### Outcome Statements for Physics Majors

Physics Standards Document – September 2001

### 1.0 Process Standards

### 1.1. Critical Thinking and Problem Solving

**1.1.1 Skill inventory**

1. Deduction

2. Inference

3. Reasoning

4. Formulating questions

5. Order of magnitude estimation

**1.1.2 Performance expectation**

1. Evaluate whether a calculated result or reported measurement is physically plausible by crude estimations of the quantity.

### 1.2 Data Analysis

**1.2.1 Skills inventory**

1. evaluate reliability of data

2. statistical analysis of data

3. analyze impact of results on society (economic, moral, and political).

**1.2.2 Performance expectations**

1. Able to propagate the uncertainty on a datum through a series of calculations in order to assess the uncertainty of a derived result.

2. Able to graphically represent data and indicate error bars appropriate to the uncertainty in the data.

3. Able to distinguish between and estimate random and statistical sources of error in a measurement.

4. Able to quantitatively calculate random error in a collection of replicate measurements by calculation of the standard deviation.

### 1.3 Accessing Information

**1.3.1 Skills inventory**

1. computer/library searching

2. using reference books

3. assessing current scientific data over the Internet

4. evaluating reliability of information

**1.3.2 Performance expectations**

1. Use databases and computer networks to access physical information.

2. Use scientific journal citations to locate articles in the physics library.

3. Understand the organization of scientific journals and journal articles and be able to efficiently extract information from individual articles.

### 2 Content Standards

**2.1 Force and Motion in 3 Dimensions**

1. The student is given a first, comprehensive introduction to the concept of units and comparison between Systeme International (SI) units, CGS units and Engineering units (British Imperial). The fundamental dimensions of length (L) mass (M) and time (T) are introduced and discussed. Topics are introduced from first principles. Laws are expressed in vector form. Emphasis is put on phenomenology and the experimental foundation of the theory. Everyday experiences of the laws of mechanics are emphasized. Students should understand where approximations, (such as the small angle approximation in oscillators) and idealizations (such as ignoring air resistance in projectile motion) significantly impact the outcome of the analysis. Description of motion.

1.1. The student can distinguish between displacement and distance traveled. The student can distinguish between average velocity (acceleration), and instantaneous velocity (acceleration and that the difference is in the limit as time tends to zero.

1.2. The student can distinguish between speed, (scalar), and velocity, (vector).

2. Differential- and integral relation among position, velocity and acceleration in 3 dimensions.

2.1. Given the position of a particle as a function of time, the student can derive expressions for velocity and acceleration as functions of time.

2.2. Given the acceleration as a function of time and initial conditions for the velocity and position, the student understands how to derive expressions for position as a function of time and velocity as a function of time.

3. Motion subject to a constant acceleration.

3.1. Given initial velocity and position of a projectile, the student understands how to calculate its position and velocity at all times, the shape of the trajectory, the highest point of the trajectory, the range of the projectile.

4. Transformation between frames moving with constant relative velocity.

4.1. Given knowledge of position and velocity of a particle relative to a given frame, the student can express the position and velocity relative to a second frame moving at constant velocity relative to the first frame.

5. Centripetal force and acceleration.

5.1. Students should understand that circular motion at constant speed is NOT uniform motion

5.2. The student understands how to calculate the acceleration of the moon from its orbital period (or its speed) and its distance from earth.

5.3. Expressed in terms of the initial position and velocity, the student can calculate, as a function of time, the centripetal force on a simple pendulum (in the small angle limit) performing SHM.

6. Newton’s three laws.

6.1. Students should understand that ma, or dp/dt, is not a force, rather it is a response to the forces acting on the net force acting on the object or system.

6.2. The student can design experiments to demonstrate each of Newton’s laws.

6.3. The student can explain the concepts of mass and weight and emphasize their difference.

6.4. The student can draw free body diagrams and use them to calculate the acceleration of a block on an incline subject to multiple constant forces (including friction).

6.5. Motion subject to a constant force (e.g. projectile motion).

7. The effect of static and kinetic friction forces on motion.

7.1. The student can perform a demonstration showing that the coefficient of static friction is greater than the coefficient of kinetic friction.

7.2. The student can design an experiment to determine the coefficient of friction (static or kinetic) for the contact between two surfaces made from known materials.

8. Work due to a variable force.

8.1. The student knows how to calculate the work done by a constant force and by a variable force (for example as a function of position) in 3D.

8.2. Students understand the distinction between conservative and non-conservative forces and work

9. Relationship between work and energy

9.1. The student understands the relationship between the work done by all the forces acting on a particle, and the kinetic energy of the particle.

9.2. Students understand the relationship between potential energy and the work done by a conservative force

10. Newton’s law and gravitation.

10.1. The student can demonstrate in detail why an inverse square law of gravity, together with Newton’s second law and Kepler’s third law accounts well for the motion of the Moon.

10.2. The student understands why Kepler’s second law is not an accident.

10.3. The student can derive Kepler’s third law for a circular orbit from Newton’s laws.

10.4. The student understands how to express the gravitational field from a distribution of point masses.

10.5. The student understands how to express the gravitational potential from a distribution of point masses.

11. Rotational Dynamics: Rotation of a rigid body about a fixed axis.

11.1. Students should understand the simple relationship between the variables used in linear dynamics and those used in rotational dynamics. They should understand that for a rotating body the rotational dynamical variables are independent of radial distance from the rotation axis, whereas the linear dynamical variables are radius dependent.

11.2. The student can distinguish between average angular velocity (acceleration), and instantaneous angular velocity (acceleration).

11.3. The student can distinguish between linear velocity and angular velocity.

11.4. The student can calculate the moment of inertia of a distribution of particles (discrete or continuous) of simple geometry.

11.5. A flywheel of known moment of inertia rotates about a fixed axis and subject to several impressions (forces and torques). The student understands how to calculate angular acceleration, velocity and position of the flywheel in terms of the given impressions.

11.6. The student can calculate as a function of time, the position of a physical pendulum oscillating at small amplitude.

11.7. A person stands on a ladder of known length, which leans on a smooth vertical wall. The student is able to express one of the following quantities in terms of (some of) the others: the mass of the ladder, the angle the ladder makes with horizontal, the mass of the person, the (minimum) coefficient of static friction present between the floor and the ladder, the friction force between the floor and the ladder, the height of the person above the floor.

12. Rotation of a rigid body about an axis of fixed direction through the center of mass.

12.1. The student understands how to calculate torques on a yo-yo, and the acceleration of its center of mass.

12.2. The student can experimentally determine the moment of inertia of simple rotationally symmetric systems (such as a basketball) by rolling them down an incline.

12.3. The Sun is eventually going to collapse and become a white dwarf star of radius similar to that of Earth. The student understands how to calculate the angular velocity of the white dwarf.

12.4. The student can account for why a planet moves faster close to the Sun than farther away.

13. Special relativity. The Lorentz transformation.

13.1. Students understand that simultaneity is relative to the observer.

13.2. The students can demonstrate that the Lorentz transformations account for time dilation and length contraction.

13.3. The student understands how to relate the velocity of a particle in different Lorentz frames.

13.4. The student understands how the Lorentz transformation accounts for the ability of muons, created at the top of the atmosphere, are able to penetrate to the surface of the Earth.

13.5. Students understand the relativistic relation between mass, energy and momentum, and its agreement with Newtonian physics at non-relativistic speeds.

### 2.2 Conservation Laws

Conservation laws are central to understanding the behavior of most physical systems. The student understands how conserved observables determine the state of a system at a later time. Ability to apply the conservation laws is emphasized.

**14. Conservation of energy.**

14.1. The student is able to recognize the conditions under which the mechanical energy of a physical system is conserved.

14.2. The student can demonstrate how to use conservation of energy to set up relationships between physical quantities (such as mass, charge, speed, position, etc.).

14.3. Given the radius of a planetary orbit and the masses of the orbiting bodies, the student can calculate the energy of the planet.

14.4. Students can account for the work done by a thermodynamic engine in terms of the energy input and the waste energy expelled.

**15. Conservation of linear momentum in 3 dimensions.**

15.1. The student understands the different role played by the internal forces and the external forces acting on a system of particles or a rigid body, in determining the motion of the system.

15.2. The student understands the relationship satisfied between the internal forces and the external forces acting on a system of particles or a rigid body, in order that the total momentum of the system be conserved (internal forces cannot change the linear momentum of the system, the sum of the external forces is zero).

15.3. The student understands the relation between the motion of the center of mass of a physical system and the external forces action on it.

**16. Conservation of angular momentum.**

16.1. The student recognizes the relation between the net torque on a system and its angular momentum.

16.2. The students understand how Kepler’s second law is a consequence of angular momentum conservation.

**17. Collisions in one and two dimensions.**

17.1. Students understand the conditions under which the total momentum of a system of particles is conserved.

17.2. Students understand the kinematics of one- and two-dimensional collisions, and how to use momentum conservation to relate initial and final states of the system for the case where external forces are small.

17.3. The student can quantitatively and qualitatively distinguish elastic and inelastic collisions.

17.4. The student understands when both energy and momentum is conserved, and how to use this to relate initial and final states of a two dimensional collision of two particles.

17.5. The student can apply momentum conservation to solve 1D and 2D collision problems.

### 2.3 Potentials and the Potential Energy Function

Many forces in Nature are approximately conservative. Systems subject to conservative forces are conveniently described in terms of a potential energy function. This function provides a powerful simplification in the understanding of energy considerations of the system.

**18. Conservative and non-conservative forces.**

18.1. Students understand the distinction between conservative and non-conservative forces.

18.2. Students understand the relationship between work done by a conservative force and the potential energy.

18.3. Students understand how to derive the force from a potential energy function, and vise versa.

**19. Electrostatic potential. Gravitational potential.**

19.1. Students know how to calculate the potential energy function for elastic forces, and for an inverse square force law.

**20. The field and potential energy associated with an electric dipole.**

20.1. Students understand how to calculate the potential due to an electric dipole.

### 2.4 Vibrations and Harmonic Oscillations

**21. Simple Harmonic Motion **(solution from substitution in the second order linear homogeneous differential equation resulting from a force analysis).

21.1. Students should understand the concept of a restoring force.

21.2. The student can relate acceleration, displacement (angular or linear) and frequency for an object performing SHM.

21.3. The student can analyze several examples of oscillators, such as a simple pendulum, physical pendulum, torsion pendulum, orbital motion, spring oscillator, and the conditions under which they execute Simple Harmonic Motion.

**22. Damped, driven, oscillations **(solution of the inhomogeneous D.E.).

22.1. The student understands that the amplitude of a driven damped oscillator varies with the driving frequency.

22.2. The student understands that for a lightly damped system, amplitude occurs close to the natural frequency of the oscillator.

**23. Energy levels of the harmonic oscillator.**

### 2.5 Waves

**24. Mechanical waves, electromagnetic waves, matter waves. **Students understand that electromagnetic wave are self propagating and mechanical waves require a propagation medium. Students understand the concept of coherence.

24.1. The student can distinguish between transmission of energy by a traveling wave, and by matter.

24.2. The student knows how to relate the velocity, angular frequency, and the wave number of a wave

24.3. The student can calculate the velocity of a wave on a string of a known substance, held in tension by a known weight.

24.4. The student can calculate the power transmission of a sinusoidal wave along a string.

24.5. The student recognizes the difference between longitudinal and transverse waves and knows that electromagnetic waves are transverse, while mechanical waves can be either.

**25. Refraction, reflection, interference and diffraction of waves.**

25.1. Students can calculate angles of reflection and refraction of a lightwave encounters the surface between two media.

25.2. Students understand that light may be elliptically polarized, partially polarized, or it may beunpolarized.

25.3. Students understand how a rainbow forms.

25.4. Students can explain how an optical fiber works.

25.5. Students understand image formation in spherical refractors or reflectors.

25.6. Students understand how to use a grating to analyze the wavelength composition of light

25.7. Students understand how to use X-ray diffraction to derive information about the structure of a crystal.

25.8. Students understand and can predict the spacing of interference fringes for the double slit experiment.

25.9. Students understand and can predict the spacing of interference fringes due to reflection from thin films, accounting for any phase changes at boundaries between media of differing refractive index.

**26. Doppler effect.**

26.1. Students understand that the frequency of a wave, perceived by an observer, changes if the observer is in relative motion with respect to the source (relativistic, non-relativistic).

### 2.6 Heat and Thermodynamics

Students are introduced to concepts of heat and temperature. The universality of the temperature concept is stressed. Laws of heat transfer, heat conduction, heat capacity, latent heat, and calorimetry is discussed from heuristic principles. Kinetic gas theory is introduced from first principles. The first two laws of thermodynamics are discussed in detail. Emphasis is laid on the graphical representation of thermodynamical processes in PV-diagrams. Reversible engines and their efficiency are discussed. The Carnot engine is discussed in detail. The concept of entropy is introduced and discussed in the context of thermodynamic processes.

**27. Heat transfer, heat conduction and absorption.**

27.1. Students can calculate the heat that must be added to a given amount of a given substance in order to transform it from the solid phase to the gaseous phase.

27.2. Students can calculate the rate at which heat is lost through the walls of a house when the internal and external temperatures are constant.

27.3. Students understand the three ways of heat transfer and the physical conditions present for each of these to dominate.

**28. First law of thermodynamics.**

28.1. Students understand how the first law of thermodynamics extends the principle of energy conservation.

28.2. Students understand that heat added to a thermodynamic system will change the internal energy of the system, or result in work done by the system on the environment, or both.

28.3. Students understand how to calculate the work done by a thermodynamic system for several common processes including the isobaric, isochoric, adiabatic and isothermal process.

**29. Entropy and second law of thermodynamics.**

29.1. Students can account for the efficiency of a Carnot engine and a Stirling engine. Students understand how a refrigerator functions.

29.2. Students understand that if heat is added at constant temperature to a thermodynamic system, the entropy of the system will increase.

29.3. Students can distinguish the free expansion of a gas from the isothermal expansion, and account for the change in the entropy of the universe in each of these two processes.

**30. Kinetic theory of gases.**

30.1. Students understand how kinetic gas theory provides for an equivalent definition of temperature expressed in terms of molecular speeds.

30.2. Students are familiar with the ideal gas approximation, its range of validity, and how to use it to obtain accurate predictions for the specific heat capacities for mono- and diatomic gases.

### 2.7 Material Properties

31. Students know how common material properties such as coefficients of friction, mass density, elastic moduli, thermal expansion coefficients, specific heat, electric conductivity, etc., are defined.

32. Elastic properties of matter (e.g. Young modulus, shear modulus).

32.1. Students understand that different materials respond to stresses in different ways.

33. Thermal properties of matter (e.g. thermal expansion, specific heat).

33.1. Given a block of a material, a ruler of a different material, and their coefficients of linear expansion, the student knows how to calculate the percent change in length of the block, measured by the ruler, as the temperature is changed by a given amount.

34. Electrical and magnetic properties of matter (e.g. conductance, dielectric properties).

34.1. Students have a qualitative as well as a quantitative understanding that the capacitance of a capacitor changes if the space between the plates is filled with a material.

34.2. Students know how to how to use Gauss law in a dielectric to calculate the electric field between the plates of a capacitor filled with a dielectric.

34.3. Students know different materials exhibit different magnetic properties, and how these properties affect the different behavior of materials in a magnetic field.

34.4. Students know how properties of magnetization is quantitatively determined by the coefficient of magnetic permeability.

34.5. Students understand how an atomic dipole moment can explain dielectric properties of matter, and how a magnetic dipole moment can explain magnetic properties of matter.

35. Properties of fluids (Pascal’s law, Archimedes’ law, Bernoulli’s law).

35.1. Students understand how to calculate the pressure at different levels in a fluid.

35.2. Students have a quantitative understanding how a submarine can lower or increase its depth in the water.

35.3. Students can explain the motion of a curve ball, and the lift on an airplane wing.

### 2.8 Electricity and Magnetism

The student is given a first, comprehensive introduction to phenomena of Electricity and Magnetism.Topics are introduced from first principles. Laws are expressed in vector form. Emphasis is put on phenomenology and the experimental foundation of the theory. Maxwell’s equations are introduced in their integral form using vector calculus. The role played by the laws of electricity and magnetism in the design

and function of devices used today is emphasized.

36. The electric field. Students should understand the vector nature of the electric field. They should also appreciate the facility of calculating the electric field using the (scalar) electric potential.

36.1. Students recognize the similar nature of electric field vector, **E** and potential, and gravitational field vector, **g**, and potential.

36.2. The students can calculate the electric field/potential due to a symmetric line, surface, or volume charge distributions such as a charged disk, rod, circular line segment, or around a spherical or cylindrical charge distribution by integrating over the charge distribution.

36.3. Students understand how to use Gauss’ law to calculate the electric field for highly symmetric charge distributions, such charge on the plates of a parallel plate capacitor, or a spherical or cylindrical capacitor.

36.4. The students can calculate the electric field/potential around a system of point charges.

37. The magnetic field around a symmetric current distribution.

37.1. Students understand how to calculate the magnetic field along a symmetry axis, due to a symmetric current distribution.

37.2. Students know how to use the force due to a magnetic field on a current carrying wire to calculate the torque on a current loop.

37.3. Students understand how to use the Biot-Savart or Ampere’s law to calculate the magnetic field due to simple, symmetric current loops, including circular and linear segments.

38. The electric field and potential energy associated with an electric dipole.

38.1. Students understand how to calculate the field and potential due to an electric dipole.

39. The relation between electricity and magnetism. Faraday’s law. Students understand the concept of magnetic flux.

39.1. Students understand how to calculate the induced emf from a simple current loop moved through a uniform magnetic field.

39.2. Students can calculate the emf produced in a current loop by a variable magnetic field.

39.3. Students understand that changing the current through a coil induces an emf in the coil.

39.4. Students know that given two coils, the emf induced in either coil is proportional to the rate at which the current changes in the other.

40. DC- and AC circuits. RLC circuits (e.g. capacitive- and inductive reactance, resonance). Students should understand the analogy between driven damped mechanical oscillators and RLC circuits.

40.1. Students understand how to apply Kirchhoff’s laws to a multi-loop circuit to calculate the current or the emf in the circuit.

40.2. Students understand the different effects on the amplitude and phase of voltage and current that various circuit components (e.g. resistors, capacitors, inductors) have in AC or DC circuits with a sinusoidal emf.

40.3. Students understand how to calculate amplitude and phase of voltage and current through an RCL circuit.

40.4. Students are able to set up a differential equation fr a RC circuit to and use it to explain how charge accumulates on the capacitor.

40.5. Students can explain predict? the Voltage-time, current-time curves in an RL circuit after the emf has been connected.

41. Electromagnetic Waves.

41.1. Students can solve Maxwell’s equations for a plane wave to obtain expressions for the electric and magnetic fields in a propagating wave.

41.2. Students understand that electromagnetic waves carry energy, and know how to calculate the intensity and radiation pressure of the wave.

### 2.9 Quantum Mechanics

Students are introduced to the dual description of matter as particles and waves. The Scrödinger equation and its solutions are discussed for the simplest systems. Barrier penetration and trapping is discussed, applications in technology are emphasized. Quantum numbers of atoms are defined, shell structure and the

periodic system is discussed in this context. A quantum description of the solid state is provided, which accounts for the conduction properties of metals semi-conductors and insulators. Applications in electronics are emphasized. Nuclear structure and models: topics include classification of nuclides, nuclidic charts,

binding energy and energy in nuclear reactions, models for radioactive decay, nuclear fission and fusion. Nuclear reactors. Radiation. A non-mathematical presentation of the classification scheme for elementary particles. Conservation laws in elementary particle physics. The early universe.

42. Photons and matter: Students should know the significance of blackbody radiation to the development of quantum mechanics

42.1. Students are able to use the blackbody spectrum to derive the surface temperature of the Sun.

42.2. Students understand how the Photoelectric effect or double slit experiments confirm that light can be interpreted as particles.

42.3. Students understand that matter can be thought of as a wave whose, and that the wave (wavefunction) is determined by a wave equation. The absolute square of the wavefunction has an interpretation as a probability density.

42.4. The student can construct and interpret the wave function for a free particle.

42.5. Students understand how to use the wavefunction and Schroedinger’s equation to account for the tunneling of a particle through a barrier.

42.6. The student understands that some physical variables such as position and momentum of a particle cannot be determined simultaneously without the introduction of an inherent uncertainty.

43. Idealized models (e.g. free particle, particle in a box, harmonic oscillator).

43.1. Students understand how to derive the energy levels and state wavefunctions for simple quantum systems such as the free particle, a particle in a box, and the harmonic oscillator.

44. Atomic structure. (e.g. Bohr model. Electron shell structure. Pauli principle).

44.1. The student is able to interpret the quantum numbers of the hydrogen atom.

44.2. Students can account for the radial and angular probability density distributions of the hydrogen atom in terms of the values of the principal and orbital quantum number, for states with principal quantum number equal to 1 or 2.

44.3. Students understand the implications of the Pauli exclusion principle on the filling of atomic shells.

44.4. Students can explain the shell structure of an atom in terms of the atomic quantum numbers.

45. Atomic orbital and spin angular momenta and electron spin.

45.1. Students recognize the relation between the magnetic dipole moment of an atom, and its angular momentum quantum number.

45.2. Students understand the experimental evidence for the spin of the electron.

45.3. Students can explain the behavior of an atom in an external magnetic field.

45.4. Students understand the basic atomic physics of how laser light is produced.

45.5. Students understand the arrangement of atoms in the periodic table.

46. Condensed matter. Semi-conductors and the transistor.

46.1. Students understand how to use the band-gap structure of solids to explain the difference between conductors, semiconductors, and insulators.

46.2. The student can account for the n-type and p-type semiconductors, and the function of the transistor.

47. Nuclear decay. Models of the nucleus.

47.1. Students can explain why the repulsive forces of the protons in the atomic nucleus do not blow itapart, and they can account for the stability of the nucleus.

47.2. The student can provide a statistical account of radioactive decay.

48. Nuclear energy: fission and fusion.

48.1. Students can account quantitatively for how energy is gained in fission and fusion processes.

49. The quark model

49.1. Students understand that particles are arranged in a classification scheme consisting of leptonsand hadrons according to their interaction.

49.2. Students understand that quarks bind, subject to certain constraints, to form baryons and mesons.

49.3. Students understand the implication of the conservation laws of baryon number, lepton number, and strangeness on particle interactions, particle decays, etc.

49.4. Students recognize interaction of the fundamental particles through three of the four forces of Nature.

49.5. Students are able to give a simple account of the thermal history of the universe, and its matter content.