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. Story: Describe 1-D motion by equations, graphs, and words. Given one type of description, I can generate any other to describe the same motion. Graphs refer specifically to position-time, velocity-time, and acceleration-time graphs. Graphs need be only qualitative, though students must be able to generate exact equations for constant-velocity and constant-acceleration motion.

03. 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.

04. Vector Operations: Add, subtract, take dot products and cross products, and find the magnitudes of vectors. Convert between polar and Cartesian coordinate descriptions of vectors, and between rotated Cartesian coordinates.

05. 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.

06. Circular: Relate period, angular velocity, speed, position, and acceleration for an object undergoing uniform circular motion. This includews the vector natures of the quantities. It does not include circular motion with changing speed.

07. 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.

08. 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.

09. Net force: Given the individual vector forces acting on an object, determine the net force acting on it.

10. N2: Given the net force acting on an object, determine its acceleration. includes magnitude and direction.

11. 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.

12. N3: Given a force, Identify its Newton’s third law partner and the object it acts upon.

13. Kinetic: Calculate the kinetic energy of an object from its speed and mass.

14. Work: Relate the work done on an object to the forces applied to it and its displacement. This includes defining work.

15. Work-energy: Relate the net work done on an object to its change in kinetic energy. This is the work-energy theorem.

16. Conservative forces: Identify and distinguish conservative and non-conservative forces.

17. Energy conservation: Use conservation of energy to analyze multi-step processes. Such processes include collisions, ballistic pendulums, Tarzan swinging on a vine, etc.

18. 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 the effects of a change in total energy.

19. 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.

20. 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.

21. 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.

22. Angular kinematics: Relate the angular velocity, angular position, and angular acceleration of a rotor undergoing a constant angular acceleration.

23. Rotor Energy: Determine the rotational kinetic energy of a rigid body.

24. 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.

25. 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.

26. 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 first and second laws. It includes statics problems involving torques and cases of nonzero angular acceleration.

27. 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. I can 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 Iω^{2}.

28. 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.

29. 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.

30. Phase angle: Explain the meaning of the phase angle and the angular frequency ω used to describe a repeating process.

31. 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.

32. SHM energy: Describe the partitioning of energy at different phases of a simple harmonic oscillator or simple pendulum. Includes recognizing that mechanical energy is conserved, and that amplitude and maximum speed are monotonically related.

33. 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
ω^{2} = g/L
or explicitly recognizing that the small-angle approximation is needed.

34. 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 ω^{2} =
k/m and
ΣE = ½ kA^{2} =
½ mv_{max}^{2}.

35. Torsion: Identify and explain the factors determining the frequency and amplitude of a torsional oscillator, including simple and physical pendulums. I can calculate the period of torsional oscillators, including physical pendulums. Includes applying the small-angle approximation.

36. Damping: Identify the characteristics of an
oscillator that result in under-damping, critical damping, and over-damping, and explain the motion of a damped oscillator under those three regimes. Requires
finding and interpreting the parameter ω'^{2} =
k/m&minusb^{2}/4m^{2},
but does not require determining all the coefficients in the equations of motion.

37. Moduli: Define and relate stress, strain, and moduli for deformed solids.

38. Big G: Calculate the gravitational force between two particles. Apply Newton’s gravitational formula. Specify direction as well as magnitude.

39. Sphere: Calculate the gravitational field inside and outside a sphere or spherical shell.

40. Gravitational energy: Calculate the gravitational potential energy between two particles or spheres and their total energy. Includes consequences such as escape speed.

41. 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.

42. Expansion: Calculate the response of an object’s volume or length to a temperature change. Correctly use coefficients of thermal expansion.

43. 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.

44. Heat transfer: Define and identify the heat transfer mechanisms conduction, convection, and radiation.

45. 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.

46. 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.

47. COP: Determine and use the formulas for the thermodynamic limits to performance of a heat engine or refrigerator.

Copyright © 2017, Richard Barrans

Revised: 4 September 2017. Maintained by Richard Barrans.

URL: http://www.barransclass.com/sci440u/SCI440U_Standards.html