1. Unit algebra: Include the units in algebraic transformations. Multiply and divide units of different quantities; cancel and combine like units.

2. Unit conversion: Convert between different units for the same quantity. Generate conversion factors from equalities, and properly use the conversion factors to perform the conversions. Includes converting compound units, such as m/s and in^{3}.

3. 1-D Story: Relate position, velocity, and acceleration in one dimension by kinematic graphs and words. Given one type of description, generate any other to describe the same motion. Kinematic graphs include position-time, velocity-time, and acceleration-time graphs.

4. Kinematic concepts: Define, distinguish, and apply position, displacement, distance, average velocity, instantaneous velocity, speed, average acceleration, and instantaneous acceleration.

5. 1-D Kinematics: Algebraically 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 one of the others and appropriate initial conditions or other sufficient information; finding the differences between positions and velocities of different objects; and finding the time or place at which particular events occur.

6. Trig: Define and use the sine, cosine, and tangent functions relating the sides and angles of a right triangle. State and apply the relationship between the lengths of the sides of a right triangle. Given two sides of a right triangle, find the angles; given a side and an angle, find the other sides. Given the lengths of two sides of a right triangle, find the third.

7. Vector basics: Express vectors in terms of polar coordinates and Cartesian components. Carry out mathematical operations involving vectors: addition, subtraction, multiplication by a scalar. Convert between polar and Cartesian coordinate descriptions of vectors, and between rotated Cartesian coordinates. Add and subtract vectors both graphically and mathematically. Find the polar coordinates (magnitude and direction) of a vector given as Cartesian components; find the Cartesian components of a vector given as polar coordinates. Convert angles given in any direction and with respect to any line to their trigonometric equivalent.

8. Trajectories: Relate quantities of motion for ballistic trajectories. For free-fall projectiles, this includes decomposing initial velocity vectors into Cartesian components, identifying the equations of motion in the vertical and horizontal directions, and finding the time at which particular events occur.

9. Ballistic kinematics: Determine and explain the properties of a projectile and its trajectory, such as flight time, range, maximum height, or velocity at any time and place in the trajectory. Disregarding drag.

10. Force: Define force, net force, exernal force, mass, and inertia.

11. N1: Relate zero net force to constant velocity. Newton’s first law: constant velocity is logically equivalent to zero net force. This holds in both logical directions.

12. N2: Relate net force, mass, and acceleration. This holds in both logical directions: given two, find the third.

13. N3: Identify the interacting objects and the paired forces in any interaction. If A applies a force to B, B applies an equal and opposite force to A. But not all equal and opposite force are Newton’s third law counterparts.

14. 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.

15. Friction: Determine the magnitude and direction of static and kinetic friction between two surfaces. Know when each force acts and what quantities influence them.

16. Common forces: Determine the magnitudes and directions of weight, tension or compression, and the normal force.

17. Net force: Relate the individual forces and the net force acting on a body. This includes identifying the force vectors that are present, adding their Cartesian components together, and finding unknown quantities.

18. Inclines: Correctly express the forces acting on a body constrained to an inclined surface as Cartesian components in inclined coordinates. “Inclined coordinates” are parallel and perpendicular to the surface.

19. Linked bodies: Recognize, express, and apply the relations between position, velocity, or acceleration of linked bodies to determine their motions. Bodies linked, for instance, by a flexible, inextensible cable over a pulley.

20. UCM: Relate the radius, tangential speed, angular speed, period, and frequency of a body traveling at a constant speed in a circular path.

21. Centripetal: Identify the direction and magnitude of the acceleration of a body traveling at a constant speed in a circular path. Express the magnitude in terms of radius and tangential speed, radius and period, or radius and angular speed.

22. Big G: Determine the gravitational force between two particles or spherical bodies. Apply
Newton’s gravitational formula F = GmM/r^{2}.
Specify direction as well as magnitude.

23. Orbits: Relate the distance, tangential speed, orbital period, angular speed, and attractor mass for a body in a circular orbit around a much more massive attractor. The centripetal force of the trajectory is the gravitational attraction between the bodies. This includes Kepler’s second law of planetary motion.

24. Dot and cross: Calculate the results, and identify and interpret the properties, of dot and cross products of vectors. In addition to finding the products, conseptually identify the geometric and mathematical relationships between the veators and their products.

25. Work: Relate work to force and displacement. This includes appreciating the vector nature of force and displacement and the properties of their dot product.

26. 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.

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

28. 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.

29. Σp: Define and calculate the momentum of an object or a system of objects. Includes defining and calculating momentum. Also applies to a single objec

30. J-p: Relate the net force on an object, the force’s duration, and the object’s momentum change.

31. p Conservation: Use conservation of momentum to predict the outcome of an isolated collision. This includes recognizing when external forces prevent conservation of momentum within the system.

32. Collisions: In a collision, recognize which quantities are conserved and which are not conserved. This includes relating the categories “elastic,” “inelastic,” and “totaly inelastic” to the characteristics of the collision and its outcome.

33. Angular variables: Define and relate angular velocity, angular position, angular acceleration, radius, tangential speed, acceleration, and tangential and radial components of acceleration of a rotor or orbiting particle. This includes knowing the magnitudes and directions of all of those quantities that are vectors.

34. Find I: Calculate the moment of inertia of an object from its distribution of mass. Includes adding together segments of known moment of inertia, using tabulated formulas, and applying the parallel-axis theorem.

35. Torque: Determine the torque applied to an object about a specified referenece point by a force. The magnitude and diretion of the torque depends on the reference point as well as on the force. 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.

36. Angular N2: Relate an object’s angular acceleration to its moment of inertia and net torque.

37. K_{rot}: 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
ΔK_{rot} = τΔθ
and to the formula
K_{rot} = ½ Iω^{2}.

38. 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.

39. 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 changing systems such as spinning ice skaters and divers.

40. Kepler: State and explain Kepler’s third law of planetqry motion. Use conservation of angular momentum.

41. Oscillation: Relate the acceleration, velocity, position, kinetic energy, potential energy, amplitude, period, frequency, mass, and spring constant of a Hooke’s law oscillator.

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. 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.
Also includes relating the properties of the medium to wave propagation speed, e.g.
the string transverse wave formula v = (F/μ)^{½} and its counterparts for sound waves.

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. Intensity: Explain and calculate the inverse-square relationship between sound intensity and distance from the source. Relate sound intensity to the logarithmic decibel scale.

46. 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.

47. 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.

48. Deformation: Calculate the response of an object’s volume or shape to a stress or a temperature change. Define and distinguish “stress” and “strain” correctly use moduli and coefficients of thermal expansion.

49. 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.

50. 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.

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

Copyright © 2014, Richard Barrans

Revised: 7 September 2024. Maintained by Richard Barrans.

URL: http://www.barransclass.com/phys1110/P1110_Standards.html