Content Outline and Competencies:

I. Kinematics and Mechanics
   A. Units and measures 
      1. Recognize and be able to apply SI/metric units. 
      2. Convert data between English and SI/metric systems. 
      3. Apply the rules for significant digits. 
      4. Convert data between ordinary format and scientific notation. 
   B. Vectors 
      1. Distinguish between vectors and scalars. 
      2. Resolve vectors into component form. 
      3. Apply vectors to composition problems. 
      4. Recognize a vector difference. 
   C. One-dimensional kinematics 
      1. Recall the mathematical models for constant velocity and uniform acceleration. 
      2. Use the appropriate model to set up and solve one-dimensional kinematics problems. 
      3. Use diagrams and reference crosses when solving problems. 
   D. Kinematics in a plane 
      1. Recall the criteria for ballistics. 
      2. Determine the types of motion both horizontally and vertically in ballistic problems. 
      3. Apply the mathematical models for constant velocity and uniform acceleration to the solution of ballistic problems. 
      4. Given the equations for level-ground ballistics, use them to solve problems. 
   E. Newton's laws of motion 
      1. Recall Newton's three laws of motion. 
      2. Apply these laws in solving dynamics problems. 
      3. Distinguish between mass and weight. 
      4. Include free-body diagrams when solving dynamics problems. 
      5. Recognize and apply the special forces: weight, tension and friction.
   F. Gravity and orbital motion 
      1. Recall and apply Newton's law of universal gravitation. 
      2. Recall and apply the mathematical model for constant speed rotation. 
      3. Explain the apparent weightlessness of satellites in orbit. 
      4. Calculate some of the features of circular near-Earth orbits. 
      5. Distinguish actual forces such as centripetal from pseudo-forces like centrifugal. 
   G. Work and mechanical energy conservation 
      1. Define work in terms of force and distance. 
      2. Recognize that work and energy are scalars. 
      3. Compare the work/energy that results from doing work against inertia, against gravity, and against friction.
      4. Define mechanical energy and describe the necessary conditions for its conservation. 
      5. Distinguish between energy and power. 
      6. Solve physics problems using the work/energy method. 
   H. Momentum and collisions 
      1. Define impulse and momentum as vectors. 
      2. Describe the conditions under which linearmomentum is conserved. 
      3. Apply momentum conservation to solving collision and simple rocket problems. 
      4. Distinguish between elastic and inelastic collisions. 
   I. Rotational motion, torque and stability, angular momentum 
      1. Interconvert angles in degrees, radians and revolutions. 
      2. Translate equations from linear to angular variable and back again. 
      3. Calculate torques from forces and pivot positions. 
      4. Recall and apply the laws of static equilibrium to simple stability problems. 
      5. Recall the factors that affect moments of inertia. 
      6. Describe the conditions under which angular momentum is conserved.
III. Fluid Mechanics 
   A. Density and pressure 
      1. Calculate densities from masses and volumes. 
      2. Calculate pressures from forces and areas. 
   B. Properties of fluids 
      1. Recall Pascal's principle and describe elementary consequences that follow from it. 
      2. Recall Archimedes' principle and describe elementary consequences that follow from it. 
      3. Calculate the buoyant force for an object submerged in a fluid. 
III. Thermal Energy and  Heat and Thermodynamics 
   A. Kinetic molecular theory 
      1. Interconvert temperatures between Celsius, Fahrenheit and Kelvin scales. 
      2. Explain the solid, liquid and gaseous states of matter from the perspective of the kinetic molecular theory. 
      3. Explain why one ideal gas equation works for all gases while no single equation describes all liquids or all solids. 
      4. Explain the connection between Kelvin temperature and molecular kinetic energy. 
      5. Use the ideal gas equation to solve problems under both static and changing conditions. 
   B. Thermal energy and heat transfer 
      1. Recall the basic definitions of heat and work. 
      2. Distinguish between the equations for heat flow used between phase changes and during phase changes. 
      3. Solve heat transfer problems involving phase changes. 4. Relate heat thermal energy to both molecular energy and mechanical energy. 
   C. Thermodynamics 
      1. State and explain the meaning of the laws of thermodynamics. 
      2. Distinguish among several forms of the same law. 
      3. Relate the first law to energy conservation. 
      4. Define entropy and use this concept to discuss the second law. 
      5. Calculate Discuss (Not ) entropy changes for heat flows. 
      6. Discuss engine efficiency and relate it to second law.
IV. Vibration and Waves 
   A. Harmonic motion 
      1. Recall the mathematical model for simple harmonic motion. 
      2. Relate SHM to Hooke's law. 
      3. Calculate the elastic PE, vibrational KE and mechanical energy of vibration for mass/spring oscillators. 
      4. Discuss the maxima and minima of harmonic variables at the turn-around points and at the central rest position.
      5. Calculate the period, frequency and repetition rate for harmonic systems. 
   B. Waves 
      1. Describe the interplay between source oscillators, detectors and wave media. 
      2. Use the traveling wave equation to relate the various wave quantities such as wavespeed, wavelength and frequency. 
      3. Distinguish between traveling waves and so-called standing waves. 
      4. Use the concept of wave interference to explain resonance. 
      5. Define wave intensity, power flux and acoustic loudness.
V. Laboratory Competencies 
   A. Identify and develop positive attitudes toward tasks and fellow students appropriate for the laboratory setting. 
   B. Identify and develop teamwork skills, including group problem solving, consensus building and self-supervision.
   C. Identify and develop productive work habits, including attention to detail, task completion, keeping an orderly work area and  using appropriate care with laboratory apparatus.
   D. Develop the ability to carefully record with measurement apparatus and analyze the resulting data with appropriate attention to errors and uncertainties.

Content Outline and Competencies:

Content Outline and Competencies:

1. Static Electricity
   1. List the basic rules that govern behavior of electric charge.
   2. Describe and apply Coulomb's law for simple charge arrangements.
   3. Distinguish between the action-at-a-distance and field approaches to the electric field.
   4. Predict the motion of charges in an electric field.
   5. Distinguish between electrical potential energy and electrical voltage.
   6. Distinguish between E-field maps and V-loop maps for electric fields.
   7. Recall the nature of parallel plate capacitors and dielectrics.
   8. Use the laws of parallel and series capacitor combinations to analyze simple capacitor circuits.
2. Electric Current and Resistance
   1. Discuss several types of current flow and identify which obey Ohm's law.
   2. Describe the operation of batteries as current sources.
   3. Describe the concepts of resistance, resistivity and Ohmic current.
   4. Use Ohm's law to solve simple DC circuits.
   5. Recall the various equations for electric power.
3. Electric Circuits
   1. Use the rules for series and parallel resistor combinations to solve simple one-source circuits.
   2. State and apply Kirchhoff's rules.
   3. Solve simple RC circuits.
   4. Discuss the design of ammeters and voltmeters.
   5. Discuss household circuits and electrical safety.
4. Magnetism
   1. Describe the origin of the magnetic field in terms of electric charge in motion.
   2. Describe and use the equations for magnetic forces on moving charges.
   3. Recall and use the equations for the magnetic fields produced by currents.
   4. Discuss magnetic materials in terms of Weiss domains.
   5. Discuss the magnetic field of the Earth.
   6. Explain the operation of galvanometers and motors in terms of magnetic torques on pivoted coils.
5. Electromagnetic Induction
   1. State and use Faraday's/Lenz's law to solve simple problems.
   2. Explain the difference between DC and AC generators.
   3. Discuss magnetic flux and transformer operation.
   4. Discuss inductance and magnetic potential energy.
6. Alternating Current
   1. Convert from RMS values to peak values for AC variables.
   2. Calculate the reactance and phase shifts for RLC circuits.
   3. Solve series RLC circuits by the impedance method.
   4. Discuss phasors as vectors in time rather than space.
   5. Discuss power and resonance in AC circuits.
7. Geometrical Optics
   1. State and apply the law of reflection to simple problems.
   2. State and apply the law of refraction to simple problems.
   3. Discuss fiber-optic application of total internal reflection.
   4. Discuss dispersion of prisms.
8. Mirrors and Lenses
   1. Use laws of reflection and refraction to explain the focusing property of curved interfaces.
   2. Use the mirror/lens equation to confirm image position and quality on ray diagrams.
   3. Distinguish between converging and diverging systems.
9. Interference and Diffraction
   1. Explain the double slit interference pattern and use it to calculate wavelengths.
   2. Discuss the colors of thin film in terms of interference.
   3. Explain how diffraction relates to wavelength.
   4. Describe the phenomena of polarization.
   5. Describe the colorization due to scattering.
10. Relativity
    1. Describe and explain the importance of the Michelson-Morley experiment.
    2. State and apply the postulates of special relativity.
    3. Calculate time dilations and length contractions.
    4. Use the velocity addition formula to justify an upper speed limit=c.
    5. Discuss mass variation in terms of relativistic energy and momentum.
11. Waves and Particles
    1. Discuss the logical inconsistencies between particle and wave representations of light.
    2. Discuss the photoelectric and Compton effects from the particle perspective.
    3. Recall and use the Einstein-Planck and DeBroglie equations to solve problems.
    4. Describe and explain the significance of the Heisenberg uncertainty principle.
12. Atomic Structure
    1. Describe the Bohr model of the atom.
    2. Use the Bohr model to explain the spectrum of hydrogen.
    3. Relate quantum principles to the structure of the periodic table.
13. Radioactivity and the Nucleus
    1. Recall and discuss alpha, beta and gamma radiation.
    2. Balance simple nuclear reactions.
    3. Discuss half-lives and radioactive dating.
    4. Distinguish fission and fusion in terms of binding energy per nucleon.

Content Outline and Competencies:

I. Scientific Method
   A. Apply the scientific method to problems in nature, specifically in
the area of physics.
   B. Perform dimensional analysis to check units of formulas derived from
algebraic principles.
   C. Convert between SI/metric and English units in detailed science
calculations.
   D. Rewrite numbers in scientific notation when performing calculations
involving large and/or small quantities.
   E. Formulate physics problems into mathematical expressions and
interpret the solutions to determine their physical significance.
II. Force
   A. Differentiate between kinematic variables including displacement,
speed, velocity and acceleration.
   B. Develop and analyze models of motion including projectile, circular
and simple harmonic motion.
   C. Construct graphs describing simple motion, both in one and two
dimensions.
   D. Illustrate the concept of impulse as it applies to momentum in
collision processes.
   E. Use Conservation of Momentum to describe the motion of objects
before and after collisions.
III. Force
   A. Distinguish between the concepts of mass and weight.
   B. Construct free-body diagrams to identify external forces acting on
objects, including tension, normal and reaction forces.
   C. Apply Newton’s Laws to structures in static equilibrium to
determine unknown forces.
   D. Apply Newton’s Laws to objects in one-dimensional, two-dimensional
and circular motion to determine their accelerations.
   E. Incorporate frictional properties into motion problems.
IV. Gravity
   A. Illustrate the motion of an object in free-fall, including its
position, velocity and acceleration as functions of time.
   B. Compare uniform circular motion to general satellite motion by
application of Newton’s Law of Gravity.
   C. Describe and illustrate general properties of gravitational fields
generated by astronomical bodies such as the Earth, Moon, Sun and other
planets in our solar system.
V. Work and Energy
   A. Describe the relationship between work and energy.
   B. Define types of energy including kinetic, gravitational potential
and elastic potential.
   C. Apply Conservation of Energy to mechanical systems to determine the
motion of objects.
   D. Identify sources of mechanical energy available for human use.
   E. Define power and show how it relates to simple machines.
VI. Heat
   A. Show the relationship between the thermodynamic variables of
temperature, internal energy and heat.
   B. Compare temperature scales, including the Celsius, Fahrenheit and
Kelvin scales.
   C. Relate temperature changes to linear and volume expansion of
materials.
   D. Illustrate heat flow between different media using the concepts of
specific heat, heat of fusion and heat of vaporization.
   E. Describe methods of heat flow, including convection, conduction and
radiation.
   F. Apply the Laws of Thermodynamics to ideal gases undergoing isobaric,
isovolumetric, isothermal and adiabatic processes.
   G. Compare and contrast devices such as heat engines, refrigerators,
air conditioners and heat pumps and how thermodynamics is involved in
their operation.
VII. Electricity and Magnetism
   A. Describe the concepts, sources and effects of electric force,
charge, fields, potential, current, resistance and power as they relate to
electric circuits.
   B. Design and setup simple DC circuits to measure currents, voltages
and resistances using ammeters, voltmeters and ohmmeters.
   C. Set up simple series and parallel circuits of resistors to
experimentally determine the equivalent resistance and compare to
theoretical calculations.
   D. Extend the ideas of resistors in series and parallel to capacitors
and compare and contrast these different types of circuits.
   E. Describe and illustrate the concepts, sources and effects of
magnetic fields of bar magnets, current-carrying wires and the Earth.
   F. Graphically illustrate magnetic forces on moving charges and their
resultant motion as determined using the Right-Hand Rule.
   G. Explain the relationship between electric currents and magnetic
fields in the operation of electric motors.
   H. Set up simple RC and/or RL circuits to oscilloscopes to visually
observe the time dependence of voltages across such devices.
   I. Describe and illustrate electromagnetic induction and its
application to alternating current, electric generators, transformers and
power production.
   J. Design and set up simple AC circuits to study frequency effects on
current and reactance.
VIII. Sound and Light Waves
   A. Differentiate between transverse and longitudinal waves.
   B. Describe the characteristics of a wave including its amplitude,
wavelength and frequency and how wave velocity is related to these
quantities.
   C. Compare and contrast sound and light waves including their
velocities in different media, their wavelengths and the conditions
necessary to produce each type.
   D. Discuss how sound intensity is measured on the decibel scale.
   E. Describe and illustrate the phenomena of forces vibrations, shock
waves and the Doppler effect observed in sound waves.
   F. Describe and illustrate phenomena dealing with waves including
reflection, refraction, total internal reflection, diffraction,
interference, superposition and polarization.
   G. Describe the electromagnetic spectrum and the properties of color
and what distinguishes visible color from other forms of electromagnetic
radiation.
   H. Illustrate properties of mirrors, lenses and how they are used in
optical devices including cameras, magnifying glasses, microscopes,
telescopes and spectrophotometers.
   I. Discuss types of lens aberrations, including spherical and
chromatic, and how such problems are corrected.
IX. The Atom
   A. Outline contributions made to our understanding of atomic particles
due to the work of Compton, De Broglie, Einstein, Heisenberg, Pauli and
Planck.
   B. Discuss the Wave-Particle Duality of photons, electrons and other
atomic particles.
   C. Describe the currently accepted model of the atom and how our
understanding has progressed from the earlier models of Thomson,
Rutherford and Bohr.
   D. Illustrate applications of atomic physics, including X-rays, lasers
and holography.
   E. Explain the organization of the periodic table and what
distinguishes one element from another on the basis of its nuclear
structure.
   F. Examine the structure of the nucleus of an atom in order to
calculate its binding energy.
   G. Identify and describe the sources and types of radioactivity and the
biological effects.
   H. Describe the concept of half-life of radioactive materials
emphasizing the environmental problems of materials with particularly long
half-lives.
   I. Distinguish between nuclear fission, both natural and artificial,
and nuclear fusion processes.
   J. Describe how radioactive materials are commonly used today in
physics, biology, chemistry and medicine.
X. Laboratory
   A. Use various measuring instruments commonly encountered in
laboratories.
   B. Develop safe and proper laboratory techniques in the setup, data
acquisition and analysis of information obtained from physics
experiments.
   C. Develop teamwork skills working in collaboration with other
physics/science students.

Content Outline and Competencies:

I. Basic Math
   A. Write the equations of circles, lines, planes and spheres.
   B. Determine if two circles or two spheres are intersecting.
   C. Use trigonometry to determine the components of a vector and the
angle produced by a vector.
   D. Analyze a trigonometric function for amplitude and period.
   E. Convert between polar and rectangular coordinates.
   F. Convert units of measurement.
   G. Construct code that will detect collisions between circles, lines,
planes and spheres.
 
II. Vectors
   A. Compare the concepts of scalar and vector.
   B. Add and subtract vectors.
   C. Multiply vectors by scalars.
   D. Normalize vectors.
   E. Find dot products and cross products of vectors.
   F. Find the angle between two vectors.
   G. Find the normal vector to a surface.
   H. Construct code that will perform vector arithmetic and
normalization.
 
III. Matrices
   A. Add, subtract, and multiply matrices.
   B. Multiply matrices by scalars.
   C. Describe translations using matrices and homogeneous coordinates.
   D. Describe scalings using matrices and homogeneous coordinates.
   E. Describe rotations using matrices and homogeneous coordinates.
   F. Construct code that will perform scaling, rotation, and translations
on vectors and geometric objects.
 
IV. Linear Motion
   A. Compute distance, displacement, velocity, speed, and acceleration
for one-dimensional motion.
   B. Use vectors to describe displacements, velocities, and accelerations
in two and three dimensions.
   C. Write equations which model the motion of projectiles.
   D. Use Newton's Laws to determine the effect of forces on the motion of
an object.
   E. Solve for the motion of an object 
   F. Calculate the work done by a force on an object.
   G. Calculate the kinetic energy, potential energy, and momentum of an
object.
   H. Use conservation of energy and conservation of momentum to model the
collision of objects.
   I. Construct code that can simulate the motion of a projectile.
   J. Construct code that can simulate the motion of an object according
to Newton’s Laws of Motion.
   K. Construct code that can simulate the collision between two objects.
 
V. Rotational Motion
   A. Compute angular displacement, angular velocity, and angular
acceleration.
   B. Determine the angular motion caused by a torque on an object.
   C. Find the kinetic energy and angular momentum of a rotating object.
   D. Construct code that can model the three-dimensional motion of a
rigid body incorporating the concepts of the conservation of energy and
momentum, and Newton’s Laws of Motion.

Content Outline and Competencies:

I. Teaching as a Career

A. Determine suitability/interest in teaching as a career through thoughtful self-reflection.

B. Explore pathways to a career in teaching.

C. Identify personal learning styles and discuss their implications for classroom interactions.

II. Strategies for Practical Lesson Design

A. Design and deliver inquiry-based hands-on lessons.

B. Write performance objectives for each lesson, including mathematics and/or science connections, and appropriate assessments for those objectives.

C. Use technology and the Internet to enhance classroom lessons, collaborate, and communicate.

III. Concepts and Components of Teaching Theory

A. Identify instructional strategies that meet the needs of diverse learners.

B. Distinguish between learner-centered and teacher-centered instructional strategies.

C. Discuss state and national science and mathematics standards and their implications for curriculum decisions.

D. Identify current issues in the theory and practice of teaching.

IV. Components of a Field Experience

A. Observe a math-science lesson taught by a cooperating teacher.

B. Interact with a population of diverse student learners in a school setting while teaching a lesson in an elementary school classroom.

C. Receive and synthesize feedback from a cooperating teacher as a peer and mentoring colleague in order to improve techniques.

Content Outline and Competencies:

I. Practical Lesson Design

A. Design inquiry-based lessons using the 5E Instructional Model.

B. Write measurable performance objectives for each lesson.

C. Develop applicable pre- and post-assessments for the performance objectives.

D. Analyze student data acquired through pre- and post-assessments to improve future lesson planning.

E. Incorporate technology into at least one lesson in a manner that encourages enhanced student interaction and learning.

II. Teaching Theory

A. Identify instructional approaches that meet the needs of diverse middle school learners.

B. Develop questioning strategies to effectively interact with students with varying abilities and learning styles in a middle school classroom.

C. Develop achievable solutions to preserve instructional equity in the classroom environment.

III. Field Experience

A. Reflect upon observations of lessons taught by an experienced math/science teacher.

B. Teach three inquiry-based lessons to a middle school math or science class.

C. Use probing questions to elicit feedback to determine students’ acquisition of knowledge.

D. Synthesize feedback from both mentor teachers and master teachers in order to improve teaching techniques.

E. Reflect on teaching experiences in order to enhance future classroom interactions.

Content Outline and Competencies:

I. Introduction to Mechanics
   A. Units and measures
      1. Describe physics and how it relates to other physical sciences. 
      2. Explain the role of scientific models and how they are used in
the sciences.
      3. Recognize and be able to apply SI metric units.
      4. Convert measurements back and forth between U.S. units and SI
units.
      5. Explain the importance of measurements and accuracy in physics.
      6. Apply significant figures to measurements.
   B. Vectors
      1. Differentiate between vectors and scalars.
      2. Work problems requiring vector math operations, especially
addition and subtraction.
      3. Resolve vectors into components and apply to addition and
subtraction problems.
   C. Motion in a straight line -- kinematics
      1. Apply concepts of displacement, velocity and acceleration.
      2. Draw motion diagrams to determine acceleration vectors for a
variety of applications.
      3. Draw graphs of position, velocity and acceleration as functions
of time for a variety of situations.
      4. Work problems with constant acceleration.
      5. Apply constant acceleration to freely falling objects.
   D. Motion in a plane
      1. Extend displacement, velocity and acceleration concepts into two
dimensions using vectors.
      2. Identify when use of constant speed or constant acceleration is
appropriate.
      3. Solve projectile problems involving position, velocity and
acceleration.
      4. Identify and apply centripetal acceleration equations.
      5. Apply relative motion ideas to one- and two-dimensional
problems.
   E. Newton’s laws
      1. Define force and apply the ideas to common applications.
      2. Define inertia and relate it to mass (Newton’s first law).
      3. Describe mass and its role in Newton’s second law.
      4. Differentiate between mass and weight.
      5. Explain the origins of friction.
      6. Draw free body diagrams for a large number of applications. 
      7. Find examples of Newton’s third law.
      8. Apply Newton’s laws to a variety of situations.

II. Development of Mechanics Concepts
   A. Work and energy
      1. List the two important aspects of a vector dot product.
      2. Define work in terms of the dot product force-distance integral.
      3. Simplify the work integral for constant forces.
      4. Solve work problems for varying forces.
      5. Construct work-energy bar charts.
      6. Apply conservation of energy to a variety of problems.
      7. Describe the difference between energy and power.
      8. Explain how the potential energy of an object can be changed.
      9. Describe conservative and nonconservative forces.
     10. Explain how conservative forces are related to potential energy.
     11. Solve problems that include gravitational and spring potential
energy.
   B. Impulse and momentum
      1. Derive the impulse and momentum expressions from Newton’s
second law.
      2. Relate impulse to collisions and explain how knowledge of impulse
can be used to create safer equipment.
      3. Show how conservation of momentum is related to Newton’s third
law.
      4. Differentiate between ideal elastic and inelastic collisions.
      5. Apply conservation of momentum to elastic and inelastic
collisions in one and two dimensions.
      6. Define center of mass and illustrate why it is an important
concept in Newtonian mechanics.
      7. Show how to find the center of mass by experiment or by
calculation.
   C. Rotational motion
      1. Define angular displacement, angular position, angular velocity
and angular acceleration and relate them mathematically to the linear
analogs.
      2. Find the relationships between linear and angular kinematics
equations and apply to a variety of situations.
      3. Expand the conservation of energy models to include rotational
energy.
      4. Recognize the relationship between angular inertia (moment of
inertia) and work Newton’s laws problems that illustrate its use.
      5. Relate torque to forces.
      6. Define vector cross products and apply them to torque and other
angular mechanics problems, paying careful attention to vector
directions.
      7. Solve problems using rotational work, power and energy.
      8. Relate the motion of the center of mass of a rolling object to
the motion of its rim.
      9. Explain the importance of conservation of angular momentum and
apply that principle to various situations of rotating objects.
   D. Static equilibrium
      1. Define the conditions of static equilibrium for a rigid object.
      2. Solve static equilibrium problems.
   E. Periodic motion
      1. Define simple harmonic motion and list examples.
      2. Solve problems that utilize standard solutions to simple harmonic
differential equations to a mass on a spring and a simple pendulum.
      3. Apply conservation of energy to simple harmonic motion
situations.
   F. Gravity
      1. Explain the terms in Newton’s law of universal gravity.
      2. Solve problems using Newton’s law of gravity.
      3. Recognize when to use the universal law of gravity and when to
use simpler formulations.
      4. Derive an equation for universal gravitational potential energy,
paying careful attention to signs.
      5. Solve problems using the universal gravitational potential energy
formula and explain when simpler forms can be used.
  
III. Mechanical Waves
   A. Distinguish between transverse and longitudinal waves and give
examples of each.
   B. Apply sinusoidal mathematics to waves in one dimension.
   C. Define the conditions of destructive and constructive interference
using superposition principles and path differences from sources.
   D. Find the speed of waves on a string.
   E. Solve problems involving reflection of waves.
   F. Find the energy carried by waves in one dimension.

IV. Thermal Properties of Matter
   A. Temperature and expansion
      1. Review the various temperature scales and the relationships
between them.
      2. Solve problems concerning thermal expansion in solids and
liquids.
      3. Define ideal gas laws and solve problems with them.
      4. Memorize basic facts about gases.
      5. Draw PV diagrams for gases, including isotherms in your
drawings.
   B. Heat and thermal properties of materials
      1. Carefully distinguish between heat and temperature.
      2. Define heat capacity and latent heat.
      3. Apply the concepts of heat capacity and latent heat to a variety
of heat transfer situations.
      4. Draw heat flow diagrams that illustrate the conservation of
energy.
   C. Introduction to thermodynamics
      1. Derive a new form of the work dot product integral for gases.
      2. Apply the first law of thermodynamics to the following processes
for ideal gases: isobaric, isovolumetric, isothermal and adiabatic.
      3. Show how the adiabatic equation of state can be used to explain
many aspects of weather.
      4. Describe the two forms of the second law of thermodynamics.
      5. Explain the importance of heat engines to our civilization.
      6. Solve heat engine problems, including the topics of efficiency
and wasted heat.
      7. Solve problems concerning heat flows and efficiencies of heat
pumps and refrigerators.
      8. Explain the concept of entropy and work example problems.
   D. Atomic and molecular properties of matter
      1. Show how our theory of atoms and molecules in constant motion can
be used to define mathematically what we mean by temperature, pressure and
internal energy.
      2. Solve problems using our definitions of specific heat of gases at
constant volume or constant pressure.
      3. Show how equipartition of energy and molecular speed
distributions can explain common observations, such as distributions can
explain common observations, such as evaporation of all materials and
planetary atmospheres.

Content Outline and Competencies:

I. Electrostatics and Electric Currents
   A. Electric fields
      1. Describe the properties of electric charges.
      2. Differentiate between insulators and conductors.
      3. State the essential features of Coulomb’s law and conditions
necessary for its application.
      4. Compare the mathematical form of Coulomb’s law to other basic
laws of physics.
      5. Define electric field and tell how it differs from electric
forces.
      6. Use calculus to develop expressions for electric fields created
by continuous charge distributions.
      7. Draw electric field lines using Coulomb’s law and explain why
field lines are useful.
      8. Apply kinematics equations to charges moving in an electric
field.
   B. Gauss’ law
      1. State Gauss’ law.
      2. Apply Gauss’ law to calculate electric fields for situations of
high symmetry.
      3. Using Gauss’ law, predict essential features of electric fields
inside and outside of insulators or conductors.
   C. Electric potential
      1. Explain the difference between electric potential and electric
potential energy.
      2. Find electric potential and electric potential energy from
various arrays of point charges or from continuous charge distributions.
      3. Derive electric fields from electric potential functions.
   D. Capacitance and dielectrics
      1. Write down the mathematical definition of capacitance.
      2. Calculate capacitance from dimensions given for two plate
capacitors.
      3. Relate charge, voltage and capacitance for series and parallel
combinations of capacitors.
      4. Find the energy stored in capacitors by knowing electrical
characteristics.
      5. Describe the effects of a dielectric on capacitance and suggest
an explanation of these effects.
   E. Current, resistance and EMF
      1. Define electric current both mathematically (using calculus) and
verbally.
      2. Identify the important mathematical parameters of an electric
circuit with a battery and resistor connected together.
      3. Solve problems using Ohm’s law.
      4. Draw graphs of voltage as a function of current for ordinary
metallic conductors.
      5. Describe the effects of temperature on resistance and solve
problems related to this.
      6. Solve problems for electrical energy and power.
      7. Explain the voltage changes as you go completely around a
circuit.
      8. Develop equations for series and parallel combinations of
resistors using conservation of energy and conservation of charge.
      9. Apply Kirchhoff’s rules to circuits with multiple voltage
sources and multiple branches.
     10.  Derive relationships for voltage and current as functions of
time for RC circuits.
     11.  Solve problems for practical applications using a variety of DC
circuits.

II. Electrodynamics
   A. Magnetic fields
      1. Compare electric and magnetic fields.
      2. Describe a magnetic pole and contrast it to an electric charge.
      3. Draw magnetic field diagrams for various arrangements of magnetic
poles.
   B. Magnetic forces
      1. Calculate the magnetic force on various arrangements of moving
charges, including current carrying conductors.
      2. Describe how to use vector cross product rules to predict the
direction of magnetic forces on moving charges.
      3. Derive relationships that describe the torque on a conducting
loop in a magnetic field.
      4. Solve problems, which are applications of interactions between
charges and magnetic fields.
      5. Explain the Hall effect and its role in determining the sign of
charge carriers.
   C. Sources of magnetic fields
      1. Using calculus, derive the strength and direction of magnetic
fields arising from moving charges.
      2. State the importance of Ampere’s law and solve problems using
it.
      3. Define magnetic flux and calculate flux in various situations.
      4. Derive the magnetic field of an ideal solenoid and compare it to
measurements.
      5. Solve problems with magnetic fields in materials.
   D. Electromagnetic induction
      1. Describe Faraday’s law of induction and solve problems in
various situations.
      2. Find the emf generated by conductors moving in a magnetic field
and by a changing magnetic field in the vicinity of conductors.
      3. State Lenz’s law and use it to find the directions of induced
emf’s and currents.
      4. Describe the operation of motors and generators.
   E. Inductance
      1. Define inductance and determine the direction of the induced emf
for a variety of situations.
      2. Determine the energy in magnetic fields caused by currents.
      3. Find current and voltage relationships as a function of time for
RC and RLC circuits.
   F. Alternating currents
      1. Derive equations for voltage and current for simple series
circuits including resistance, inductance and capacitance.
      2. Find the reactances and impedances of RLC circuits.
      3. Solve problems for AC circuits that include finding the current,
voltage and power in series circuits.
      4. Describe various AC phenomena including resonance, transformers
and filters.
   G. Electromagnetic waves
      1. Describe the origin and form of electromagnetic waves.
      2. Relate Maxwell’s equations to the electromagnetic spectrum.
      3. Calculate power and pressure produced by electromagnetic waves,
such as sunlight, lasers, room lights or TV signals.
      4. Describe the electromagnetic spectrum.

III. Fundamental Waves
   A. Sound waves
      1. Describe the nature and origins of sound waves.
      2. Calculate typical frequencies and wavelengths of sound waves.
      3. Describe the mathematics of sound waves.
      4. Draw examples of waves illustrating superposition and
interference of waves.
      5. Describe interference in water and sound waves generated by two
point sources.
      6. State the conditions for constructive and destructive
interference in terms of the differences in path length from two sources
to the point of interference.
      7. Draw diagrams showing the nodes and antinodes of standing waves
and derive expressions for the possible lengths and frequencies for
standing waves in a string fixed at both ends.
      8. Derive the mathematical conditions of standing waves for sound in
tubes open or closed at both ends and for tubes open at one end.
      9. Describe the conditions that create beats.

IV. Optics
   A. Nature and propagation of light
      1. Observe and describe mathematically (where possible) the nature
of light interaction with materials: reflection, refraction, diffraction,
scattering and transmission.
      2. Solve problems using Snell’s law.
      3. Explain the formation of a rainbow, why the sky is blue and why
the sun is red at sunset and sunrise.
   B. Interference, diffraction and polarization of light
      1. Describe the conditions necessary for interference in light in
terms of both path differences and in phase differences.
      2. Solve problems concerning double slit interference, intensity in
interference patterns, phase change upon reflection and thin film
interference.
      3. Observe, describe mathematically and solve problems relating to
single slit diffraction and diffraction grating interference patterns.
      4. Observe light polarization, describe its origins and solve
problems concerning intensity of polarized light.
      5. Explain common applications of polarized light, such as
calculator displays and polarizing sunglasses.

V. Modern Physics
   A. Modern quantum mechanical views of light and atoms
      1. Observe and explain the origins of light (especially light
spectra) from heated gases, heated solids and light emitting diodes.
      2. Draw electron energy diagrams and apply them to the three sources
of light mentioned above.
      3. Describe the existence of energy levels in isolated atoms and the
creation of energy bands as atoms crowd together to form solids.
      4. Explain the operation of an LED in terms of the voltages
necessary to cause light production.
   B. Quantum wave theory
      1. Explain the problems with classical theories of atoms and the
experimental basis for quantum wave mechanics.
      2. Describe the characteristics of quantum waves used to describe
electrons.
      3. Discuss the origins of quantum uncertainty and its implications
on observing nature in the submicroscopic realm.