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, static and kinetic friction, and tension in a Hooke’s law spring.
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, surface gravitational potential energy, and elastic 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. 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.
37. COP: Determine and use the formulas for the thermodynamic limits to performance of a heat engine or refrigerator.
38. Oscillation: Relate the acceleration, velocity, position, kinetic energy, potential energy, amplitude, period, frequency, mass, and spring constant of a Hooke’s law oscillator.
39. 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.
40. Moduli: Define and relate stress, strain, and moduli for deformed solids.
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. Intensity: Explain and calculate the inverse-square relationship between sound intensity and distance from the source. Relate sound intensity to the logarithmic decibel scale.
43. 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.
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.
Copyright © 2017, Richard Barrans
Revised: 25 September 2017. Maintained by Richard Barrans.