Content Outline and Competencies:

I. Conceptual Frameworks

A. Recognize key physics terms.

B. Distinguish between physics concepts.

C. Identify appropriate solutions.

II. Physical Models

A. Select appropriate physical model.

B. Generate symbolic formulas.

C. Generate numeric solutions.

III. Problem Solving Techniques

A. Analyze multi-step problems.

B. Select relevant information.

C. Identify an approach to solving a multi-step problem.

D. Generate solutions to multi-step problems.

IV. Topics in Mechanics

A. Convert units and work with measurements.

1. Recognize and be able to apply metric units.

2. Convert data between different metric prefixes.

3. Apply the rules for significant digits.

4. Convert data between ordinary format and scientific notation.

B. Analyze vectors.

1. Distinguish between vectors and scalars.

2. Resolve vectors into component form.

3. Perform vector addition and subtraction.

C. Analyze motion in one dimension.

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 when solving problems.

D. Analyze motion in two dimensions.

1. Recall the criteria for projectile motion.

2. Determine the types of motion both horizontally and vertically in projectile problems.

3. Apply the mathematical models for constant velocity and uniform acceleration to the solution of projectile problems.

4. Given the equations for projectile motion, use them to solve problems.

E. Apply 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. Sketch free-body diagrams to solve dynamics problems.

5. Recognize and apply the forces: gravitational (weight), normal, tension and friction.

F. Apply gravity and describe 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 orbits.

5. Distinguish actual forces such as centripetal from pseudo-forces like centrifugal.

G. Relate the concepts of 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 gravity and against friction.

4. Define mechanical energy and describe the necessary conditions for its conservation.

5. Distinguish between energy and power.

6. Solve problems using the work-energy theorem.

7. Analyze simple harmonic motion for an oscillating system.

H. Develop the topics of momentum and impulse.

1. Define impulse and momentum as vectors.

2. Describe the conditions under which linear momentum is conserved.

3. Apply momentum conservation to solve problems.

4. Distinguish between elastic and inelastic collisions.

I. Analyze rotational motion, torque, equilibrium, and angular momentum.

1. Interconvert angles in degrees, radians, and revolutions.

2. Recall and apply the equations for acceleration of an object moving in a circle.

3. Calculate torques from forces and pivot positions.

4. Recall and apply static equilibrium equations.

5. Recall the factors that affect moments of inertia.

6. Describe the conditions under which angular momentum is conserved.

V. Topics in Fluid Mechanics

A. Apply density and pressure.

1. Calculate densities from masses and volumes.

2. Calculate pressures from forces and areas.

B. Investigate 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.

VI. Topics in Thermal Energy and Thermodynamics

A. Develop the kinetic molecular theory.

1. Interconvert temperatures between Celsius and Kelvin scales.

2. Explain the solid, liquid, and gaseous states of matter from the perspective of the kinetic molecular theory.

3. Explain the connection between Kelvin temperature and molecular kinetic energy.

4. Use the ideal gas equation to solve problems under both static and changing conditions.

B. Compare thermal energy and heat transfer.

1. Recall the basic definitions of heat and work.

2. Distinguish between the equations for thermal energy added to or removed between phase changes and during phase changes.

3. Solve thermal energy transfer problems.

4. Relate thermal energy to both molecular energy and mechanical energy.

C. Analyze thermodynamics.

1. State and explain the meaning of the laws of thermodynamics.

2. Distinguish among various forms of the laws of thermodynamics.

3. Relate the first law to energy conservation.

4. Define entropy and use this concept to discuss entropy changes and the second law.

5. Discuss engine efficiency and relate it to the second law.

6. Solve thermodynamics problems using the first and second laws.

VII. Measurements with Laboratory Apparatus

A. Demonstrate the ability to carefully record data from measurement apparatus.

B. Analyze data with appropriate attention to errors and uncertainties.

C. Utilize numeric data and/or graphs of data to extract information and draw conclusions.

Content Outline and Competencies:

I. Conceptual Frameworks

A. Recognize key physics terms.

B. Distinguish between physics concepts.

C. Identify appropriate solutions.

II. Physical Models

A. Select appropriate physical model.

B. Generate symbolic formulas.

C. Generate numeric solutions.

III. Problem Solving Techniques

A. Analyze multi-step problems.

B. Select relevant information.

C. Identify an approach to solving a multi-step problem.

D. Generate solutions to multi-step problems.

IV. Topics in Electricity and Magnetism

A. Develop topics with 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 electric field lines and surfaces of constant potential.

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.

B. Relate the topics of electric current and resistance.

1. Describe the operation of batteries as current sources.

2. Describe the concepts of resistance, resistivity, and current.

3. Use Ohm's law to solve simple DC circuits.

4. Recall the various equations for electric power.

C. Analyze electric circuits.

1. Use the rules for series and parallel resistor combinations to solve simple one-source circuits.

2. Show an understanding of Kirchhoff’s rules.

3. Solve simple RC circuits.

4. Discuss the differences in how ammeters and voltmeters are used in circuits and be able to correctly place these meters in a circuit.

5. Discuss household circuits and electrical safety.

D. Analyze magnetism.

1. Describe how moving charges produce magnetic fields.

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.

E. Investigate electromagnetic induction.

1. State and use Faraday's/Lenz's law to solve simple problems.

2. Explain how AC generators work.

3. Discuss magnetic flux and transformer operation.

4. Discuss inductance and magnetic potential energy.

F. Analyze alternating current.

1. Interconvert RMS values and peak values for AC variables.

2. Calculate the reactance and phase shifts for RLC circuits.

3. Solve series RLC circuits.

4. Discuss phasors.

5. Discuss power and resonance in AC circuits.

V. Topics in Waves and Optics

A. Analyze waves.

1. Describe characteristics of waves.

2. Calculate wave properties.

B. Analyze 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 applications of total internal reflection.

4. Discuss dispersion of prisms.

C. Compare mirrors and lenses.

1. Use laws of reflection and refraction to explain the focusing property of curved interfaces.

2. Use the mirror/lens equations to calculate image position and type (real/virtual, upright/inverted).

3. Distinguish between converging and diverging systems.

D. Investigate 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 colorization due to scattering.

VI. Topics in Introductory Modern Physics

A. Investigate relativity.

1. Describe and explain some of the basic experimental evidence for special relativity.

2. State and apply the postulates of special relativity.

3. Calculate time dilations and length contractions.

4. Explain how the equations of relativity have an upper speed limit (the speed of light) built into them.

5. Discuss how rest mass fits into the concepts of energy and momentum.

B. Differentiate between waves and particles.

1. Discuss the differences between the particle and wave models of light.

2. Discuss the photoelectric and Compton effects from the particle perspective.

3. Recall and use the Einstein-Planck and de Broglie equations to solve problems.

4. Describe and explain the significance of the Heisenberg uncertainty principle.

C. Describe atomic structure.

1. Describe the Bohr model of the atom.

2. Use the Bohr model to explain the spectrum of hydrogen.

D. Relate 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. Explain the difference between fission and fusion and when one expects them to occur.

VII. Measurements with Laboratory Apparatus

A. Demonstrate the ability to carefully record data from measurement apparatus.

B. Analyze data with appropriate attention to errors and uncertainties.

C. Utilize numeric data and/or graphs of data to extract information and draw conclusions.

Content Outline and Competencies:

I. Vector Algebra and Transformations

A. Use trigonometry to determine the components and direction angles of a vector.

B. Compare the concepts of scalar and vector.

C. Compute vector arithmetic graphically and numerically.

D. Compute the angle between two vectors.

E. Normalize vectors.

F. Compute the normal vector to a surface.

G. Construct code that will perform vector arithmetic and normalization.

H. Convert between polar and rectangular coordinates.

I. Convert units of measurement.

J. Compute matrix arithmetic graphically and numerically.

K. Describe scaling using matrices and homogeneous coordinates.

L. Construct code that will perform scaling on vectors and geometric objects using matrices.

II. 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. Use Newton's Laws to determine the effect of forces on the motion of an object.

D. Derive and solve the equations of motion of an object.

E. Calculate the work done by a force on an object.

F. Calculate the kinetic energy, potential energy, and momentum of an object.

G. Compute the force vector acting on an object resulting from a scalar potential energy field.

H. Describe the Forward Euler and Velocity Verlet integration methods.

I. Compare the advantages and disadvantages of the Forward Euler and Velocity Verlet integration methods.

J. Construct code that can simulate the motion of an object according to Newton’s Laws of Motion.

K. Describe translations using matrices and homogeneous coordinates.

L. Construct code that will perform translation on vectors and geometric objects using matrices.

III. Collision Detection and Resolution

A. Determine the distance between an object and a line or plane.

B. Construct code that will compute the distance between an object and a line or plane.

C. Determine if two circles or two spheres are intersecting.

D. Calculate the point of intersection of two line segments.

E. Determine if two axially-aligned bounding boxes are intersecting.

F. Construct code that will detect collisions between circles, spheres, axially aligned bounding boxes and line segments.

G. Use conservation of energy and conservation of momentum to model the collision of objects.

H. Construct code that can simulate the collision between two objects.

IV. Rotational Motion

A. Describe rotations using matrices and homogeneous coordinates.

B. Construct code that will rotate an object using matrices.

C. Compute angular displacement, angular velocity and angular acceleration.

D. Determine the angular motion caused by a torque on an object.

E. Calculate the rotational kinetic energy and angular momentum of a rotating object.

F. Construct code that can model the two-dimensional motion of a rigid body incorporating the concepts of the conservation of energy and momentum and Newton’s Laws of Motion.

G. Compute quaternion arithmetic numerically.

H. Construct code that will rotate an object using quaternions.

Content Outline and Competencies:

I. Conceptual Frameworks

A. Recognize key physics terms.

B. Distinguish between physics concepts.

C. Identify appropriate solutions.

II. Physical Models

A. Select appropriate physical model.

B. Generate symbolic formulas.

C. Generate numeric solutions.

III. Problem Solving Techniques

A. Analyze multi-step problems.

B. Select relevant information.

C. Identify an approach to solving a multi-step problem.

D. Generate solutions to multi-step problems.

IV. Topics in Mechanics

A. Convert units and work with measurements.

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 data between different metric prefixes.

5. Explain the importance of measurements and accuracy in physics.

6. Apply significant figures to measurements.

B. Analyze 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. Analyze motion in a straight line.

1. Apply concepts of displacement, velocity and acceleration.

2. Construct motion diagrams to determine acceleration vectors for a variety of applications.

3. Construct graphs of position, velocity and acceleration as functions of time for a variety of situations.

4. Analyze problems with constant acceleration.

5. Apply constant acceleration to freely falling objects.

D. Analyze 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. Develop relative motion ideas and apply to one and two-dimensional problems.

E. Apply Newton’s Laws to force problems.

1. Define force and apply the ideas to common applications.

2. Define inertia and relate it to mass and to 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 force diagrams for force problems.

7. Identify examples of Newton’s third law.

8. Apply Newton’s laws to a variety of situations.

F. Relate the concepts of work and energy.

1. Understand the definition 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. Contrast conservative and nonconservative forces.

10. Explain how conservative forces are related to potential energy.

11. Solve problems that include gravitational and spring potential energy.

G. Develop the concepts of momentum and impulse.

1. Derive the impulse and momentum expressions from Newton’s second law.

2. Relate impulse to collisions.

3. Show how conservation of momentum is related to Newton’s third law.

4. Differentiate between 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.

H. Analyze rotational motion.

1. Define angular displacement, angular position, angular velocity and angular acceleration and relate them mathematically to the linear analogs.

2. Derive 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 rotational problems using 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.

I. Examine rigid bodies in static equilibrium.

1. Define the conditions of static equilibrium for a rigid object.

2. Solve static equilibrium problems.

J. Investigate 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.

K. Describe gravity and the gravitational field.

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. Understand the derivation of the equation for universal gravitational potential energy.

5. Solve problems using the universal gravitational potential energy formula and explain when simpler forms can be used.

V. Topics in Wave Motion

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 a wave on a string.

E. Solve problems involving reflection of waves.

F. Find the energy carried by waves in one dimension.

VI. Topics in Thermodynamics

A. Relate temperature and thermal 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. Construct PV diagrams for gases, including isotherms in your drawings.

B. Discuss the concept of heat the thermal properties of materials.

1. Carefully distinguish between thermal energy 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. Construct heat flow diagrams that illustrate the conservation of energy.

C. Develop the laws of thermodynamics.

1. Derive the work integral for gases.

2. Apply the first law of thermodynamics to the following processes for ideal gases: isobaric, isovolumetric, isothermal and adiabatic.

3. Describe two forms of the second law of thermodynamics.

4. Explain the importance of heat engines to our civilization.

5. Solve heat engine problems, including the topics of efficiency and wasted heat.

6. Solve problems concerning heat flows and efficiencies of heat pumps and refrigerators.

7. Examine the concept of entropy and work example problems.

D. Describe the 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 evaporation of all materials and planetary atmospheres.

VII. Measurements with Laboratory Apparatus

A. Demonstrate the ability to carefully record data from various measurement apparatus.

B. Analyze data with appropriate attention to errors and uncertainties.

C. Utilize numeric data and/or graphs of data to extract information and draw conclusions about physics principles under investigation.

Content Outline and Competencies:

I. Conceptual Frameworks

A. Recognize key physics terms.

B. Distinguish between physical concepts.

C. Identify appropriate solutions.

II. Physical Models

A. Select appropriate physical model.

B. Generate symbolic formulas.

C. Generate numeric solutions.

III. Problem Solving Techniques

A. Analyze multi-step problems.

B. Select relevant information.

C. Identify an approach to solving multi-step problems.

D. Generate solutions to multi-step problems.

IV. Topics in Electricity

A. Describe the properties of 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 explain how it differs from electric force.

6. Use calculus to develop expressions for electric fields created by continuous charge distributions.

7. Construct 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. Apply Gauss’s Law to various charge distributions.

1. State Gauss’s Law.

2. Apply Gauss’s Law to calculate electric fields for situations of high symmetry.

3. Using Gauss’s Law, predict essential features of electric fields inside and outside of insulators or conductors.

C. Develop the concept of electric potential.

1. Explain the difference between electric potential and electric potential energy.

2. Calculate 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. Relate the concepts of capacitance and dielectrics.

1. Write down the mathematical definition of capacitance.

2. Calculate capacitance from dimensions given for parallel 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. Explain the effects of a dielectric on capacitance and suggest an explanation of these effects.

E. Relate the concepts of 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 connected to a resistor.

3. Solve current, voltage, and resistance problems using Ohm’s law.

4. Create graphs of voltage as a function of current for ordinary metallic conductors.

5. Analyze 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 in single and multiloop circuits.

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.

V. Problems in Magnetism

A. Describe the properties of magnetic fields.

1. Compare and contrast 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. Calculate 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. Identify 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 this law.

3. Define magnetic flux and calculate flux in various situations.

4. Derive the magnetic field of an ideal solenoid.

5. Solve problems with magnetic fields in materials.

D. Investigate 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 predict the directions of induced emf’s and currents.

4. Explain the operation of motors and generators.

E. Develop the concept of 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. Investigate alternating current circuits.

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 and transformers.

VI. Topics in Electromagnetic Waves

A. Describe the origin and form of electromagnetic waves.

B. Relate Maxwell’s equations to the electromagnetic spectrum.

C. Calculate power and pressure produced by electromagnetic waves.

D. Describe the electromagnetic spectrum.

VII. Topics in Optics

A. Investigate the 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. Relate interference, diffraction, and polarization of light.

1. Describe the conditions necessary for interference of light in terms of path differences and 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.

VIII. Measurements with Laboratory Apparatus

A. Demonstrate the ability to carefully record data from various measurement apparatus.

B. Analyze data with appropriate attention to errors and uncertainties.

C. Utilize numeric data and/or graphs of data to extract information and draw conclusions about physics principles under investigation.