Request for Interdepartmental input in Introductory Physics Program
Dear Colleague:
Attached is a list of items that we either currently cover, or could cover in our introductory Physics 121-122 sequence. There is never enough time to cover all the topics we wish to cover, and we are always considering what items could be dropped and which others added. We would like you opinion on whether any entire areas could be dropped, or whether any sub-topics within areas could be omitted (for the majors in your department). We would also like to know what topics we should cover that are not listed here, or any topics that ARE listed here that you think stand out in importance.
Items in normal type are covered, and we expect to continue to cover them. Items in bold italic are not currently covered, but have been in the past or could be easily added (with other cuts).
Note also that the depth and breadth of material we can cover is dependent on the quality of our students AND on how many of them we are willing to fail at least once. We would very much appreciate your input on how much pampering you wish us to do of your students. If you tell us you want an extremely rigorous program, we would gladly filter out those with weaker backgrounds or less agile minds.. There is the related problem of losing otherwise good students who have had poor or non-existent high-school physics. In our opinion, our introductory physics sequence IS INAPPROPRIATE for students without a good high-school physics course under their belt. We do not yet have a good solution to this problem.
LIST A: CURRICULUM TOPICS – Phys 121
Units & Vectors
SI Units
Metric Prefixes from ()
Vector Addition and Subtraction
Dot Product
Cross Product
1-D and 3-D Motion
Constant Accelerated Motion
Acceleration of gravity
Falling objects
Acceleration of vehicles
Relative reference frames
Motion for non-constant acceleration
Circular & Projectile motions
Centripetal Acceleration
Range and Trajectory of projectiles without air-resistance
Corrections for Air-resistance
Motion and Force
Acceleration of single body system
Static and Dynamic Friction
Normal forces and Tension
Effective weight in an elevator
Applying Newton’s Laws
Free-body diagrams (and drawing them properly!)
Ramps / Pulleys / Cables
Acceleration of multi-body systems
Force couples
Pushing motion / Pulling motion
When will a block slip off an accelerating table?
Equilibrium (Statics) of simple point mass systems
Work and Kinetic Energy
Work / KE Theorem
Definition of work
For constant vector forces
For varying scalar forces
For varying vector forces
Calculating Work done by non-conservative forces
Calculating average collision force for collision occurring over known distance.
Introduction to springs (what is means for force to be proportional to length change and not length)
Potential Energy and Power
Conservative and Nonconservative Forces
Law of Energy Conservation
Deriving Potentials for gravity and for springs
Ramp problems by energy methods
Accounting for work lost to friction
Definition of instantaneous and average power
Basic calculations in units like kWh
Mom. Cons. & Collisions
Concept and definition of center of mass
Vector calculation of center of mass for a multi-point mass system
Definition of Impulse and calculation of average collision force.
Conservation of center of mass momentum
Internal forces and momentum conservation
Center of mass stays at rest if it begins at rest and only internal forces are present.
Inelastic collisions
Elastic collisions
General formula for 1-D elastic collisions between two bodies of arbitrary mass, one of which is initially at rest.
General formula for 1-D elastic collisions between two bodies of arbitrary mass and velocity
Rotation and constant angular acceleration
Analog between linear 1-D motion and rotational motion
Vector definitions of angular velocity and acceleration
Relation between angular velocity and acceleration and linear velocity/acceleration.
Definition and derivation of moment of inertia.
Moment of inertia of regular solids
Parallel axis theorem
Rotation, Torque and Angular Momentum
Definition of Rolling
Velocities of objects rolling down ramps
Partition of Energy between CM motion and rotation.
Torque as a cross product
Concept of moment arm
Newton’s 2nd law for rotation
Precession and Nutation (covered in lab only)
Statics
Statics of extended multibody systems that includes force and torque equilibrium
Definition of Young’s Modulus of Elasticity
Definition of Stress and Strain and Applications of Young’s modulus to same
Gravitation and Orbital Mechanics
Newton’s Law of Universal Gravitation
Cavendish Experiment
Vector calculation of Gravitational force for a collection of point masses
Proof that spherical mass distributions may be treated as point masses.
Kepler’s three laws of planetary motion
Derivation of Kepler’s third law for the case of circular motion
Derivation of Kepler’s second law from angular momentum conservation
Central forces exert zero torque.
Derivation of Kepler’s third law for the case of elliptical motion
Categorization of types of orbit by eccentricity or by total energy and momentum
Derivation of Gravitational potential energy
Calculation of Escape Velocities
Calculation of Schwarzchild radius (black holes)
Special Relativity
Michelson-Morley Experiment
Time Dilation
Length Contraction
Lorentz Transformation
Minkowski Space
Four-Vector invariance
Space-time interval
Doppler Effect
Relativistic velocity addition formulae
Relativistic momentum
Relativistic Kinetic and Total Energies
Relativistic Forces and Accelerations.
Nuclear energy and particle physics
The “electron volt” and the Joule.
General Relativity
Curvature of light in a gravitational field
Einstein Lensing
Temperature and Kinetic Theory of Gases
Definition of temperature as internal kinetic Energy
Direction of heat flow (thermal equilibrium)
Types of thermometers
Heat of Vaporization / Heat of Fusion
Heat transfer
Conduction
Convection
Radiation
Stefan Boltzman Law
Wien’s Law
Black body radiation
Emissivity
Kinetic Theory of Gases
Deriving ideal gas law from basic kinetic principles
Corrections to ideal gas law.
for monatomic gas.
Definition of heat capacity
R and k
Deriving molar heat capacities from basic kinetic principles
Equipartition of Energy
Law of Dulong and Petit for heat capacities of solids.
Thermodynamics
Vocabulary (isotherms, adiabats, equations of state, critical points)
First Law
Calculating net work/cycle from p-V diagram
Calculating work done in isothermal expansion by integration
= Constant (adiabatic expansion)
pV= Constant (isothermal expansion)
Deriving from first principle calculations of
Entropy
Definition as dQ/T
Carnot Cycle
Carnot efficiency
Stirling Cycle engines
Second law of thermodynamics.
Understanding in terms of statistical probabilities
LIST B: TECHNICAL LITERACY TOPICS
A)Mathematics
- Vectors
- Magnitude and Direction from Components (and vice versa)
- Graphical method for Addition and Subtraction of Vectors
- Addition and Subtraction of Vectors by components
- Vector Dot Product
- Vector Cross Product
- Trigonometry
- Definitions of sin/cos/tan committed to memory
- Definition of radian measure and the relationship
- Pythagorean theorem in 3-dimensions
- Surface area, volume and circumference for Spheres and Circles
- Algebra
- Solutions of systems of equations
- Multiplying whole equations by constants, getting common denominators of algebraic expressions etc.
- Calculus
- How to take a derivative
- Chain rule
- Product Rule
- Integration by Parts
- Integration by Substitution
- Interpretation of integrals as area under a curve
- Line integrals
- Gradients
- Gradient as direction of steepest descent
- Gradient as inverse of line integral
- Approximations to complex functions for small arguments
- Use of Taylor / McLaurin series to expand f(x) about f(0)
- Statement of Binomial theorem
- Use of binomial theorem to approximate f(x) about f(0)
- Binomial theorem
B)Problem Solving
- Physical units
- Using formulae like F=ma to guide conversions
- (e.g. 1 N = 1 kg m/s*s)
- Memorizing important English to metric conversion factors and important physical constants, # of seconds in a day, # of feet in a mile, speed of light, speed of sound
- Understanding how to convert
- Proper use of calculators
- The degree/radian trap in arcsin
- The “wrong quadrant” trap in arctan
- How to handle problems that are beyond the limit of calculator precision (e.g. subtracting two large quantities that differ by a small quantity).
- Maintaining 4-significant figure precision throughout a long calculation. (How to prevent accumulation of rounding errors).
- The sketch
- Sketches should be 3”x3” and labeled
- Sketches should capture the essence of the problem, or at least the relationships in space or time between the important parts of the problem
- Sketches may be used to translate a word problem into a picture to aid the solution process.
- The “ISEE” method (Identify / Set-up / Execute / Evaluate)
- Identify – Draw a properly labeled diagram, identify known and unknown variables, characterize the overall type of problem in terms of what approaches or formulae may yield success.
- Set-up – Break vector equations into component equations, specialize general equations to the problem at hand (drop zero factors).
- Execute – Crunch the equations, do not plug actual #s in until have full algebraic solution.
- Evaluate –
- Checking of units.
- Units matching on left and right of = sign.
- Noting if you end up with funny units like or .
- Looking for alternate methods of solution.
- Adding vectors graphically to check that the algebraic method didn’t give a wildly erroneous result.
- Comparing magnitudes with rule of thumb magnitudes to check validity.
- Checking calculator work by estimation with pencil and paper.
C)The Scientific Method
- History and Philosophy of Science
- Thomas Kuhn and the structure of scientific revolutions
- From Aristotle to Newton
- From Newton to Einstein
- The Correspondence Principle
- BS Detection in life and technical careers (importance of the “back of the envelope” calculation)
- Perpetual Motion
- Experimental Method
- How to write a lab report
- Using Common laboratory instruments
- The multimeter
- The oscilloscope
- The photogate and timer
- Calipers
- Acoustic, optical and force transducers
- Error Analysis
- Reporting data with error bars
- Discussing sources of error realistically
- Propagating errors through different types of calculations