01. Units: Convert between different units for the same quantity; multiply and divide units of different quantities; and multiply and divide units of the same quantity. Provide proper units with answers.
02. Vectors: Distinguish vectors and scalars. Express vectors graphically, as magnitude and direction, as components, and as linear combinations of unit basis vectors; and convert between these representations.&nbbsp; Add, subtract; and take scalar multiples of vectors. Add and subtract vectors graphically and by components.
03. Vector Operations: Calculate dot products and cross products of vectors. Students may carry out any of these operations using either component or magnitude-and-direction descriptions of the vectors, as long as the final result is in the requested format.
04. Story: Describe 1-D motion by equations, graphs, and words. Given one type of description, generate any other to describe the same motion. Graphs refer specifically to position-time, velocity-time, and acceleration-time graphs. Graphs may be qualitative or quantitative, depending on the specifications of the problem. Students must be able to generate exact equations for constant-velocity and constant-acceleration motion.
05. 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.
06. 1D Kinematics: Relate absolute and relative position, velocity, and time in a 1-D constant-velocity or constant-acceleration situation. This includes creating the position or velocity equation given the other and appropriate initial conditions or other sufficient information; finding the differences between positions and velocities of different constant-velocity objects; and finding the time at which particular events occur.
07. Constant acceleration: Recall the formulas useful for constant velocity and constant acceleration motion. Without notes.
08. Ballistic: Predict, calculate, and describe; and relate the horizontal and vertical components of position, velocity, and acceleration to time for a ballistic trajectory. This includes all free-fall projectile problems, including decomposing initial velocity vectors into components, deriving and using the range equation, finding the time at which particular events occur, determining the time and place of the apex of a trajectory, and so on.
09. Circular: Relate period, angular velocity, speed, position, and acceleration for an object undergoing uniform circular motion. This includes specifying the vector natures of the quantities. It does not include circular motion with changing speed.
10. UCM formulas: Define quantities describing uniform circular motion. Recall the formulas relating period, angular velocity, speed, position, and acceleration. Without notes.
11. N1: Determine the unknown force in a system in mechanical equilibrium. Equate mechanical equilibrium and zero net force (Newton’s first law). Includes statics problems not involving torques. Desired results may be directions or magnitudes or both.
12. fbd: Draw a qualitatively correct (appropriate forces with approximate directions and magnitudes) free-body diagram for a body. Applies to objects with balanced or unbalanced forces.
13. Net force: Given the individual vector forces acting on an object, determine the net force acting on it. Also includes finding one component force when the net force is known.
14. N2: Given the net force acting on an object, determine its acceleration. includes magnitude and direction.
15. Forces: Determine the magnitudes and directions of the following forces: static and kinetic friction, normal force, tension, constant-field gravity, viscous drag, and a Hooke’s law spring.
16. N3: Given a force, Identify its source, its Newton’s third law partner, and the object it acts upon.
17. Kinetic: Calculate the translational kinetic energy of an object from its speed and mass.
18. Work: Relate the work done on an object to the forces applied to it and its displacement. This includes defining work.
19. Work-energy: Relate the net work done on an object to its change in kinetic energy. This applies the work-energy theorem.
20. Conservative forces: Identify and distinguish conservative and non-conservative forces.
21. Energy conservation: Use conservation of energy to analyze multi-step processes. Such processes include collisions, ballistic pendulums, Tarzan swinging on a vine, etc.
22. Potential Diagrams: Interpret and apply energy diagrams. This includes knowing kinetic and potential energy at any position, relating force to shape of the potential, qualitatively describing a trajectory given starting position and velocity, and explaining the effects of a change in total energy.
23. Σp: Relate the total momentum of a system of objects to the individual momenta of the objects in the system. This also applies to a single object.
24. J-p: Relate the net force on an object, the force’s duration, and the object’s momentum change. This includes applying the impulse-momentum theorem, but does not require knowing the definition of impulse.
25. p Conservation: Apply conservation of momentum to analyze an isolated collision. This includes predicting final velocities, reconstructing initial velocities, and relating whether a collision is elastic, inelastic, or totally inelastic to the characteristics of the collision. It also includes relating initial and final total momentum.
26. Angular kinematics: Relate the angular velocity, angular position, and angular acceleration of a rotor undergoing a constant angular acceleration.
27. Angular fomrmulas: Produce the formulas relating tangential and angular position, velocity, and acceleration for rigid rotors with fixed axes as well as circular rotors rolling without slipping. Without notes.
28. Rotor Energy: Determine the rotational kinetic energy of a rigid body.
29. Kinetic Sum: Relate the total kinnetic energy of a system of particles or an extended object to the characteristics of its center of mass and of its particles relative to its center of mass.
30. Find I: Calculate the moment of inertia of an object from its distribution of mass. Includes adding together segments of known angular momentum, looking up an angular momentum formula from a table and applying it properly, applying the parallel-axis theorem, and integrating to find the moment of inertia of a continuous body.
31. Torque: Relate the torques and forces applied to a body, and the net torque to the individual torques. This includes the definition of torque, with full appreciation of its vector nature. It also includes applying the cross product.
32. Static torques: Find an unknown force or position of its application on an object in mechanical equilibrium.
33. Angular N2: Relate the net torque on a rotor to the rotor’s moment of inertia and angular acceleration. This refers to angular Newton’s second law. It includes statics problems involving torques and cases of nonzero angular acceleration.
34. Angular work: Relate the rotational work done on a rotor to applied torque and angular displacement, and to the rotor’s change in rotational kinetic energy. Also relate the rotational kinetic energy of a rotor to its angular velocity and moment of inertia. These refer to the work-energy theorem in the angular case and to the formula K = ½ Iω2.
35. Angular momentum: Relate a rotor’s angular momentum to its moment of inertia and rotational velocity, and a particle’s angular momentum to its momentum and its position relative to a reference. These refer to the formulas L = Iω and L = r×p. Also determine the angular momentum of an extended rotor with respect to a reference point not at its center of mass.
36. L conservation: Use conservation of angular momentum to analyze collisions involving rotors, and to predict the motion of an object whose moment of inertia changes. This includes collisions involving objects like swinging doors and pendulums, and to systems such as spinning ice skaters and bolas.
37. Phase angle: Explain the meaning of the phase angle and the angular frequency ω used to describe a repeating process.
38. SHM relations: Identify the functional form of the net force on and the position of an object undergoing simple harmonic motion, and identify and explain the factors determining the frequency and amplitude of a simple harmonic oscillator. Includes knowing that Hooke’s law describes the net force, that ma = −kx is the governing differential equation, that a sinusoid x = A cos(ωt + φ) is the general solution, and that frequency increases with k and decreases with m.
39. SHM energy: Describe the distribution of energy at different phases of the cycle of a simple harmonic oscillator or simple pendulum. Includes recognizing that mechanical energy is conserved, and that amplitude and maximum speed are monotonically related.
40. Simple pendulum: Identify and explain the factors determining the frequency and amplitude of a simple pendulum. Includes recognizing that frequency increases with g, decreases as L increases, and does not depend on m. Does not include deriving the relation ω2 = g/L or explicitly recognizing that the small-angle approximation is needed.
41. SHM kinematics: Relate the position, velocity, acceleration, frequency and period, amplitude, kinetic and potential energies, and phase of an object undergoing simple harmonic motion. Includes symbolically and quantitatively determining one equation of motion from another, and determining extreme values of any of the quantities. Includes integrating or differentiating the equations of motion and applying the formulas ω2 = k/m and ΣE = ½ kA2 = ½ mvmax2.
42. Oscillator formulas: Produce the formulas for the frequency or angular frequency of a simple harmonic oscillator and of a simple pendulum. Without notes.
43. Torsion: Identify and explain the factors determining the frequency and amplitude of a torsional oscillator, including simple and physical pendulums. Calculate the period of torsional oscillators, including physical pendulums. Includes applying the small-angle approximation, and recognizing a simple pendulum as a limiting case of a physical pendulum.
44. Big G: Calculate the gravitational force between two particles. Apply Newton’s gravitational formula. Specify direction as well as magnitude.
45. Sphere gravity: Calculate the gravitational field inside and outside a sphere or spherical shell.
46. Gravitational energy: Calculate the gravitational potential energy between two particles or spheres and their total energy. Includes consequences such as escape speed.
47. Orbit conservation: Use conservation of momentum, energy, and angular momentum to describe the motion of bodies in all types (circular, elliptical, parabolic, and hyperbolic) of orbit. This includes justifying Kepler’s laws.
Copyright © 2023, Richard Barrans
Revised: 17 September 2023. Maintained by Richard Barrans.