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. Constant acceleration: Recall the formulas useful for constant velocity and constant acceleration motion. Without notes.
04. 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.
05. N1: Relate zero net force to constant velocity. This includes both logical directions.
06. N2: Relate net force to acceleration. This includes all logical directions.
07. Common forces: Determine the magnitudes and directions of weight, tension, normal force, and static and kinetic friction.
08. 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. Without notes.
09. Vector addition: Form linear combinations of vectors: addition, subtraction, multiplication by a scalar, and combinations of these. This includes both graphically and mathematically.
10. 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.
11. Statics: Relate all forces on a body in mechanical equilibrium. This includes identifying the forces that are present, choosing and applying appropriate coordinate axes, decomposing all forces into vector components, and finding unknown quantities.
12. Net force: Relate the individual and net forces acting on a body. This differs from the “statics” standard principally in that this standard is not restricted to mechanical equilibrium. Scenarios with a nonzero net force will often be intertwined with a Newton’s second law problem.
13. Trajectories: 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.
14. UCM formulas: Define quantities describing uniform circular motion. Recall the formulas relating period, angular velocity, speed, position, and acceleration. Without notes.
15. Uniform circular motion: Relate and determine quantities of motion for uniform circular motion. This includes relating period, angular velocity, speed, position, and acceleration.
16. Uniform 3-D circular motion: Relate quantities and outcomes for uniform circular motion involving an axial force, such as banked turns and conical pendulums.
17. Dot product: Calculate the dot product of two vectors. Interpret it geometrically. Calculate the dot product of vectors expressed as components or as magnitudes and directions.
18. Work definitions: Define work in words and by formulas; identify and analyze the units of work and energy. Without notes.
19. Work: Relate work to force and displacement. This includes appreciating the vector nature of force and displacement and the properties of their dot product.
20. Work-Energy: Relate the net work done on an object to its change in kinetic energy. This is the work-energy theorem.
21. Energy Formulas: Define and calculate kinetic energy and surface gravitational potential energy. This includes relating each to the quantities in their formulas.
22. 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.
23. Momentum: Define and calculate the (vector) momentum of an object or a system of objects. Without notes.
24. I-p: Relate the net force on an object, the force’s duration, and the object’s momentum change.
25. Newton’s laws: Recall and identify Newton’s three laws of motion. Without notes.
26. N3: Identify and relate the interacting objects and the paired forces in any interaction. Includes relating related quantities such as impulse and momentum change.
27. 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.
28. 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.
29. Angular variables: Relate angular and linear variables for rotational motion. This includes converting revolutions to radians or degrees, and linking angular and linear quantities for rolling on a surface.
30. 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.
31. Cross product: Calculate the cross product of two vectors. Interpret it geometrically. Calculation needs to be done only from magnitudes and relative angle; it is not necessary to calculate from components. Knowing the direction of the cross product is essential. Understand how the product is affected by changes in the vectors being crossed.
32. 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 the relationship between torque and force vectors τ = r × F, and between net torque and angular acceleration τ = Iα.
33. Static Torques: Given sufficient information, determine the torques and forces acting on a body in mechanical equilibrium.
34. Rigid rotor: Relate the forces or torques, mass distribution, and kinematics of a rigid body. Extends Standard 33 to include when the net torque is not zero. Includes finding the moment of inertia of the rotor.
35. 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.
36. 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.
37. Conservation laws: State and give examples of the laws of conservation of energy, momentum, and angular momentum. Identify their corresponding conjugate variables and continuous symmetries. Without notes.
38. Hooke: Relate stiffness, tension, and extension of a Hooke’s law spring. This includes using the formula F = −kx.
39. Spring work: Determine the work exerted on or by a spring as it compresses or extends. This includes using the formula W = ½kx2.
40. Oscillation: Relate the acceleration, velocity, position, kinetic energy, potential energy, amplitude, and phase of a Hooke’s law oscillator.
41. Spring Mechanics: Relate the motion of a simple harmonic oscillator to its mechanical characteristics. Specifically, relate period, frequency, mass, and spring constant.
42. Pendulum: Identify and explain the factors determining the frequency and amplitude of simple and physical pendulums. Calculate the period of torsional oscillators, including physical pendulums. Includes using the angular form of Hooke’s law and applying the small-angle approximation.
43. Pressure: Define density and pressure. Distinguish between gases and liquids.
44. Pressure formulas: Recall the formulas for density, for pressure relating force and contact area, for pressure with depth in an incompressible fluid, and for buoyancy of an object immersed in a fluid. Without notes.
45. Pascal:Describe how a pressure stress transfers through a fluid. Relate input and output work, pressure, volume, force, and area in hydraulic systems.
46. Depth: Define pressure and density, explain how pressure varies with depth in a fluid, and calculate how pressure varies with depth in an incompressible fluid.
47. 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.
48. 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.
49. Flow formulas: Recall the continuity equations for mass flow and volume flow, and the Bernoulli equation. Without notes.
50. Expansion: Calculate the response of an objectís volume or length to a temperature change. Correctly use coefficients of thermal expansion. Use both linear and volume coefficients, and know when to use which.
51. 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.
52. Heat transfer: Define and identify the heat transfer mechanisms conduction, convection, and radiation.
53. Heat flow: Predict the rate of heat flow through a thermal conductor. Apply the Fourier heat conduction law.
54. Kinetic theory: Qualitatively and quantitatively explain and apply the relationships between the quantities in the ideal gas equation of state pV = nRT
55. 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.
56. Thermodynamic steps: Classify thermodynamic pathways. Calculate the work done in different thermodynamic tansformation.Includes interpreting p-V graphs.
57. 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.
58. COP: Determine and use the formulas for the thermodynamic limits to performance of a heat engine or refrigerator.
59. Waves: Explain and describe wave motion in one dimension. This involves 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.
60. Wave speed formula: Given two of the following, find the third: wave length, frequency or period, wave speed.
61. 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.
62. 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.
63. Interference: Describe, explain, 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.
64. Coulomb: Calculate the force between two or more electric charges.
65. Polarization: Explain the force between charged and uncharged objects.
66. Fields: Create and interpret vector, potential, and field line depictions of fields. This includes gravitational, electric, and magnetic fields.
67. Potential: Define electric potential, and relate potential and field. Includes calculations as well as relating electric field lines and equal-potential surfaces.
68. Static conductors: Describe and explain the electric field within an electrical conductor. Includes describing the electric potential.
69. Capacitance: Relate charge, voltage, capacitance, and work to charge a capacitor. This includes the formulas C = Q/V and W = ½QV.
70. Dielectric: Explain how a dielectric responds to and affects an external electric field. Includes electronic polarization and the electric field inside the bulk dielectric. Also includes dielectric breakdown and the breakdown voltage of a capacitor.
71. 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.
72. 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.
73. Kirchoff: State, explain, and apply Kirchoff’s circuit laws. Includes setting up the specific equation for any node or loop in a circuit.
74. 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.
75. Capacitor sets: Calculate and the equivalent capacitance of capacitors in series and parallel.
76. Resistivity: Relate the resistance of a component to its composition and dimensions. Includes deriving, calculating, and explaining the drift speed of a charge carrier in a conductor.
77. RC: Explain and calculate the development over time of charge, voltage, and current associated with a capacitor and resistor in series. Includes calculating and understanding the time constant τ.
78. Magnets: Describe the interaction between dipole magnets and the effect of a magnetic field on a magnetic pole or dipole. Unlike poles attract and like poles repel; field direction is force direction on a north pole. Dipoles receive a torque to align them with the field.
79. 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.
80. Laplace: Describe the interaction between an electric current and 9 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.
81. 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.
82. Ampère: Relate electric current to the magnetic field it creates. Includes using formulas for specific situations. Use Ampère’s law quantitatively to derive formulas for high-symmetry situations.
83. 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.
84. 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.
85. 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.
86. RMS: Relate peak to rms current and voltage in an AC circuit.
87. 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.
88. Phasors: Determine and describe currents, voltages, and power in an AC circuit in terms of phasors. Includes identifying the phase angle relationships between phasors describing different components in the circuit.
89. Impedance: Generalize Ohm’s law to impedances in AC circuits. Calculate voltages, currents, and power. Includes calculating the phase angle and power factor, and distinguishing resistance, reactance, and impedance.
90. Nature of light: Describe the medium of electromagnetic radiation. Includes the electromagnetic spectrum, the angular relationship between electric and magnetic field, and the transverse nature of the electromagnetic waves.
91. Polarized Light: Describe the polarization of light and the interaction of polarized and unpolarized light with matter. Includes polarizing filters, anisotropy, crossed polarizers, optical activity, scattering, and Brewster’s angle.
92. Reflection: Describe and explain specular and diffuse reflection from planar surfaces.
93. Rays: Locate and characterize images from single lenses and mirrors by ray-tracing.
94. Optics Math: Mathematically locate and characterize images and foci of single lenses and mirrors. This includes the laws of mirrors and lenses. Characterization may include position, orientation, magnification, and angular magnification.
95. Refraction: Describe and calculate refraction of light between transmitting media. This includes total internal reflection, Snell’s law, and dispersion.
96. Compound Optics: Locate and characterize images from compound optical devices such as microscopes and telescopes. Includes both ray-tracing and mathematically.
97. Grating: Explain and characterize interference patterns of light. Includes two-slit, air wedge, and thin film interference, and diffraction gratings.
98. Radioactivity: Identify and characterize atomic nuclei and their decays. includes counting statistics, half-life, radioactive dating, and shielding.
99. Nukes: Identify and describe reactions and products in the nuclear fuel cycle, nuclear weapons, and stars. includes fission and fusion, neutron activation, and the properties of nuclear waste.
Copyright © 2017, Richard Barrans
Revised: 21 April 2020. Maintained by Richard Barrans.