UNIT C:  Conservation Laws Constrain Interactions

 

C1:    The Art of Model Building

C2:    Particles and Interactions

C3:    Vectors

C4:    Systems and Frames

C5:    Conservation of Momentum

C6:    Conservation of Angular Momentum

C7:    More about Angular Momentum (optional*)

C8:    Conservation of Energy

C9:    Potential Energy Graphs

C10:  Work

C11:  Rotational Energy

C12:  Thermal Energy

C13:  Other Forms of Internal Energy

C14:  Collisions (optional*)

CA: The Standard Model (optional appendix)

 

*Chapter C7 is very valuable for chapters N4, N11, and N12, but is not strictly necessary. Similarly Chapter C14 is valuable preparation for chapters R8 and R9, but is also not necessary. All other chapters are crucial and should be discussed in the order stated. Chapters C1-C5 and C8 are required background for all units, C9 for units N and Q, C10 for units N and T, C12 and C13 for unit T. The climate-change chapter T11 does not really depend on the rest of unit T, and could in principle be presented any time after chapter C13.

UNIT N:  The Laws of Physics are Universal

 

N1:    Newton's Laws

N2:    Forces from Motion

N3:    Motion from Forces

N4:    Statics

N5:    Linearly Constrained Motion

N6:    Coupled Objects

N7:    Circularly Constrained Motion

N8:    Noninertial Frames

N9:    Projectile Motion

N10:  Oscillatory Motion

N11:  Kepler's Laws

N12:  Orbits and Conservation Laws (optional)

NA:   Differential Calculus (optional appendix for those needing a review)

NB:   Integral calculus (optional appendix for those needing a review)

 

One can also omit the sections about torque in sections N4. Chapter N10, though useful background for units Q and T, is also not strictly required. In a pinch, one can omit N6. Though this unit is valuable background for units R, E, Q, and T, we have seen that having a good high-school background in mechanics is really all that is necessary for those units.

UNIT R:  The Laws of Physics are Frame-Independent

 

R1:    The Principle of Relativity

R2:    Coordinate Time

R3:    The Spacetime Interval

R4:    Proper Time

R5:    Coordinate Transformations

R6:    Lorentz Contraction

R7:    The Cosmic Speed Limit

R8:    Four-Momentum

R9:    Conservation of Four-Momentum

RA:    Converting Equations to SI Units (optional appendix)

RB:    The Relativistic Doppler Effect (optional appendix)

 

Though this unit is valuable as background for units E (specifically chapters R1-R3 and R5-R7), it is not absolutely necessary. Chapter R9 is useful for unit Q, but again is not required. The shortest version of this unit that makes sense is R1-R3 and R5-R6. A shorter tour that includes dynamics would be R1-R3, R5, a single class session covering R4.1-R4.4, R7.1, and R7.4, followed by R8-R9. If you want to assign appendix RB, it can appear any time after section R4.2, and can either displace the latter sections in R4 or supplement R6 (alternatively, both appendices can be assigned as a single additional class section).

UNIT E:  Electric and Magnetic Fields are Unified

 

E1:    Electric Fields

E2:    Charge Distributions

E3:    Electric Potential

E4:    Static Equilibrium

E5:    Current

E6:    Dynamic Equilibrium

E7:    Analyzing Circuits (optional)

E8:    Magnetic Fields

E9:    Currents and Magnetic Fields

E10:  Magnets and Electromagnets (optional)

E11:  The Electromagnetic Field

E12:  Gauss's Law

E13:  Ampere's Law

E14:  Calculating Fields (optional)

E15:  Integral Forms (optional)

E16:  Dynamic Fields

E17:  Maxwell Sees the Light

E18:  Electromagnetic Wave Physics

E19:  Faraday's Law

E20:  Induction (optional)

Chapters E1–E11 (optionally omitting chapters E7 and/or E10) provide a basic introduction to E&M that addresses the unit's great idea (in such a case, one can also omit section E11.5 which is only relevant for chapters E16 and E18). One might also end with chapter E16 (optionally omitting chapters E14 and E15). Chapters E19 is required for chapter E20, though either E20 or both might be omitted.

 

Unit R is valuable as background for this unit, but students really only need to know

• the Principle of Relativity,
• that nothing, not even information, can move faster than light, and
• that moving objects are Lorentz contracted.

These ideas are simple enough to be taken on faith, so unit R is not really required.

UNIT Q:  Particles Behave Like Waves

 

Q1:    Wave Models

Q2:    Standing Waves and Resonance

Q3:    Interference and Diffraction

Q4:    The Particle Nature of Light

Q5:    The Wave Nature of Particles

Q6:    Spin

Q7:    The Rules of Quantum Mechanics

Q8:    Quantum Weirdness (optional)

Q9:    The Wavefunction

Q10:  Simple Quantum Models

Q11:  Spectra

Q12:  The Schrödinger Equation (optional)

Q13:  Introduction to Nuclei (optional, but needed for Q14, Q15)

Q14:  Nuclear Stability (optional, but needed for Q15)

Q15:  Nuclear Technology (optional)

QA:   Complex Numbers (optional chapter: insert after Q7 if desired)

 

One also has a lot of flexibility in truncating this unit. Chapters Q1-Q11 (optionally omitting Q8) provide a basic introduction to quantum mechanics. Chapter Q12 is not needed for what follows it. The section on nuclear physics is also optional, and Q15 is optional even if one one elects to cover Q13 and Q14. Appendix QA appears in the form of an entire chapter on complex numbers, which one can include after chapter Q7 in a class for more advanced students. One can also skip from Q5 to Q10 by having students read chapters Q9A and Q9B posted on the Resources page of this website. In summary, one can easily adjust this unit to be from 9 to 16 class sessions long.

 

In the default sequence, this unit follows units R and E. Chapters Q13 through Q15 draw on the relativistic idea that mass is a form of energy, but this idea is sufficiently well-known that unit R is not really required. No other chapters depend on unit R. Concepts specifically from unit E that are useful include the curved paths of particles in a magnetic field, the dipole model of magnets, and electrostatic potential, but students often see these ideas in high school. At Pomona, we find that a good high-school class and chapters C1-C6 and C8-C9 are really the only crucial prerequisites.

UNIT T:  Some Processes are Irreversible

 

T1:    Temperature

T2:    Microstates and Macrostates

T3:    Entropy and Temperature

T4:    The Boltzmann Factor

T5:    The Ideal Gas

T6:    Molecular Motion in Gases (optional)

T7:    Photon Gases (optional)

T8:    Gas Processes

T9:    Calculating Entropy Changes

T10:    Heat Engines (optional)

T11:  The Physics of Climate Change (optional)

 

Chapters T1-T4 provide the irreducible core of the unit. Adding T5 provides a valuable introduction to ideal gases. Chapter T6 is needed for T7, and chapter T7 is useful for chapter T11, but can be omitted. Chapter T5 is essential for chapter T8, which is essential for chapter T9, which is essential for chapter T10, but one could in principle end the unit after any of these chapters. Chapter T11 benefits from (but does not require) chapters T1 and T7, but is otherwise completely independent, and could be discussed any time after chapter C13.