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Science One Physics

After taking this course, students should be able to:

• identify the important physical quantities that are relevant in understanding or making predictions about any physical system.
• describe the basic physical principles or laws that govern how these physical quantities change with time (or explain why these quantities exist in a certain equilibrium configuration).
• use these principles and laws to make qualitative and quantitative predictions about what will happen to a system in the future. 
• make use of computational resources to numerically solve problems that are not possible or feasible to solve by hand.

• explain the experimental and theoretical basis for believing certain "facts" about the natural world (e.g. that matter is made of atoms or light is made of photons)
• evaluate whether various claims are consistent with the laws of physics.
• argue that physics goes beyond a collection of empirical laws, and involves a deeper conceptual framework that is inferred from experiment but is not at all obvious from our everyday experience.
• better understand articles on current research in physics and answer questions about physics from curious friends and relatives.
• see value in achieving a deeper understanding physics.

Topic Specific Goals:

• Represent the motion of an object using a motion diagram, a position versus time graph, a velocity versus time graph, or an acceleration versus time graph. 
• Qualitatively describe the motion of an object given one of these representations of its motion.
• Translate between graphs of position versus time, velocity versus time, and acceleration versus time  
• Provide a mathematical description of an object's motion by introducing a set of coordinates and giving the position as a function of time, (x(t),y(t),z(t)).
• Identify the magnitude and direction of position, velocity, and acceleration for a moving object at a particular time given some description of its motion.
• Explain the difference between average and instantaneous velocity
• Calculate average or instantaneous velocity and acceleration numerically using position vs time data

• Calculate the momentum of a moving solid object or the total momentum of a collection of objects, adding vector components where necessary
• Explain how mass can be defined without gravity
• Explain what is meant by "conservation of momentum"
• Explain how momentum conservation leads to Newton's first law
• Explain how momentum conservation may be used to predict the location of an isolated object at a future time given its position and velocity at some initial time
• Evaluate whether a hypothetical collision process conserves momentum
• Use momentum conservation to deduce initial or final velocites of objects in collisions problems in one, two or three dimensions.
• Explain how momentum conservation can be used to argue that the change in momentum will be the same for any two objects under the same external influence.
• Describe the relationship between Force and change in momentum (impulse)
• Qualitatively describe the force vs time and momentum change vs time for some simple interactions (e.g. throwing a ball)
• Explain how momentum conservation leads to Newton's Third Law
• To evaluate which components of momentum are conserved in a particular situation

• To identify the forces acting on an object in various simple situations, to identify the magnitudes of these forces and draw a force diagram showing the directions of these forces (if they are from gravity, a spring, the normal force, friction, air drag, a rope).
• To write the different component equations (for the x, y and z directions for some choice of coordinate axes) coming from Newton's second law for an object acted on by known forces.
• To explain why Newton's second law can be used to determine position and velocity of an object at future times given the initial position and velocity.
• To use equations of motion derived from Newton's second law to determine the approximate location of an object at a slightly later time given its position and velocity at the present time.
• To determine whether a given vector function of time is the correct solution of given equations of motion with a specified initial position and velocity, or to use initial conditions to decide which of a family of possible solutions is the correct one.
• To find the future positions and/or velocities of an object given the initial position and velocity when the forces are constant or specific functions of time.

• Explain what is meant by "conservation of energy"
• Calculate the kinetic energy of a moving object or collection of objects (slow compared to the speed of light) 
• Calculate the potential energy of an object in a uniform gravitational field, or of a stretched or compressed spring (solid)
• Describe the relation between thermal energy and kinetic energy
• Compare the potential energy of two configurations to decide which is higher
• To evaluate whether mechanical energy is conserved in specific scenarios
• To use conservation of mechanical energy to determine final velocities or configurations in situations where it applies
• To use conservation of energy together with conservation of momentum to determine final velocities of objects in elastic collisions in terms of their initial velocities.

• Describe qualitiatively the types of energy transfer occurring in various physical processes
• Calculate the energy expended in a certain process given the applied force at each location (whether the force is parallel to the displacement or in a different direction).
• Calculate the force on an object due to a spatially varying potential energy
• Identify the equilibrium position of an object given its potential energy as a function of position

RELATIVITY

Newton’s Laws and Relativity

• explain what is meant by the principle of relativity
• explain what is meant by a “frame of reference” and an “inertial frame”
• give examples of how relativity manifests itself in ordinary situations
• explain why the equivalence of physical laws in different frames implies that it is impossible to set up an experiment to measure an absolute velocity

Length contraction, time dilation, and the relativity of simultaneity

• state Einstein’s principle relativity 
• explain why Einstein's principle implies that all observers should measure the same speed for any light or electromagnetic radiation
  
• explain how a given observer can set up a coordinate system for making measurements of time and position
• be able to describe what is meant by an event
  
• give simple examples to show how Einstein's principle of relativity imply that observers at large relative velocities will not agree on distances, time intervals or whether two events are simultaneous
• describe qualitatively the meaning of length contraction, time dilation, and the relativity of simultenaity
• correctly calculate the lengths and times differences that an observer will measure, properly accounting for length contraction and/or time dilation.
• analyze basic scenarios involving large velocities to calculate times and distances for various events, or physically relevant time/distance intervals. Know when basic length contraction and time dilation formulae are applicable.
  
• be able to calculate relativistic effects in cases when velocities are much smaller than the speed of light, using Taylor (binomial) approximations to the exact formulae

Relativistic Energy and Momentum

• argue why classical formulae for momentum and energy must be modified
• state the relativistic formulae for energy and momentum
• explain the precise meaning of conservation of energy and conservation of momentum
  
• analyze high-energy particle decay processes or collision processes using energy and momentum conservation
• provide a definition for mass in terms of energy, and apply this to make predictions about the masses of stable and unstable bound states relative to the masses of their constituents
• determine the mass of an object given its energy and momentum
  
• explain why the conservation of mass can be violated in relativistic dynamics
  
• give evidence for and explain basic implications of the equivalence between energy and mass

• Determine the center of mass of an object in various simple cases (e.g. when the object is a combination of parts with equal )
• Explain how the center of mass of an object will move given the forces on the object.

• Explain what is meant by angular position, angular velocity, and angular acceleration and describe the relation between these.
• Calculate angular velocity and/or acceleration given the angular position as a function of time.
• Calculate angular position as a function of time given the angular acceleration as a function of time and initial angular position and angular velocity.
• Qualitatively describe the rotational motion of an object given a description of its angular velocity and/or angular acceleration as a function of time.
• Translate between graphs of angular position versus time, angular velocity versus time, and angular acceleration versus time.
• Calculate the velocity of some point on an object rotating around an axis given the angular velocity.
• Determine how the linear motion of an object is related to the rotational motion of another object to which it is connected (e.g. by a rope wound around the rotating object)

• Calculate the angular momentum of an object rotation around a fixed axis
• Calculate the angular momentum of a freely moving object around a certain axis (e.g. a planet in orbit). 
• Explain qualitatively how one can tell which of two objects has a higher moment of inertia
• Explain how one could determine the relative moment of inertia of two objects (by a direct experiment)
• Explain what is meant by "conservation of angular momentum"
• Use angular momentum conservation to determine the final angular speed of a rotating object that undergoes a change in its moment of inertia.
• Use angular momentum conservation to deduce the final rotational velocity of an object formed from an inelastic collision of two objects.
• To evaluate whether angular momentum is conserved in a given situation

• To calculate the net torque on an object in various simple situations, given the forces acting on the object (or given enough information to determine these forces)
• To determine the angular acceleration of an object given the net torque 
• To find the future angular positions and/or velocities of an object given the initial position and velocity when the torques are constant or specific functions of time.

• Calculate the rotational kinetic energy of an object rotating about a fixed axis
• To use conservation of mechanical energy to determine final angular velocities or angular positions in situations where it applies

• Determine the acceleration of an objcet in uniform circular motion given any two of the period, angular velocity, radius, or velocity
• Determine velocity, period, angular velocity, or radius given any two of the other quantities.
• To use conservation of mechanical energy to determine final angular velocities or angular positions in situations where it applies
• Determine the properties of a circular orbit given the mass of the central object, using Newton's Law of Gravity.

• Explain how macroscopic properties of a gas are related to averaged microscopic properties (i.e. properties of the molecules)
• Define pressure, number density
• Calculate forces caused by a gas of uniform pressure
• Give a microscopic explanation of why a gas exerts a force on its container walls
• To describe what properties of the underlying gas molucules affect gas pressure and the quantitative effect on the pressure of changing each of these properties while holding the others fixed
• To describe what properties of the underlying gas molucules affect gas temperature and the quantitative effect on the pressure of changing each of these properties while holding the others fixed
• To use the relation between temperature and average translational kinetic energy to make a prediction for the temperature change during the free expansion of an ideal gas, or the free expansion of a gas with attractive forces between the molecules

• To state the ideal gas law, explain its microscopic origins, and use it to analyze various simple processes.
• To decide whether a certain process is isothermal, isochoric, isobaric or adiabatic (or none of these)
• For one of these types of processes, to state which combinations of P,V,T remain constant.
• To determine the change in P,V, or T given the change in one of the other quantities for isothermal, isochoric, isobaric or adiabatic processes.
• To sketch various types of processes on a PV diagram

• To describe the different contributions to the energy of a gas
• To explain what is meant by the molar specific heat of a gas and describe how this could be measured
• To explain why the molar specific heat is smaller for monatomic gases than gases with more complicated molecules
• To define and describe the differences between  heat, work, and energy in a gas
• To calculate the work done on a gas  given the pressure as a function of volume for a process (e.g. given a sketch of a process on a PV diagram)

• To calculate the work done on the gas (W),  heat added to the gas (Q), or change in internal energy of a gas in isothermal, isochoric, isobaric, or adiabatic processes, using the First Law of Thermodynamics and the ideal gas law. 
• To calculate the amount of heat that must be added to produce a certain amount of net work for a given thermodynamic cycle

• To state the Second Law of Thermodynamics and explain why it is fundamentally different from other laws of physics that we have learned about
• To explain why heat always flows from hotter to colder objects
• To explain the microscopic definition of entropy
• To evaluate two macroscopic configurations of a system and determine which has higher entropy

Static Electricity
• explain the difference between an insulator and a conductor.
• using the concept of polarization, explain why a charged object will attract to a neutral one.
• use Coulomb's law and superposition to calculate the force between multiple charges.
• explain why the leaves on an electroscope separate.
• explain how to charge an object using either friction, conduction, or induction.
• given a description of events, predict whether two objects with attract or repel (think tape, or balloons on walls.)

The Electric field Model and the Various Potentials
• use superposition to calculate the elctric field and potential of configurations involving many charges.
• describe the interactions in a system of charges using each of the 4 standard descriptions: forces, electric fields, potential energy, or electric potential.
• given one of the above, determine the charge configuration responsible for it.
• translate between electric field, electric potentials, forces, and potential energy descriptions of systems.
• state the difference between potential energy, electric potential, force, and electric field.
• plot the electric field, potential, or potential energy as a function of distance for various charge configurations.
• draw force and electric field vectors with appropriate lengths.


• given a charge configuration, draw equipotential lines at equal volatage intervals.
• given the potential of a system, find the electric field.
• use the symmetries of a charge confuguration to guess what the electric field might look like.


• determine the accleration of a charged object in an electric field.
• use the force on charges in electric fields to describe why charges arrangethemselves such that the electric field in a conductor is zero.
• predict the motion of a charge in an electric field.
• determine the kinetic energy of a particle a various points in a potential.
• determine the of a charged particle in a potential.

Electric Dipoles
• explain what the polarization vector of a dipole is and how to increase and decrease the strength of a dipole.
• describe how a dipole will move (both rotations and translations) in both uniform and non-uniform electric field (i.e. next to a point charge).
• calculate the force between a permenant dipole and an ion, two permenant dipoles, or a permenant dipole and an indiced dipole.
• explain how a dipole can be induced in an electric field.

Gauss's law
• given a charge distrubution, determine the flux through an arbitrary closed surface.
• calculate the flux through a surface.
• state Gauss's law in words and justify its meaning using the water analogy.
• use Gauss's law to determine the electric field made by complex (though symmetric) charge configurations.
• use Gauss's law to explain why all the charge inside a conductor rests on the surface.
• explain why only charges inside a closed surface contribute to the flux through close surface.
• explain how Gauss's law contains all of electrostatics, and thus makes it into the pantheon of Maxwell's Equations.

Current
• descibe current microscopically using the Plinko model of conduction.
• descibe conductivity in terms of the microscopic quantities that make it up.
• use the current to predict the electric field strength in a conductor.
• use the electric field to predict the current and drift velocity of electrons.
• given the necessary information, calucate the drift velocity.
• predict how the current will change when microscopic properties are changed.

Resistance
• describe what resistivity is, and how it is related to conductivity.
• describe what resistance is.
• predict how a resistance will change if the geometry of the resistor changes.
• find the equivalent resistance of two or more resistors in series or parallel.

Capacitance
• explain why capacitance only depends of the physical geometry of the capacitor.
• predict the behaviour of a capacitor when the geometry is changed (both connected to a voltage source, or charged and disconnected)
• determine the electric field inside a capacitor
• given the necessary information (i.e., dimension of hte capacitor) calculate the capacitance.
• find the equivalent capacitance of two or more capacitors in parallel or in sersies.

Circuit Analysis
• Use kirchoff's loop law to analyze a circuit.
• Determine the voltage difference between two points in a circuit.
• Find the current running through a component of a circuit.


• Determine the amount of current in an RC circuit, or the amount of charge on a capacitor, a given amount of time after a switch is flipped.
• Calculate the time constant of an RC curcuit.
• Predict the voltage across the capacitor or resistor in an RC circuit the moment after a switch is flipped.
• Predict the voltage across the capacitor or resistor in an RC circuit very long after a switch is flipped.
• Describe the current through a capacitor the instant it starts to charge.
• Describe the current through a capacitor when it's fully charged.
• Plot the voltage across a component as a capacitor is dischraging.

• To descibe bassic magnetic phenomena (e.g. what will be the forces between magnets in various orientations or the torque on a magnet in some orientation near another magnet)
• To argue that the interactions between magnets is like the interaction between electric dipoles
• To describe an experiment that would show that magentic forces are not the same thing as electric forces (e.g. that magnets are not actually just permanent electric dipoles)
• To explain how we can define the direction and strength of a magnetic field using a test magnet.
• To qualitatively describe the magnetic field at various locations around a magnet or around the Earth. 

• To qualitatively describe the magnetic field near a moving charge, and various configurations of current-carrying wire (long straight wire, loop, solenoid)
• To give the orientation of a magnet or the direction of the current in a wire given the magnetic field produced.
• To determine the cross product of two vectors
• To determine the direction and magnitude of the magnetic field at any location near a moving charge or current-carrying wire, inside a solenoid, or in the center of a loop of current-carrying wire
• To use the principle of superposition to find the magnetic field at a point due to a collection of moving charges/currents/etc...

• To explain the origin of magnetic field in permanent magnets
• To explain why a permanent magnet will attract certain metal objects

• To calculate the magnitude and direction of the fore on a moving charge in a magnetic field
• To describe the trajectory of a charge that is initially moving perpendicular to a uniform magnetic field
• To describe the trajectory of a charge that is initially moving at some angle to a uniform magnetic field
• To determine the magnitude and direction of the force on a current-carrying wire
• To determine the torque on a loop of current-carrying wire in a constant magnetic field
• To determine the direction/magnitude of the force on a moving charge near a specified configuration of current-carrying wire
• To qualitatively describe the forces between current-carrying wires or magnets and current-carrying wires (for straight wires, loops, etc...)

• To explain how the strength of a magnet can be quantified (or describe an experiment to determine the relative strength of two magnets)
• To determine the torque on a magnet in a uniform field given its magnetic moment.
• To describe a simple design for an electric motor and explain how/why it works

• To explain why the flux of the magnetic field through any closed surface is zero
• To calculate the line integral of a magnetic field in simple cases (e.g. straight line path through constant magnetic field, paths where magnetic field is everywhere parallel or perpendicular to path)
• To verify that Ampere's Law is satisfied in simple cases (circular loop around a current-carrying wire, rectangular loop through a solenoid) or explain how Ampere's Law could be used to determine the strength of a magnetic field for a long straight wire or solenoid.

•  Regognize situations in which current will be induce due to a changing magnetic flux
• Predict the direction of induced currents using Lenz's law

Motional Electromotive Force (emf)
• Describe qualitatively and quantitatively (using the Lorentz force law) why a motional emf appears in a conductor moved through a magntic field.
• Calculate the current generated by a motional emf in a conductor and rail system.
• Find the direction of the force caused by the induced current.
• Calculate the magnitude of the force caused by the induced current

• Calculate the magnitude of an induced EMF using Faraday's law:

• Given a magnetic field and a surface, find the magnetic flux.
• Calculate the emf in a loop of wire caused by changing magnetic field.
• Calculate the emf in a loop of wire caused by a changing area.

• Explain the underlying mechanism for Faraday's law both in the situation where the loop of conductor is changing and in the situation where the magnetic field is changing

• Determine the strength of a current induced in a cicuit with a given resistance.
• Determine the strength of a force on a wire loop given change in flux.


• Determine the direction of an induced electric field given a changing magnetic field.


• Use a plot of flux vs. time to plot the current in a loop.
• Plot the flux vs. time given a plot of the current in a loop.

• describe the electric and magnetic fields inside a beam of light; explain what is meant by the wavelength, period and frequency in this description
• state the relation between frequency and wavelegth for light and explain why this must be true
  
• explain how basic observable properties of light (colour, brightness, polarization) are related to details of the mathematical description as an electromagnetic wave (e.g. amplitude, wavelength)
• describe how the energy density in a light beam are related to the wavelegth and the amplitude
• explain precisely what is meant by the intensity of a light beam and how this is related to the other quantities associated with the classical electromagnetic description
• describe the basic mechanism for producing electromagnetic radation

• Explain qualitatively why disturbing a continuous system from equilibrium results in a wave.
• Describe the difference between a transverse wave and a longitudinal wave.
• Draw both history and snapshot graphs of one dimensional waves.
• Given a history graph, draw a snapshot graph, and vise versa.
• Given a displacement graph for a longitudinal, draw a representation of the longitudinal displacements.

• Describe what the displacement function D(x,t) represents.
• Describe the form of D(x,t) for left and right  moving pulses
• Predict whether or not a wave pulse on a string will be inverted upon reflection (given a fixed or free end).
• Explain what the Superposition Principle tells us, and use this to predict the displacement function for pulses passing though each other.

• Explain what a sinusoidal wave is.
• Determine the speed of a sinusoidal wave given the snapshot and history graphs of a sinusoidal wave.
• Determine the wavelength and frequency of a sinusoudal wave given D(x,t).
• Calculate the speed of a sinusoidal wave given D(x,t).
• State the relationship between wavelength, frequency, and velocity, and explain how to derive this.

• Determine the wavelength, frequency, and velocity of a light wave in a medium with some given index of refraction, if the wavelength/frequency for the wave outside the medium are given
• Explain why the frequency of a wave is the same everywhere.

• Plot subsequent snap shot graphs of two pulses travelling towards each other and interfering with each other.
• Determine if a point at a distance from two sources is interfering constructively or deconstructively.
• Calcualte the locations at which destructive interference (or constructive interfernce) will occur from two sources.
• Explain qualitatively why we get an interference pattern from a double slit apparatus.

• Use superposition to explain how a standing wave is created.
• Draw the fundamentals and harmonics of fixed-fixed (closed-closed), fixed-free (closed-open), and free-free (open-open) systems.
• Apply the theory of standing waves to wind intruments and stringed instruments (i.e., determine frequency, harmonics, string tension, linear density, speed of sound, length etc...)

QUANTUM MECHANICS

Light as a Particle

• Describe the photon model of light and explain how the wavelength/frequecy and amplitude/intensity of a light beam are related to the underlying properties of the photons

Properties of Quanta of Light ("Photons")

• predict the likelihood of various outcomes in simple experiments governed by probabilistic behavior
• to relate the macrscopic properties of a light beam (wavelength, power) to properties of photons 
  

The quantum description of particles

• describe the double slit experiment for light or electrons and explain why this provides evidence that quantum particles do not have definite positions and can exist in quantum superpositions
• explain why the results of the double slit experiment imply that the initial electrons  do not have well defined positions
• explain why the double slit experiment suggests that the behavior of single particles is probabalistic and how the classical intensity pattern is related to the relative probability for hitting various points on the screen
• Describe what is meant by probability density and evaluate whether or not a given function is a valid probability density for finding a particle
• Explain what is meant by a position eigenstate and what is meant by a quantum superposition of position eigenstates.
• explain how the process of describing general quantum superpositions of position eigenstates leads to the concept of a wavefunction 
• Use the wavefunction to determine the probability for finding a particle in a given region of space. 
• Explain what happens to the wavefunction after a measurement of the particle's position
  

• explain why the double slit experiment suggets that we can associate a wavelength to electrons with a particular momentum 
• state de Broglie’s relationship between wavelength and momentum of an electron or other particle
• describe the wavefunction for a particle with definite momentum
• explain what is meant by a wavepacket and why the wavefunction for a real travelling electron should take this form instead of a pure wave
• give a simple explanation for why particles with well defined momentum cannot have a definite position
• explain the physical interpretation of the mathematical fact that wavepackets and other wavefunctions can be written as a sum of pure waves
• explain qualitatively how the width of a wavepacket and its wavelength relate to the combination of pure waves (momentum eigenstates) that it is built from
• explain what is meant by uncertainty in position and uncertainty in momentum for a state

The Schrödinger Equation

• predict the velocity of a given wavepacket by looking at the wavepacket at some initial time
• to qualitatively describe the time evolution of a wavefunction that is a pure wave, and describe how this evolution depends on the wavelength.
  
• given two wavepackets, predict which will spread out faster
• explain why the speed of electron wavepackets should be inversely proportional to wavelength
• to predict the frequency of oscillation of an electon's wavefunction, given the wavelength and the potential energy in the region 
• explain why knowing the time dependence of momentum eigenstate wavefunctions allows us to determine the time-dependence for general wavefunctions (of a free particle)
• explain why the Schrodinger equation determines the time-dependence of a wavefunction
• write down the potential function for simple physical systems including electrons in wires or electrons near other charges

Bound states and atomic spectra

• Explain how to tell, by watching a movie of a wavfunction evolving with time, whether the particle being described is in a state of definine energy
• describe what is meant by a bound state (either in classical physics or in quantum mechanics)
• explain the crucial difference between the allowed energies for bound states in quantum mechanics as compared to classical mechanics