01. Units: Convert between different units for the same quantity; multiply and divide units of different quantities; multiply and divide units of the same quantity; and provide proper units for answers.
02. 1-D Story: Relate position, velocity, and acceleration in one dimension by graphs and words. Given one type of description, can generate any other to describe the same motion.
03. 1-D Kinematics: Relate absolute and relative position, velocity, and time in a 1-D constant-velocity or constant-acceleration situation. This includes finding the position, velocity, or acceleration equation of motion given sufficient information, finding the differences between positions and velocities of different objects, and finding the time, place, or velocity at particular events.
04. Trig: Define the sine, cosine, and tangent functions relating the sides and angles of a right triangle. Convert between polar and Cartesian coordinate descriptions of vectors, and between rotated Cartesian coordinates.
05. Vector addition: Form linear combinations of vectors: addition, subtraction, multiplication by a scalar, and combinations of these. This includes both graphically and mathematically.
06. 2-D Kinematics: Relate quantities of motion for ballistic trajectories. This includes decomposing initial velocity vectors into components, finding the times, positions, and velocities at which particular events occur, and finding the necessary conditions corresponding to particular outcomes.
07. N1: Relate zero net force to constant velocity. This includes both logical directions.
08. N2: Relate net force to acceleration. This includes both logical directions.
09. FBD: Construct a qualitatively correct free-body diagram for a body. All forces should be present with no extraneous forces; directions and magnitudes should be approximately correct, showing the key characteristics of the situation.
10. Common forces: Determine the magnitudes and directions of weight, tension, normal force, and static and kinetic friction.
11. Net: Relate the individual and net forces acting on a body.
This includes identifying the forces that are present, choosing and applying appropriate coordinate axes, decomposing all forces into vector components, and finding unknown quantities.
G12. N3: Identify the interacting objects and the paired forces in any interaction.
13. Uniform circular motion: Relate quantities of motion for uniform circular motion. This includes relating period, angular velocity, speed, position, and acceleration.
14. Uniform 3-D circular motion: Relate quantities and outcomes for uniform circular motion involving an axial quantity, such as banked turns and conical pendulums.
15. Vector multiplication: Calculate the dot product and cross product of two vectors. Interpret these quantities geometrically.
16. Work: Relate work to force and displacement. This includes appreciating the vector nature of force and displacement and the properties of their dot product.
17. Work-Energy: Relate the net work done on an object to its change in kinetic energy. This is the work-energy theorem.
18. Energy Formulas: Define and calculate kinetic energy and surface gravitational potential energy. This includes relating each to the quantities in their formulas. “Elastic” refers to a Hooke’s law force.
19. Energy conservation: Use conservation of energy to analyze multi-step processes. This includes knowing kinetic and potential energy at any position, qualitatively describing a trajectory given starting position and velocity, and describing the changes in any of these resulting from non-conservative work.
20. Momentum: Define and calculate the momentum of an object or a system of objects.
21. I-p: Relate the net force on an object, the force’s duration, and the object’s momentum change.
22. p Conservation: Use conservation of momentum to predict the outcome of an interaction between systems. This includes recognizing when external forces prevent conservation of momentum within the system.
23. Collisions: In a collision, recognize which quantities are conserved and which are not conserved. This includes relating the categories “elastic,” “inelastic,” and “totally inelastic” to the characteristics of the collision and its outcome.
24. Angular kinematics: Relate the angular velocity, angular position, angular acceleration, radius, tangential speed, acceleration, and tangential and radial components of acceleration of a rotor undergoing a constant angular velocity or angular acceleration. This includes off-axis rotation and rolling.
25. Torque: Relate the torques and forces applied to a body, and relate the net torque to the individual torques. This includes the definition of torque, with full appreciation of its vector nature. Should be able to find torque using both τ = r × F and τ = Iα.
26. Krot: Relate the rotational kinetic energy of a rotor to its angular velocity and moment of inertia, and its change in rotational kinetic energy to rotational work done. These refer to the work-energy theorem in the angular case ΔKrot = τΔθ and to the formula Krot = ½ Iω2.
27. Angular momentum: Relate a rotor’s angular momentum to its moment of inertia and rotational velocity, Iω. predict the motion of an object whose moment of inertia changes.
28. Pressure: Define pressure and density, explain how pressure varies with depth in a fluid, and calculate how pressure varies with depth in an incompressible fluid. Density ρ = m/V; pressure = F/A; p = p0 + ρgh.
29. Buoyancy: Relate buoyancy, displaced weight, and density. Specifically, apply the relation F = ρgV. Know when displaced weight is the same as the object’s weight and when it is not.
30. Flow: Relate mass and volume flow rates, speed, and density, and relate flow rates at different points in a fluid stream. Apply the continuity equations, including rearranging a continuity equation to find an unknown. Use the Bernoulli equation to relate fluid pressure, height, and speed at different points. Rearrange the Bernoulli equation to find an unknown, and eliminating zero terms to find special cases such as Torricelli’s law.
31. Expansion: Calculate the response of an objectís volume or length to a temperature change. Correctly use coefficients of thermal expansion.
32. Heat: Relate energy input to phase changes and temperature changes. Use heat capacity and specific heat capacity formulas; define and apply the concept of latent heat.
33. Heat transfer: Define and identify the heat transfer mechanisms conduction, convection, and radiation.
34. Kinetic theory: Qualitatively and quantitatively explain and apply the relationships between the quantities in the ideal gas equation of state pV = nRT
35. First law of thermodynamics: Correctly define and relate heat, work, and internal energy. Understand the mechanical equivalent of heat and conservation of energy in heating.
36. Thermodynamic steps: Classify thermodynamic pathways. Calculate the work done in different thermodynamic tansformation.Includes interpreting p-V graphs.
37. Entropy: Describe, explain, and give examples of the tendency of matter and energy to spread out. This is the second law of thermodynamics, subsuming the direction of heat flow.
38. COP: Determine and use the formulas for the thermodynamic limits to performance of a heat engine or refrigerator.
39. Hooke: Relate stiffness, tension, extension, and elastic potential energy of a Hooke’s law spring. This includes using the formulas F = −kx and PE = ½kx2.
40. Oscillation: Relate the acceleration, velocity, position, kinetic energy, potential energy, amplitude, period, frequency, mass, and spring constant of a Hooke’s law oscillator.
41. Waves: Explain and describe wave motion in one dimension. This includes relating wave speed to wavelength and period as well as qualitatively describing the motion of the medium in common waves. Defining, recognizing, and distinguishing between transverse and longitudinal waves are part of this standard. Defining and distinguishing between the motion of the medium (amplitude, velocity, acceleration) and the wave phase (phase velocity, wavelength) is also part of this standard.
42. Wave speed formula: Given two of the following, find the third: wave length, frequency or period, wave speed.
43. Sound intensity: Explain and calculate the inverse-square relationship between sound intensity and distance from the source. Relate sound intensity to the logarithmic decibel scale.
44. Interference: Describe and carry out the linear combination of waves. Describe how standing waves and beats are generated, and identify and describe nodes and antinodes of standing transverse and longitudinal waves. Includes defining and recognizing nodes and antinodes of different kinds of waves, including longitudinal waves.
45. Doppler: Explain, calculate, and relate the received and emitted frequencies of a wave and the velocities of the source and detector. Apply the formula for non-relativistic Doppler shift and conceptually explain its predictions.
46. Coulomb: Calculate the force between two or more electric charges.
47. Polarization: Explain the force between charges and uncharged objects.
48. Fields: Create and interpret vector, potential, and field line depictions of fields. This includes gravitational, electric, and magnetic fields.
49. Potential: Define electric potential, and relate potential and field. Includes calculations as well as relating electric field lines and equal-potential surfaces.
50. Resistors: Relate current through, voltage across, resistance of, and power dissipated by an ohmic resistor. Includes the formulas I = V/R, P = VI, and their combinations. The prepositions are important.
51. Circuits: Analyze current, voltage, and power in DC circuits containing single, series, and parallel resistors. It is the student’s choice to use the specific series and parallel formulas or Kirchoff’s rules.
52. Capacitance: Relate charge, voltage, capacitance, and work to charge a capacitor. This includes the formulas C = Q/V and W = ½QV.
53. Plates: Relate the construction of a capacitor to its capacitance. This includes the formula C = κε0A/d and the effect of filling a capacitor with a dielectric.
54. RC: Explain and calculate the development of charge, voltage, and current associated with a capacitor and resistor in series. Includes calculating and understanding the time constant τ.
55. Magnets: Describe the interaction between dipole magnets and the effect of a magnetic field on a magnetic pole or dipole. Like poles attract and unlike poles repel; field direction is force direction on a north pole. Dipoles receive a torque to align them with the field.
56. Lorentz: Describe and calculate the force a magnetic field exerts on an electric charge and its effect on the charge’s motion. Lorentz force F = qv×B; F⊥v so acceleration is centripetal.
57. Laplace: Describe the interaction between an electric current and a magnetic field. Includes both the Laplace formula F = ILB sinθ for a linear current in a uniform field and the torque on a loop τ = μB sinθ.
58. Magnetic fields: Describe and calculate the magnetic fields created by permanent magnets, linear currents, current loops, and solenoids. Includes finding the magnetic moment of a current loop.
59. Emf: Define emf and distinguish it from electric potential. Calculate the emf of a conductor moving through a magnetic field. Includes ε = vBL in optimal conditions.
60. Faraday: Explain the electric potential created by a changing magnetic flux. Includes using Faraday’s and Lenz’s laws. Also includes defining and calculating magnetic flux.
61. Inductance: Relate rate of current change, voltage, and inductance of an inductor. Determine and explain the work needed to change the current through an inductor. This includes relating the work to the energy in the magnetic field.
62. Transformers: Explain and apply the relationship between primary and secondary windings, magnetic flux, current, and voltage in AC transformers. V1/V2 = N1/N2 and V1I1 = V2I2.
63. RMS: Relate peak to rms current and voltage in an AC circuit.
64. Phasors: Determine and describe currents, voltages, and power in an AC circuit in terms of phasors.
65. Impedance: Generalize Ohm’s law to impedances in AC circuits. Calculate voltages, currents, and power. Includes calculating the phase angle and power factor.
Copyright © 2017, Richard Barrans
Revised: 16 April 2018. Maintained by Richard Barrans.