii. Nothing in Rutherford’s model accounted for each element having a unique series of spectral lines d. Bohr Model of Hydrogen Gas i. 1913 Niels Bohr ii. Contained explanation of atomic spectrum iii. Only certain orbits are stable- never between orbits iv. Transitions between stable orbits with different energy levels accounts for the discrete spectral lines v. Ground state – Bohr radius vi. Excited state vii. Explains color emitted from the Northern lights viii. Scientists search for new models to explain why some states are stable III. Nuclear and Particle Physics a. Nucleus Properties i. Mass number – no. of nucleons (protons and neutrons) ii. Atomic number – no. of protons iii. Neutron number – no of neutrons iv. Isotopes – atoms of an element having the same atomic no. but different neutron and mass no. v. Relationship between mass and rest energy 1. Rest energy – amt of energy associated with a mass 2. mass = rest energy / (speed of light)2 3. neutrons most massive therefore stabilize nucleus 4. Binding energy – energy released when nucleons bind together to form a stable nucleus E = mc2 b. Nuclear Reactions i. Nuclear decay – unstable nuclei break apart 1. Natural or induced artificially 2. Radioactivity – the spontaneous emission of energy due to nuclear decay 3. Rules for Nuclear Decay a. Total atomic number is conserved b. Total mass number is conserved 4. Alpha – emits He nuclei a. 5. Beta – emits electrons or positrons a. 6. Gamma – emits high energy photons 7. Half-Life – measures nuclear decay a. T1/2 = 0.693/decay constant ii. Fission and Fusion 1. Fission – heavy nucleus splits into 2 2. Fusion – light nuclei combine to form 1 IV. Relativity a. Einstein’s theory of relativity i. Time depends upon observer’s motion ii. An observer beside a moving train sees the light travel a greater distance and measures a longer period of time interval than the passenger does – time dilation iii. Time dilation equation