LO_physics.yml

Math:
    Topic Outcome:
        - Use proportional reasoning 
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    Graphs:
        - Calculate the total displacement given the position as a function of time.{84}
        - Determine the total distance traveled.{85}
        - Calculate the average velocity given the displacement and elapsed time.{86}
        - Calculate the average acceleration between two points in time.{97}
        - Find instantaneous acceleration at a specified time on a graph of velocity versus time.{101}
        - Create and interpret graphs of potential energy.{279}
        - Analyze elasticity and plasticity on a stress-strain diagram.{439} 
        - Qualitatively analyze position vs time graphs
        - Qualitatively analyze velocity vs time graphs
        - Qualitatively analyze acceleration vs time graphs
        - Qualitatively analyze position(x) vs position(y) graphs
    Significant Figures:
        - Determine the correct number of significant figures for the result of a computation.{33}
    Order of Magnitude:
        - Calculate the order of magnitude of a quantity.{8}
        - Estimate the values of physical quantities.{29}
    Algebra:
        Subtopic Outcome:
            - Describe how derived units are created from base units.{15}
            - Apply analytical methods of vector algebra to find resultant vectors and to solve vector equations for unknown vectors.{68}
            - Determine the scalar product of two vectors.{75}
            - Determine the vector product of two vectors.{76}
            - Solve an inequality 
            - Isolate a variable
            - Solve a rational equation
            - Use the quadratic formula to solve a quadratic equation
            - Simplify a rational expression
        Dimensional Analysis:
            - Find the dimensions of a mathematical expression involving physical quantities.{24}
            - Determine whether an equation involving physical quantities is dimensionally consistent.{25}
    Limits:
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    Derivatives:
        Subtopic Outcome:
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        Slope:
            - Calculate the average velocity given the displacement and elapsed time.{86}
            - Calculate the average acceleration between two points in time.{97}
            - Calculate the instantaneous acceleration given the functional form of velocity.{98}
            - Find instantaneous acceleration at a specified time on a graph of velocity versus time.{101}
            - Calculate the velocity vector given the position vector as a function of time.{128}
            - Calculate the average velocity in multiple dimensions.{129}
        Product rule:
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        Quotient Rule:
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        Power Rule:
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        Chain rule:
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        Max/Min:
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        Increasing/Decreasing Test:
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        First Derivative Test:
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        Second Derivative Test:
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    Integrals:
        Subtopic Outcome:
            - Derive the kinematic equations for constant acceleration using integral calculus.{117}
            - Find the functional form of velocity versus time given the acceleration function.{119}
            - Find the functional form of position versus time given the velocity function.{120}
        Area Under Curve:
            - Determine the total distance traveled.{85}
            - Relate the work done during a time interval to the power delivered.{254}
        Area Between Two Curves:
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        Substitution Rule:
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        Integration by Parts:
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        Trigonometric Substitution:
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        Partial Fractions:
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    Exponential Functions:
        Subtopic Outcome:
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        Derivative:
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        Integral:
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    Logarithmic Functions:
        Subtopic Outcome:
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        Derivative:
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        Integral:
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    System of Equations:
        Subtopic Outcome:
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        Set Up:
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        Solve:
            - Solve a system of two equations
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    Quadratic formula:
        Subtopic Outcome:
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        Non-Physical Roots:
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    Polar Coordinates:
        - Explain the connection between polar coordinates and Cartesian coordinates in a plane.{64}
        - Express a vector in polar form.
    Conics:
        - Describe the conic sections and how they relate to orbital motion.{469}
    Diagnostic:
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# Topic Break

Physics in General:
    Topic Outcome:
        - Describe the scope of physics.{7}
        - Describe the relationships among models, theories, and laws.{10} 
        - Compare measurable length, mass, and timescales quantitatively.{9}
        - Apply physical principles to real world application
    Units:
        - Describe how SI base units are defined.{14}
        - Describe how derived units are created from base units.{15}
        - Express quantities given in SI units using metric prefixes.{16} 
        - Use conversion factors to express the value of a given quantity in different units.{20}
        - Express quantities given in SI units using metric prefixes.{700} 
        - Convert temperatures between the Celsius, Fahrenheit, and Kelvin scales.{694} 
    Solving Problems in Physics:
        - Describe the process for developing a problem-solving strategy.{42}
        - Explain how to find the numerical solution to a problem.{43}
        - Summarize the process for assessing the significance of the numerical solution to a problem.{44} 
    Uncertainty:
        - Describe the relationship between the concepts of accuracy, precision, uncertainty, and discrepancy.{34} 
        - Calculate the percent uncertainty of a measurement, given its value and its uncertainty.{36}
        - Determine the uncertainty of the result of a computation involving quantities with given uncertainties.{37}

# Topic Break

Vectors:
    Topic Outcome:
        - Describe the difference between vector and scalar quantities.{50}
        - Distinguish between a vector equation and a scalar equation.{55} 
        - Interpret physical situations in terms of vector expressions.{70} 
        - Explain the difference between the scalar product and the vector product of two vectors.{74} 
        - Describe how the products of vectors are used in physics.{77}
    Notation:
        - Describe vectors in two and three dimensions in terms of their components, using unit vectors along the axes.{59}
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    Scalars:
        - Distinguish between the vector components of a vector and the scalar components of a vector.{61}
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    Properties of Vectors:
        - Identify the magnitude and direction of a vector.{51}
        - Explain the effect of multiplying a vector quantity by a scalar.{52}
        - Explain how the magnitude of a vector is defined in terms of the components of a vector.{62}
    Coordinate System and Vector Components:
        - Identify the magnitude and direction of a vector.{51}
        - Explain the geometric construction for the addition or subtraction of vectors in a plane.{54}
        - Describe how one-dimensional vector quantities are added or subtracted.{53}
        - Describe vectors in two and three dimensions in terms of their components, using unit vectors along the axes.{59}
        - Distinguish between the vector components of a vector and the scalar components of a vector.{61}
        - Explain how the magnitude of a vector is defined in terms of the components of a vector.{62}
        - Identify the direction angle of a vector in a plane.{63}
        - Explain the connection between polar coordinates and Cartesian coordinates in a plane.{64}
    Vector Algebra:
        - Apply analytical methods of vector algebra to find resultant vectors and to solve vector equations for unknown vectors.{68}
        - Interpret physical situations in terms of vector expressions.{70} 
    Dot Product:
        - Determine the scalar product of two vectors.{75}
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    Cross Product:
        - Determine the vector product of two vectors.{76}
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# Topic Break

Kinematics(1D):
    Topic Outcome:
        - Define position, displacement, and distance traveled.{83}
        - Identify which equations of motion are to be used to solve for unknowns.{105}
    Motion Diagrams:
        - Understand and interpret motion diagrams
        - Understand the relationship between position, velocity, and acceleration using diagrams of motion
        - Construct the motion diagram for a given motion, showing properly-spaced dots, velocity vectors, and acceleration vectors.
    Position:
        - Find the functional form of position versus time given the velocity function.{120}
        - Determine the total distance traveled.{85}
        - Qualitatively analyze position vs time graphs
        - Qualitatively analyze position(x) vs position(y) graphs
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    Displacement:
        - Calculate the total displacement given the position as a function of time.{84}
        - Find the functional form of displacement versus time given the velocity function.
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    Speed:
        - Calculate the speed given the instantaneous velocity.{93} 
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    Velocity:
        Subtopic Outcome:
            - Explain the difference between average velocity and instantaneous velocity.{90}
            - Describe the difference between velocity and speed.{91}
            - Explain the vector nature of instantaneous acceleration and velocity.{99}
            - Find the functional form of velocity versus time given the acceleration function.{119}
            - Qualitatively analyze velocity vs time graphs
        Average:
            - Calculate the average velocity given the displacement and elapsed time.{86}
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        Instantaneous:
            - Calculate the instantaneous velocity given the mathematical equation for the velocity.{92}
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    Acceleration:
        Subtopic Outcome:
            - Explain the difference between average acceleration and instantaneous acceleration.{100}
            - Explain the vector nature of instantaneous acceleration and velocity.{99}
            - Qualitatively analyze acceleration vs time graphs
        Average:
            - Calculate the average acceleration between two points in time.{97}
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        Instantaneous:
            - Calculate the instantaneous acceleration given the functional form of velocity.{98}
            - Find instantaneous acceleration at a specified time on a graph of velocity versus time.{101}
    Uniform Motion:
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    Non-Uniform Motion (Constant Acceleration):
        - Use appropriate equations of motion to solve a two-body pursuit problem.{106} 
        - Derive the kinematic equations for constant acceleration using integral calculus.{117}
        - Use the integral formulation of the kinematic equations in analyzing motion.{118}
    Free Fall:
        - Use the kinematic equations with the variables y and g to analyze free-fall motion.{110}
        - Describe how the values of the position, velocity, and acceleration change during a free fall.{111}
        - Solve for the position, velocity, and acceleration as functions of time when an object is in a free fall.{112}
    
# Topic Break

Kinematics(2D and 3D):
    Topic Outcome:
        - Use the one-dimensional motion equations along perpendicular axes to solve a problem in two or three dimensions with a constant acceleration.{135}
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    Displacement Vector:
        - Calculate position vectors in a multidimensional displacement problem.{126}
        - Solve for the displacement in two or three dimensions.{127}
    Velocity Vector:
        - Calculate the velocity vector given the position vector as a function of time.{128}
        - Calculate the average velocity in multiple dimensions.{129} 
    Acceleration Vector:
        - Calculate the acceleration vector given the velocity function in unit vector notation.{133}
        - Describe the motion of a particle with a constant acceleration in three dimensions.{134}
        - Express the acceleration in unit vector notation.{136}
    Projectile Motion:
        - Use one-dimensional motion in perpendicular directions to analyze projectile motion.{140}
        - Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface.{141}
        - Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch.{142}
        - Calculate the trajectory of a projectile.{143} 
    Uniform Circular Motion:
        Subtopic Outcome:
            - Use the equations of circular motion to find the position, velocity, and acceleration of a particle executing circular motion.{148}
            - 
        Velocity:
            - Explain how angular velocity is related to tangential speed.{339}
            - Calculate the instantaneous angular velocity given the angular position function.{340}
        Acceleration:
            - Solve for the centripetal acceleration of an object moving on a circular path.{147}
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    Non-Uniform Circular Motion:
        Subtopic Outcome:
            - Explain the differences between centripetal acceleration and tangential acceleration resulting from nonuniform circular motion.{149}
            - Evaluate centripetal and tangential acceleration in nonuniform circular motion, and find the total acceleration vector.{150}
            - Find the angular velocity and angular acceleration in a rotating system.{341}
        Angular Acceleration:
            - Calculate the average angular acceleration when the angular velocity is changing.{342}
            - Calculate the instantaneous angular acceleration given the angular velocity function.{343} 
    Relative Motion:
        - Explain the concept of reference frames.{154}
        - Write the position and velocity vector equations for relative motion.{155}
        - Draw the position and velocity vectors for relative motion.{156}
        - Analyze one-dimensional and two-dimensional relative motion problems using the position and velocity vector equations.{157} 
    Constrained Motion of Connected Particles:
        - Analyze a system of connected particles to solve for the velocity and acceleration of one of the particles.

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Force:
    Topic Outcome:
        - Distinguish between kinematics and dynamics.{163}
        - Understand the definition of force.{164}
        - Define the SI unit of force, the newton.{166}
        - Describe force as a vector.{167}
        - Apply Newton's laws of motion to solve problems involving a variety of forces.{199}
        - Apply problem-solving techniques to solve for quantities in more complex systems of forces.{210}
        - Use concepts from kinematics to solve problems using Newton's laws of motion.{211}
        - Solve more complex equilibrium problems.{212}
        - Solve more complex acceleration problems.{213}
        - Apply calculus to more advanced dynamics problems.{214} 
        - Calculate force given pressure and area.{497} 
    Types of Forces:
        - Distinguish between external and internal forces.{179}
        - Identify the action and reaction forces in different situations.{192}
        - Define normal and tension forces.{197}
        - Distinguish between real and fictitious forces.{198}
        - Define buoyant force.{514}
    Free Body Diagrams:
        - Identify simple free-body diagrams.{165}
        - Explain the rules for drawing a free-body diagram.{203}
        - Construct free-body diagrams for different situations.{204} 
        - Draw a free-body diagram for a rigid body acted on by forces.{421}
        - Set up a free-body diagram for an extended object in static equilibrium.{427}
    Newton's First Law:
        - Describe Newton's first law of motion.{171}
        - Recognize friction as an external force.{172}
        - Define inertia.{173}
        - Identify inertial reference frames.{174}
        - Calculate equilibrium for a system.{175}
    Newton's Second Law:
        - Distinguish between external and internal forces.{179}
        - Describe Newton's second law of motion.{180}
        - Explain the dependence of acceleration on net force and mass.{181}
        - Apply Newton's second law to develop the equation for centripetal force.{225}
    Newton's Third Law:
        Subtopic Outcome:
            - State Newton's third law of motion.{191}
            - Identify the action and reaction forces in different situations.{192}
            - Apply Newton's third law to define systems and solve problems of motion.{193}
        Ropes and Pulleys:
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    Equilibrium:
        - Calculate equilibrium for a system.{175}
        - Solve more complex equilibrium problems.{212}
    Mass, Weight and Gravity:
        - Explain the difference between mass and weight.{185}
        - Explain why falling objects on Earth are never truly in free fall.{186}
        - Describe the concept of weightlessness.{187}
    Friction:
        - Recognize friction as an external force.{172}
        - Describe the general characteristics of friction.{218}
        - List the various types of friction.{219}
        - Calculate the magnitude of static and kinetic friction, and use these in problems involving Newton's laws of motion.{220} 
        - Calculate the static friction force associated with rolling motion without slipping.{395}
    Drag:
        Subtopic Outcome:
            - Express the drag force mathematically.{230}
            - Describe applications of the drag force.{231}
        Terminal Velocity:
            - Define terminal velocity.{232}
            - Determine an object's terminal velocity given its mass.{233} 
        Projectile Motion with Drag:
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    Springs:
        Subtopic Outcome:
            - Define the units of the spring constant
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        Hooke's Law:
            - Define Hooke's Law
            - Use Hooke's Law to determine the force, displacement from equilibrium, or spring constant of a system
    Dynamics of Circular Motion:
        Subtopic Outcome:
            - Explain the equation for centripetal acceleration.{224}
            - Use circular motion concepts in solving problems involving Newton's laws of motion.{226}
        Centripetal Force:
            - Apply Newton's second law to develop the equation for centripetal force.{225}
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        Uniform:
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Momentum and Impulse:
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    Momentum:
        Subtopic Outcome:
            - Explain what momentum is, physically.{291}
            - Calculate the momentum of a moving object.{292}
            - Express momentum as a two-dimensional vector.{317}
            - Calculate momentum in two dimensions, as a vector quantity.{319}
            - Relate momentum to force.
            - Determine the net force on an object from the momentum as a function of time
            - Define momentum 
        Linear:
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        Angular:
            - Describe the vector nature of angular momentum.{400}
            - Find the total angular momentum and torque about a designated origin of a system of particles.{401}
            - Calculate the angular momentum of a rigid body rotating about a fixed axis.{402}
            - Use conservation of angular momentum in the analysis of objects that change their rotation rate.{404}
    Impulse:
        - Explain what an impulse is, physically.{296}
        - Describe what an impulse does.{297}
        - Relate impulses to collisions.{298}
        - Apply the impulse-momentum theorem to solve problems.{299}
        - Relate the impulse delivered to an object to the average applied force and duration of the force.
    Collisions:
        Subtopic Outcome:
            - Identify the type of collision.{311}
            - Correctly label a collision as elastic or inelastic.{312}
            - Use kinetic energy along with momentum and impulse to analyze a collision.{313}
        Elastic:
            - Solve problems involving the distance and time between a gas molecule’s collisions.{732}
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        Inelastic:
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        Explosions:
            - Describe the application of conservation of momentum when the mass changes with time, as well as the velocity.{330}
            - Calculate the speed of a rocket in empty space, at some time, given initial conditions.{331}
            - Calculate the speed of a rocket in Earth's gravity field, at some time, given initial conditions.{332} 
    Conservation of Momentum:
        Subtopic Outcome:
            - Explain the meaning of "conservation of momentum".{303}
            - Correctly identify if a system is, or is not, closed.{304}
            - Define a system whose momentum is conserved.{305}
            - Mathematically express conservation of momentum for a given system.{306}
            - Calculate an unknown quantity using conservation of momentum.{307}
            - Write equations for momentum conservation in component form.{318}
            - Describe the application of conservation of momentum when the mass changes with time, as well as the velocity.{330}
            - Use conservation of momentum and conservation of mechanical energy to solve an elastic collision problem.
            - Use conservation of momentum to solve an elastic collision problem.
            - Use conservation of momentum to solve a problem.
        Linear:
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        Angular:
            - Use conservation of angular momentum in the analysis of objects that change their rotation rate.{404}
            - Apply conservation of angular momentum to determine the angular velocity of a rotating system in which the moment of inertia is changing.{408}
            - Explain how the rotational kinetic energy changes when a system undergoes changes in both moment of inertia and angular velocity.{409}
            - Describe how orbital velocity is related to conservation of angular momentum.{470}
    2D Collisions:
        - Express momentum as a two-dimensional vector.{317}
        - Write equations for momentum conservation in component form.{318}
        - Calculate momentum in two dimensions, as a vector quantity.{319} 
    Precession:
        - Describe the physical processes underlying the phenomenon of precession.{413}
        - Calculate the precessional angular velocity of a gyroscope.{414}

# Topic Break

Energy:
    Topic Outcome:
        - Describe energy transformations and conversions in general terms.{284}
        - Explain what it means for an energy source to be renewable or nonrenewable.{285}
    Kinetic Energy:
        - Calculate the kinetic energy of a particle given its mass and its velocity or momentum.{244}
        - Evaluate the kinetic energy of a body, relative to different frames of reference.{245}
        - Describe the differences between rotational and translational kinetic energy.{358}
        - Explain how the rotational kinetic energy changes when a system undergoes changes in both moment of inertia and angular velocity.{409}
        - Calculate the kinetic energy of a simple pendulum.
        - Define kinetic energy
    Potential Energy:
        Subtopic Outcome:
            - Relate the difference of potential energy to work done on a particle for a system without friction or air drag.{261}
            - Explain the meaning of the zero of the potential energy function for a system.{262}
            - Create and interpret graphs of potential energy.{279}
            - Explain the connection between stability and potential energy.{280}
        Gravitational Potential Energy:
            - Calculate and apply the gravitational potential energy for an object near Earth's surface and the elastic potential energy of a mass-spring system.{263} 
            - Determine changes in gravitational potential energy over great distances.{457}
            - Apply conservation of energy to determine escape velocity.{458}
            - Determine whether astronomical bodies are gravitationally bound.{459} 
            - Calculate the gravitational potential energy of a simple pendulum.
        Elastic Potential Energy:
            - Calculate and apply the gravitational potential energy for an object near Earth's surface and the elastic potential energy of a mass-spring system.{263} 
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    Energy Diagrams:
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    Conservation of Energy:
        Subtopic Outcome:
            - Formulate the principle of conservation of mechanical energy, with or without the presence of non-conservative forces.{274}
            - Use the conservation of mechanical energy to calculate various properties of simple systems.{275}
            - Use conservation of mechanical energy to analyze systems undergoing both rotation and translation.{361}
            - Apply conservation of energy to determine escape velocity.{458}
            - Explain how Bernoulli's equation is related to the conservation of energy.{528}
        Conservative Forces:
            - Characterize a conservative force in several different ways.{267}
            - Specify mathematical conditions that must be satisfied by a conservative force and its components.{268}
            - Relate the conservative force between particles of a system to the potential energy of the system.{269}
            - Calculate the components of a conservative force in various cases.{270}
        Non-Conservative Forces:
            - Calculate the angular velocity of a rotating system when there are energy losses due to nonconservative forces.{362}
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# Topic Break

Work:
    Topic Outcome:
        - Represent the work done by any force.{239}
        - Evaluate the work done for various forces.{240}
    Work-Energy Theorem:
        - Apply the work-energy theorem to find information about the motion of a particle, given the forces acting on it.{249}
        - Use the work-energy theorem to find information about the forces acting on a particle, given information about its motion.{250}
        - Use the work-energy theorem to analyze rotation to find the work done on a system when it is rotated about a fixed axis for a finite angular displacement.{383}
        - Solve for the angular velocity of a rotating rigid body using the work-energy theorem.{384}
    Power:
        - Relate the work done during a time interval to the power delivered.{254}
        - Find the power expended by a force acting on a moving body.{255} 
    Work For Rotational Motion:
        - Use the work-energy theorem to analyze rotation to find the work done on a system when it is rotated about a fixed axis for a finite angular displacement.{383}
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    Power For Rotational Motion:
        - Find the power delivered to a rotating rigid body given the applied torque and angular velocity.{385}
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# Topic Break

Rotational Motion:
    Topic Outcome:
        - Derive the kinematic equations for rotational motion with constant angular acceleration.{347}
        - Select from the kinematic equations for rotational motion with constant angular acceleration the appropriate equations to solve for unknowns in the analysis of systems undergoing fixed-axis rotation.{348}
        - Use solutions found with the kinematic equations to verify the graphical analysis of fixed-axis rotation with constant angular acceleration.{349}
    Relating Rotational to Translational Motion:
        - Given the linear kinematic equation, write the corresponding rotational kinematic equation.{353}
        - Calculate the linear distances, velocities, and accelerations of points on a rotating system given the angular velocities and accelerations.{354}
        - Summarize the rotational variables and equations and relate them to their translational counterparts.{386}
    Rolling Motion:
        Subtopic Outcome:
            - Use energy conservation to analyze rolling motion.{396} 
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        Without Slipping:
            - Describe the physics of rolling motion without slipping.{392}
            - Explain how linear variables are related to angular variables for the case of rolling motion without slipping.{393}
            - Find the linear and angular accelerations in rolling motion with and without slipping.{394}
            - Calculate the static friction force associated with rolling motion without slipping.{395}
        With Slipping:
            - Find the linear and angular accelerations in rolling motion with and without slipping.{394}
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    Center of Mass:
        - Explain the meaning and usefulness of the concept of center of mass.{323}
        - Calculate the center of mass of a given system.{324}
        - Apply the center of mass concept in two and three dimensions.{325}
        - Calculate the velocity and acceleration of the center of mass.{326}
    Rotational Energy:
        Subtopic Outcome:
            - Describe the differences between rotational and translational kinetic energy.{358}
            - Use conservation of mechanical energy to analyze systems undergoing both rotation and translation.{361}
            - Calculate the angular velocity of a rotating system when there are energy losses due to nonconservative forces.{362} 
        Moment of Inertia:
            - Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis.{359}
            - Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy.{360}
            - Calculate the moment of inertia for uniformly shaped, rigid bodies.{366}
            - Calculate the moment of inertia for compound objects.{368} 
        Parallel-Axis Theorem:
            - Apply the parallel axis theorem to find the moment of inertia about any axis parallel to one already known.{367}
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    Center of Gravity:
        - Calculate the center of gravity of a given system.
        - Calculate the center of gravity of a uniform object.
#Topic Break

Rotational Dynamics:
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    Newton's Second Law for Rotational Motion:
        - Calculate the torques on rotating systems about a fixed axis to find the angular acceleration.{378}
        - Explain how changes in the moment of inertia of a rotating system affect angular acceleration with a fixed applied torque.{379}
    Torque:
        - Describe how the magnitude of a torque depends on the magnitude of the lever arm and the angle the force vector makes with the lever arm.{372}
        - Determine the sign (positive or negative) of a torque using the right-hand rule.{373}
        - Calculate individual torques about a common axis and sum them to find the net torque.{374} 
        - Find the total angular momentum and torque about a designated origin of a system of particles.{401}
        - Calculate the torque on a rigid body rotating about a fixed axis.{403}
    Rotation about a Fixed Axis:
        - Describe the physical meaning of rotational variables as applied to fixed-axis rotation.{338}
        - Calculate the angular momentum of a rigid body rotating about a fixed axis.{402}
        - Calculate the torque on a rigid body rotating about a fixed axis.{403}
    Static Equilibrium:
        - Identify the physical conditions of static equilibrium.{420}
        - Draw a free-body diagram for a rigid body acted on by forces.{421}
        - Explain how the conditions for equilibrium allow us to solve statics problems.{422}
        - Identify and analyze static equilibrium situations.{426}
        - Set up a free-body diagram for an extended object in static equilibrium.{427}
        - Set up and solve static equilibrium conditions for objects in equilibrium in various physical situations.{428}

# Topic Break

Gravitation:
    Topic Outcome:
        - List the significant milestones in the history of gravitation.{445}
        - Determine the mass of an astronomical body from free-fall acceleration at its surface.{452}
        - Describe how the value of g varies due to location and Earth's rotation.{453}
        - Understanding the concept of gravitational force and its role in determining the motion of celestial bodies.
        - Apply the inverse square law of gravitation to explain how the gravitational force between the Sun and planets varies with distance.
        - Relate the gravitation and celestial mechanics concepts to explain the interaction between the Sun, planets, and moons.
    Newton's Law of Gravity:
        - Calculate the gravitational force between two point masses.{446}
        - Estimate the gravitational force between collections of mass.{447}
        - Explain the connection between the constants G and g.{451}
    Orbits:
        - Describe the mechanism for circular orbits.{463}
        - Find the orbital periods and speeds of satellites.{464}
        - Determine whether objects are gravitationally bound.{465} 
    Kepler's Laws:
        Subtopic Outcome:
            - Describe the conic sections and how they relate to orbital motion.{469}
            - Describe how orbital velocity is related to conservation of angular momentum.{470}
            - Determine the period of an elliptical orbit from its major axis.{471}
        Kepler's First Law:
            - Paste un-numbered outcome here
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        Kepler's Second Law:
            - Paste un-numbered outcome here
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        Kepler's Third Law:
            - Paste un-numbered outcome here
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    Tides:
        - Explain the origins of Earth's ocean tides.{475}
        - Describe how neap and leap tides differ.{476}
        - Describe how tidal forces affect binary systems.{477}
    Einstein's Theory of Gravity:
        - Describe how the theory of general relativity approaches gravitation.{481}
        - Explain the principle of equivalence.{482}
        - Calculate the Schwarzschild radius of an object.{483}
        - Summarize the evidence for black holes.{484} 

# Topic Break

Fluids:
    Topic Outcome:
        - State the different phases of matter.{490}
        - Describe the characteristics of the phases of matter at the molecular or atomic level.{491}
        - Distinguish between compressible and incompressible materials.{492}
    Density:
        - Define density and its related SI units.{493}
        - Compare and contrast the densities of various substances.{494}
        - Relate the density of an object to its mass and volume
    Pressure:
        - Define pressure and its related SI units.{495}
        - Explain the relationship between pressure and force.{496}
        - Calculate force given pressure and area.{497} 
        - Define gauge pressure and absolute pressure.{501}
        - Explain various methods for measuring pressure.{502}
        - Understand the working of open-tube barometers.{503}
        - Describe in detail how manometers and barometers operate.{504}
    Pascal's Law:
        Subtopic Outcome:
            - State Pascal's principle.{508}
            - Describe applications of Pascal's principle.{509}
        Hydraulics:
            - Derive relationships between forces in a hydraulic system.{510} 
            - Paste un-numbered outcome here
    Archimedes' Principle:
        Subtopic Outcome:
            - State Archimedes' principle.{515}
            - Describe the relationship between density and Archimedes' principle.{516}
        Buoyancy:
            - Define buoyant force.{514}
            - Paste un-numbered outcome here
    Fluid Dynamics:
        Subtopic Outcome:
            - Describe the characteristics of flow.{520}
            - Paste un-numbered outcome here
        Flow Rate:
            - Calculate flow rate.{521}
            - Describe the relationship between flow rate and velocity.{522}
        Laminar/Turbulent Flow:
            - Calculate flow and resistance with Poiseuille's law.{536}
            - Explain how pressure drops due to resistance.{537}
            - Calculate the Reynolds number for an object moving through a fluid.{538}
            - Use the Reynolds number for a system to determine whether it is laminar or turbulent.{539}
        Viscosity:
            - Explain what viscosity is.{535}
            - Describe the conditions under which an object has a terminal speed.{540}
        Equation of Continuity:
            - Explain the consequences of the equation of continuity to the conservation of mass.{523}
            - Paste un-numbered outcome here
        Bernoulli's Equation:
            - Explain the terms in Bernoulli's equation.{527}
            - Explain how Bernoulli's equation is related to the conservation of energy.{528}
            - Describe how to derive Bernoulli's principle from Bernoulli's equation.{529}
            - Perform calculations using Bernoulli's principle.{530}
            - Describe some applications of Bernoulli's principle.{531}

# Topic Break

Elasticity:
    Topic Outcome:
        - Explain the concepts of stress and strain in describing elastic deformations of materials.{432}
        - Describe the types of elastic deformation of objects and materials.{433}
        - Explain the limit where a deformation of material is elastic.{437}
        - Analyze elasticity and plasticity on a stress-strain diagram.{439} 
    Stress:
        - Paste un-numbered outcome here
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    Strain:
        - Paste un-numbered outcome here
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    Elastic Modulus:
        - Paste un-numbered outcome here
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    Plasticity:
        - Describe the range where materials show plastic behavior.{438}
        - Paste un-numbered outcome here

# Topic Break

Oscillations:
    Topic Outcome:
        - Paste un-numbered outcome here
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    Simple Harmonic Motion:
        Subtopic Outcome:
            - Define the terms period and frequency.{549}
            - List the characteristics of simple harmonic motion.{550}
            - Explain the concept of phase shift.{551}
            - Write the equations of motion for the system of a mass and spring undergoing simple harmonic motion.{552}
            - Describe the motion of a mass oscillating on a vertical spring.{553} 
        Energy in Simple Harmonic Motion:
            - Describe the energy conservation of the system of a mass and a spring.{557}
            - Explain the concepts of stable and unstable equilibrium points.{558}
        Comparing Simple Harmonic Motion to Circular Motion:
            - Describe how the sine and cosine functions relate to the concepts of circular motion.{567}
            - Describe the connection between simple harmonic motion and circular motion.{568}
    Vertical Oscillations:
        - Describe the motion of a mass oscillating on a vertical spring.{553}
        - Paste un-numbered outcome here
    Pendulum:
        - State the forces that act on a simple pendulum.{572}
        - Determine the angular frequency, frequency, and period of a simple pendulum in terms of the length of the pendulum and the acceleration due to gravity.{573}
        - Define the period for a physical pendulum.{574}
        - Define the period for a torsional pendulum.{575} 
    Damped Oscillations:
        - Describe the motion of damped harmonic motion.{579}
        - Write the equations of motion for damped harmonic oscillations.{580}
        - Describe the motion of driven, or forced, damped harmonic motion.{581}
        - Write the equations of motion for forced, damped harmonic motion. {582}
    Forced Oscillations:
        - Define forced oscillations.{586}
        - List the equations of motion associated with forced oscillations.{587}
        - Explain the concept of resonance and its impact on the amplitude of an oscillator.{588}
        - List the characteristics of a system oscillating in resonance. {589} 
    Resonance:
        - Paste un-numbered outcome here
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# Topic Break

Waves:
    Topic Outcome:
        - Describe the basic characteristics of wave motion.{595}
        - Define the terms wavelength, amplitude, period, frequency, and wave speed.{596}
        - List the different types of waves.{598}
        - Model a wave, moving with a constant wave velocity, with a mathematical expression.{602}
        - Calculate the velocity and acceleration of the medium.{603}
        - Show how the velocity of the medium differs from the wave velocity (propagation velocity).{604} 
        - Determine the factors that affect the speed of a wave on a string.{608} 
        - Write a mathematical expression for the speed of a wave on a string and generalize these concepts for other media.{609} 
    Traveling Waves:
        - Explain the difference between longitudinal and transverse waves, and give examples of each type.{597}
        - Explain how the displacement of particles in different waveforms changes over time.
        - Paste un-numbered outcome here.
    Standing Waves:
        - Describe standing waves and explain how they are produced.{624}
        - Describe the modes of a standing wave on a string.{625}
        - Provide examples of standing waves beyond the waves on a string.{626}
        - Describe resonance in a tube closed at one end and open at the other end.{653}
        - Describe resonance in a tube open at both ends.{654} .{655}
    Energy of a Wave:
        - Explain how energy travels with a pulse or wave.{613}
        - Describe, using a mathematical expression, how the energy in a wave depends on the amplitude of the wave.{614}
    Power of a Wave:
        - Paste un-numbered outcome here
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    Interference:
        - Explain how mechanical waves are reflected and transmitted at the boundaries of a medium.{618}
        - Define the terms interference and superposition.{619}
        - Find the resultant wave of two identical sinusoidal waves that differ only by a phase shift.{620}
        - Understanding of nodal/antinodal lines and their significance in wave interference patterns.
        - Analyze the alignment of troughs along antinodal lines and the impact on the intensity of the resulting wave.
        - Compare the intensity of the wave resulting from interference to the intensity of the individual source waves.
    Sound:
        Subtopic Outcome:
            - Explain the difference between sound and hearing.{632}
            - Describe sound as a wave.{633}
            - List the equations used to model sound waves.{634}
            - Describe compression and rarefactions as they relate to sound. {635}
            - Describe the resonant frequencies in instruments that can be modeled as a tube with symmetrical boundary conditions.{658}
            - Describe the resonant frequencies in instruments that can be modeled as a tube with anti-symmetrical boundary conditions.{659}
            - Explain the mechanism behind sound-reducing headphones.{652}
            - Describe resonance in a tube closed at one end and open at the other end.{653}
            - Describe resonance in a tube open at both ends.{654} .{655}
            - Determine the beat frequency produced by two sound waves that differ in frequency.{663}
            - Describe how beats are produced by musical instruments.{664} 
            - Explain the mechanism behind sonic booms.{673}
            - Describe the difference between sonic booms and shock waves.{674}
            - Describe a bow wake.{675}
        Speed of Sound:
            - Explain the relationship between wavelength and frequency of sound.{639}
            - Determine the speed of sound in different media.{640}
            - Derive the equation for the speed of sound in air.{641}
            - Determine the speed of sound in air for a given temperature. {642}
        Sound Intensity(Decibels):
            - Define the term intensity.{646}
            - Explain the concept of sound intensity level.{647}
            - Describe how the human ear translates sound.{648}
    The Doppler Effect:
        - Explain the change in observed frequency as a moving source of sound approaches or departs from a stationary observer.{668}
        - Explain the change in observed frequency as an observer moves toward or away from a stationary source of sound.{669} 
    Photons:
        Subtopic outcome:
            - Paste un-numbered outcome here
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        Blackbody radiation:
            - Apply Wien’s and Stefan’s laws to analyze radiation emitted by a blackbody.
            - Explain Planck’s hypothesis of energy quanta.
        Photoelectric effect:
            - Describe physical characteristics of the photoelectric effect.
            - Explain why the photoelectric effect cannot be explained by classical physics.
            - Describe how Einstein’s idea of a particle of radiation explains the photoelectric effect.
        Compton effect:
            - Describe Compton’s experiment.
            - Explain the Compton wavelength shift.
            - Describe how experiments with X-rays confirm the particle nature of radiation.
        Bohr's atomic model:
            - Explain the difference between the absorption spectrum and the emission spectrum of radiation emitted by atoms.
            - Describe the Rutherford gold foil experiment and the discovery of the atomic nucleus.
            - Explain the atomic structure of hydrogen.
            - Describe the postulates of the early quantum theory for the hydrogen atom.
            - Summarize how Bohr’s quantum model of the hydrogen atom explains the radiation spectrum of atomic hydrogen.
        De Broglie’s matter waves:
            - Describe de Broglie’s hypothesis of matter waves.
            - Explain how the de Broglie’s hypothesis gives the rationale for the quantization of angular momentum in Bohr’s quantum theory of the hydrogen atom.
            - Describe the Davisson–Germer experiment.
            - Interpret de Broglie’s idea of matter waves and how they account for electron diffraction phenomena.
        Wave-particle duality:
            - Identify phenomena in which electromagnetic waves behave like a beam of photons and particles behave like waves.
            - Describe the physics principles behind electron microscopy.
            - Summarize the evolution of scientific thought that led to the development of quantum mechanics.
    Light:
        - Identify to the concept of diffraction in relation to microscopy.
        - Explore how waves bend or spread when passing through apertures or obstacles.
        - Utilize principles such as wavelength of light, mass of electrons and neutrons, Planck's constant, and particle speed.

# Topic Break

Thermodynamics:
    Topic Outcome:
        - Define a thermodynamic system, its boundary, and its surroundings.{749}
        - Explain the roles of all the components involved in thermodynamics.{750}
        - Link an equation of state to a system.{752} 
        - Define a thermodynamic process.{766}
        - Distinguish between quasi-static and non-quasi-static processes.{767}
        - Calculate physical quantities, such as the heat transferred, work done, and internal energy change for isothermal, adiabatic, and cyclical thermodynamic processes.{768} 
        - Define reversible and irreversible processes.{786}
        - Define a dissipative process. 
    Temperature:
        Subtopic Outcome:
            - Define temperature and describe it qualitatively.{687}
            - Define thermal equilibrium and thermodynamic temperature.{751}
        Thermometers:
            - Describe several different types of thermometers.{693}
            - Convert temperatures between the Celsius, Fahrenheit, and Kelvin scales.{694} 
    Thermal Equilibrium:
        - Explain thermal equilibrium.{688}
        - Explain the zeroth law of thermodynamics.{689}
        - Define thermal equilibrium and thermodynamic temperature.{751}
    Heat Transfer:
        Subtopic Outcome:
            - Explain phenomena involving heat as a form of energy transfer.{704}
            - Solve problems involving heat transfer.{705} 
            - Explain some phenomena that involve conductive, convective, and radiative heat transfer.{715}
            - Solve problems on the relationships between heat transfer, time, and rate of heat transfer.{716}
            - Explain some phenomena that involve conductive, convective, and radiative heat transfer.{723}
            - Solve problems involving heat transfer to and from ideal monatomic gases whose volumes are held constant.{736}
        Convection:
            - Paste un-numbered outcome here
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        Conduction:
            - Solve problems using the formulas for conduction and radiation.{717}
            - Paste un-numbered outcome here
        Radiation:
            - Solve problems using the formulas for conduction and radiation.{717}
            - Paste un-numbered outcome here
    Pressure:
        - Paste un-numbered outcome here
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    Thermal Expansion:
        - Answer qualitative questions about the effects of thermal expansion.{698}
        - Solve problems involving thermal expansion, including those involving thermal stress.{699}
    Specific Heat:
        - Calculate the specific heat of an ideal gas for either an isobaric or isochoric process.{773}
        - Estimate the change in specific heat of a gas over temperature ranges.{775}
    Calorimetry:
        - Solve calorimetry problems involving phase changes.{711}
        - Paste un-numbered outcome here
    Phase Changes:
        - Describe phase transitions and equilibrium between phases.{709}
        - Solve problems involving latent heat.{710}
        - Solve calorimetry problems involving phase changes.{711} 
    Ideal Gas:
        Subtopic Outcome:
            - Use the unit of moles in relation to numbers of molecules, and molecular and macroscopic masses.{724}
            - Explain the ideal gas law in terms of moles rather than numbers of molecules.{725}
            - Apply the van der Waals gas law to situations where the ideal gas law is inadequate.{726}
            - Explain the relations between microscopic and macroscopic quantities in a gas.{730}
            - Solve problems involving mixtures of gases.{731}
            - Solve problems involving the distance and time between a gas molecule’s collisions.{732}
            - Describe the distribution of molecular speeds in an ideal gas.{742}
            - Find the average and most probable molecular speeds in an ideal gas.{743}
        Heat Capacity:
            - Estimate the heat capacities of metals using a model based on degrees of freedom.{738} 
            - Define heat capacity of an ideal gas for a specific process.{772}
            - Calculate the specific heat of an ideal gas for either an isobaric or isochoric process.{773}
            - Explain the difference between the heat capacities of an ideal gas and a real gas.{774}
            - Estimate the change in specific heat of a gas over temperature ranges.{775}
        Equipartition Theorem:
            - Paste un-numbered outcome here
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        Degrees of Freedom:
            - Solve similar problems for non-monatomic ideal gases based on the number of degrees of freedom of a molecule.{737}
            - Estimate the heat capacities of metals using a model based on degrees of freedom.{738}
        Adiabatic Processes:
            - Define adiabatic expansion of an ideal gas.{779}
            - Demonstrate the qualitative difference between adiabatic and isothermal expansions.{780}
    First Law of Thermodynamics:
        - State the first law of thermodynamics and explain how it is applied.{761}
        - Explain how heat transfer, work done, and internal energy change are related in any thermodynamic process.{762}
        - Describe the work done by a system, heat transfer between objects, and internal energy change of a system.{756}
        - Calculate the work, heat transfer, and internal energy change in a simple process.{757}
    Second Law of Thermodynamics:
        - State the second law of thermodynamics via an irreversible process.{787}
        - Contrast the second law of thermodynamics statements according to Kelvin and Clausius formulations.{802}
        - Interpret the second of thermodynamics via irreversibility.{803} 
    Entropy:
        - Describe the meaning of entropy.{813}
        - Calculate the change of entropy for some simple processes.{814} 
        - Interpret the meaning of entropy at a microscopic scale.{818}
        - Calculate a change in entropy for an irreversible process of a system and contrast with the change in entropy of the universe.{819}
    Heat Engines:
        Subtopic Outcome:
            - Describe the function and components of a heat engine.{791}
            - Explain the efficiency of an engine.{792}
            - Calculate the efficiency of an engine for a given cycle of an ideal gas.{793} 
        The Carnot Cycle:
            - Describe the Carnot cycle with the roles of all four processes involved.{807}
            - Outline the Carnot principle and its implications.{808}
            - Demonstrate the equivalence of the Carnot principle and the second law of thermodynamics.{809}
    Refrigerators:
        - Describe a refrigerator and a heat pump and list their differences.{797}
        - Calculate the performance coefficients of simple refrigerators and heat pumps.{798}
    Third Law of Thermodynamics:
        - Explain the third law of thermodynamics.{820}
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# Topic Break

Electrostatics:
    Topic Outcome:
        - Describe the electric force, both qualitatively and quantitatively.{840}
        - Determine the direction of the electric force for different source charges.{842}
        - Describe some of the many practical applications of electrostatics, including several printing technologies.{937}
        - Relate these applications to Newton’s second law and the electric force.{938}
    Electric Charge:
        - Describe the concept of electric charge.{828}
        - Explain qualitatively the force electric charge creates.{829} 
        - Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge.{853}
        - Describe line charges, surface charges, and volume charges.{854}
    Conductors and Insulators:
        - Explain what a conductor is.{833}
        - Explain what an insulator is.{834}
        - List the differences and similarities between conductors and insulators.{835}
    Induction:
        - Describe the process of charging by induction.{836}
        - Paste un-numbered outcome here
    Coulomb's Law:
        - Calculate the force that charges exert on each other.{841}
        - Paste un-numbered outcome here
    Electric Field:
        Subtopic Outcome:
            - Explain the purpose of the electric field concept.{847}
            - Describe the properties of the electric field.{848}
            - Correctly describe and apply the superposition principle for multiple source charges.{843}
            - Calculate the field of a collection of source charges of either sign.{849}
            - Calculate the field of a continuous source charge distribution of either sign.{855}
        Electric Field Lines:
            - Explain the purpose of an electric field diagram.{859}
            - Describe the relationship between a vector diagram and a field line diagram.{860}
            - Explain the rules for creating a field diagram and why these rules make physical sense.{861}
            - Sketch the field of an arbitrary source charge.{862}
    Electric Dipoles:
        - Describe an electric dipole.{917}
        - Describe a permanent dipole.{866}
        - Describe an induced dipole.{867}
        - Define dipole moment.{918}
        - Define and calculate an electric dipole moment.{868}
        - Explain the physical meaning of the dipole moment.{869} 
    Electric Flux:
        - Define the concept of flux.{875}
        - Describe electric flux.{876}
        - Calculate electric flux for a given situation.{877}
    Gauss's Law:
        - State Gauss’s law.{881}
        - Explain the conditions under which Gauss’s law may be used.{882}
        - Apply Gauss’s law in appropriate systems.{883} 
        - Explain what spherical, cylindrical, and planar symmetry are.{887}
        - Recognize whether or not a given system possesses one of these symmetries.{888}
        - Apply Gauss’s law to determine the electric field of a system with one of these symmetries.{889}
    Conductors in Electrostatics Equilibrium:
        - Describe the electric field within a conductor at equilibrium.{893}
        - Describe the electric field immediately outside the surface of a charged conductor at equilibrium.{894}
        - Explain why if the field is not as described in the first two objectives, the conductor is not at equilibrium.{895}
    Electric Potential:
        Subtopic Outcome:
            - Define the work done by an electric force.{901}
            - Define electric potential, voltage, and potential difference.{907}
            - Define the electron-volt.{908}
            - Describe systems in which the electron-volt is a useful unit.{910}
            - Apply work and potential energy in systems with electric charges.{903}
            - Apply conservation of energy to electric systems.{911} 
        Electric Potential Energy:
            - Define electric potential energy.{902}
            - Calculate electric potential and potential difference from potential energy and electric field.{909}
            - Calculate the potential due to a point charge.{915}
            - Calculate the potential of a system of multiple point charges.{916}
            - Calculate the potential of a continuous charge distribution.{919} 
        Potential Difference:
            - Calculate electric potential and potential difference from potential energy and electric field.{909}
            - Paste un-numbered outcome here
        Equipotential Surfaces:
            - Define equipotential surfaces and equipotential lines.{929}
            - Explain the relationship between equipotential lines and electric field lines.{930}
            - Map equipotential lines for one or two point charges.{931}
            - Describe the potential of a conductor.{932}
            - Compare and contrast equipotential lines and elevation lines on topographic maps.{933}
        Connecting Potential and Field:
            - Explain how to calculate the electric field in a system from the given potential.{923}
            - Calculate the electric field in a given direction from a given potential.{924}
            - Calculate the electric field throughout space from a given potential.{925} 

# Topic Break

Magnetism:
    Topic Outcome:
        - Explain attraction and repulsion by magnets.{1054}
        - Describe the historical and contemporary applications of magnetism.{1055}
        - Explain how a mass spectrometer works to separate charges.{1086}
        - Explain how a cyclotron works.{1087} 
    Magnetic Field:
        Subtopic Outcome:
            - Define the magnetic field based on a moving charge experiencing a force.{1059}
            - Solve for the electric field based on a changing magnetic flux in time.{1149}
            - Explain how energy can be stored in a magnetic field.{1187}
            - Derive the equation for energy stored in a coaxial cable given the magnetic energy density.{1188}
            - Sketch the magnetic field created from a thin, straight wire by using the second right-hand rule.{1100}
        Magnetic Field Lines:
            - Sketch magnetic field lines to understand which way the magnetic field points and how strong it is in a region of space.{1061}
            - Paste un-numbered outcome here
        Motion of Charged Particle in Magnetic Field:
            - Explain how a charged particle in an external magnetic field undergoes circular motion.{1065}
            - Describe how to determine the radius of the circular motion of a charged particle in a magnetic field.{1066} 
        Magnetic Field Produced by Electrical Currents(Ampere's Law and Biot-Savart Law):
            - Explain how Ampère’s law relates the magnetic field produced by a current to the value of the current.{1115}
            - Calculate the magnetic field from a long straight wire, either thin or thick, by Ampère’s law.{1116} 
            - Explain how to derive a magnetic field from an arbitrary current in a line segment.{1093}
            - Calculate magnetic field from the Biot-Savart law in specific geometries, such as a current in a line and a current in a circular arc.{1094}
            - Explain how the Biot-Savart law is used to determine the magnetic field due to a thin, straight wire.{1098}
            - Determine the dependence of the magnetic field from a thin, straight wire based on the distance from it and the current flowing in the wire.{1099}
            - Explain how the Biot-Savart law is used to determine the magnetic field due to a current in a loop of wire at a point along a line perpendicular to the plane of the loop.{1110}
            - Determine the magnetic field of an arc of current.{1111}
    Magnetic Force:
        Subtopic Outcome:
            - Paste un-numbered outcome here
            - Paste un-numbered outcome here
        Magnetic Force on Moving Charges:
            - Apply the right-hand rule to determine the direction of a magnetic force based on the motion of a charge in a magnetic field.{1060}
            - Paste un-numbered outcome here
        Magnetic Force on Current-Carrying Wires:
            - Determine the direction in which a current-carrying wire experiences a force in an external magnetic field.{1070}
            - Calculate the force on a current-carrying wire in an external magnetic field.{1071}
            - Explain how parallel wires carrying currents can attract or repel each other.{1104}
            - Define the ampere and describe how it is related to current-carrying wires.{1105}
            - Calculate the force of attraction or repulsion between two current-carrying wires.{1106}
        Magnetic Force and Torque on Current Loops:
            - Evaluate the net force on a current loop in an external magnetic field.{1075}
            - Evaluate the net torque on a current loop in an external magnetic field.{1076}
            - Define the magnetic dipole moment of a current loop.{1077} 
    Magnetic Properties of Matter:
        - Classify magnetic materials as paramagnetic, diamagnetic, or ferromagnetic, based on their response to a magnetic field.{1125}
        - Sketch how magnetic dipoles align with the magnetic field in each type of substance.{1126}
        - Define hysteresis and magnetic susceptibility, which determines the type of magnetic material.{1127}
    The Hall Effect:
        - Explain a scenario where the magnetic and electric fields are crossed and their forces balance each other as a charged particle moves through a velocity selector.{1081}
        - Compare how charge carriers move in a conductive material and explain how this relates to the Hall effect.{1082} 
    Solenoids:
        - Establish a relationship for how the magnetic field of a solenoid varies with distance and current by using both the Biot-Savart law and Ampère’s law.{1120}
        - Establish a relationship for how the magnetic field of a toroid varies with distance and current by using Ampère’s law.{1121} 
        - Derive the self-inductance for a cylindrical solenoid.{1182}
        - Derive the self-inductance for a rectangular toroid.{1183} 
    Magnetic Flux:
        - Determine the magnetic flux through a surface, knowing the strength of the magnetic field, the surface area, and the angle between the normal to the surface and the magnetic field.{1133}
        - Paste un-numbered outcome here
    Electromagnetic Induction:
        Subtopic Outcome:
            - Use Faraday’s law with Lenz’s law to determine the induced emf in a coil and in a solenoid.{1139}
            - Explain how computer hard drives and graphic tablets operate using magnetic induction.{1164}
            - Explain how hybrid/electric vehicles and transcranial magnetic stimulation use magnetic induction to their advantage.{1165} 
            - Explain how an electric generator works.{1158}
            - Determine the induced emf in a loop at any time interval, rotating at a constant rate in a magnetic field.{1159}
            - Show that rotating coils have an induced emf; in motors this is called back emf because it opposes the emf input to the motor.{1160} 
        Induced Currents:
            - Explain the concept of induced currents resulting from changes in magnetic flux.
            - Predict the direction of induced currents in conductive materials based on the changing magnetic flux.
            - Calculate the magnitude of induced currents in conductors when exposed to changing magnetic fields.
            - Identify practical applications of induced currents, such as electromagnetic braking, induction heating, and metal detection.
        Induced Fields:
            - Predict the direction and magnitude of induced magnetic fields when there are changes in magnetic flux.
            - Calculate the magnitude of induced magnetic fields around a current-carrying conductor when the current changes.
            - Apply the right-hand rule to determine the direction of induced magnetic fields in relation to current changes.
            - Identify real-world applications of induced magnetic fields, such as in transformers, solenoids, and magnetic sensors.
        Motional EMF:
            - Determine the magnitude of an induced emf in a wire moving at a constant speed through a magnetic field.{1143}
            - Discuss examples that use motional emf, such as a rail gun and a tethered satellite.{1144} 
        Eddy Currents:
            - Explain how eddy currents are created in metals.{1153}
            - Describe situations where eddy currents are beneficial and where they are not helpful.{1154} 
        Faraday's Law:
            - Define Faraday’s law and explain its fundamental principle in the context of electromagnetic induction.
            - Use Faraday’s law to determine the magnitude of induced emf in a closed loop due to changing magnetic flux through the loop.{1134} 
            - Connect the relationship between an induced emf from Faraday’s law to an electric field, thereby showing that a changing magnetic flux creates an electric field.{1148}
            - Analyze practical scenarios where  Faraday’s laws are applied, such as generators, transformers, and induction cooktops.
        Lenz's Law:
            - Use Lenz’s law to determine the direction and polarity of induced emf whenever a magnetic flux changes.{1138}
            - Define Lenz’s law and explain its fundamental principle in the context of electromagnetic induction and describe how Lenz’s law is a consequence of the law of conservation of energy.
            - Apply Lenz’s law to predict the direction of induced currents in conductors when exposed to changing magnetic fields.
            - Analyze how Lenz’s law applies to real-world situations involving changing magnetic fields.

# Topic Break

Electromagnetic Waves:
    Topic Outcome:
        - Describe how electromagnetic waves are produced and detected.{1252}
        - Calculate the relative magnitude of the electric and magnetic fields in an electromagnetic plane wave.{1251}
        - Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes.{1256}
        - Calculate the Poynting vector and the energy intensity of electromagnetic waves.{1257}
        - Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequency.{1258} 
        - Describe the relationship of the radiation pressure and the energy density of an electromagnetic wave.{1262}
        - Explain how the radiation pressure of light, while small, can produce observable astronomical effects.{1263} 
    Electromagnetic Spectrum:
        - Explain how electromagnetic waves are divided into different ranges, depending on wavelength and corresponding frequency.{1267}
        - Describe how electromagnetic waves in different categories are produced.{1268}
        - Describe some of the many practical everyday applications of electromagnetic waves.{1269}
    Maxwell's Equations:
        - Explain Maxwell’s correction of Ampère’s law by including the displacement current.{1242}
        - State and apply Maxwell’s equations in integral form.{1243}
        - Describe how the symmetry between changing electric and changing magnetic fields explains Maxwell’s prediction of electromagnetic waves.{1244}
        - Describe how Hertz confirmed Maxwell’s prediction of electromagnetic waves.{1245}
        - Describe how Maxwell’s equations predict the relative directions of the electric fields and magnetic fields, and the direction of propagation of plane electromagnetic waves.{1249}
        - Explain how Maxwell’s equations predict that the speed of propagation of electromagnetic waves in free space is exactly the speed of light.{1250}

# Topic Break

Circuits:
    Topic Outcome:
        - Define the drift velocity of charges moving through a metal.{984}
        - Describe the operation of an incandescent lamp.{986} 
        - Explain the differences between direct current (dc) and alternating current (ac).{1209}
        - List the basic concepts involved in house wiring.{1045}
        - Define the terms thermal hazard and shock hazard.{1046}
        - Describe the effects of electrical shock on human physiology and their relationship to the amount of current through the body.{1047}
        - Explain the function of fuses and circuit breakers.{1048}
    Current:
        Subtopic Outcome:
            - Describe an electrical current.{978}
            - Define the unit of electrical current.{979}
            - Explain the direction of current flow.{980}
            - Define the drift velocity of charges moving through a metal.{984}
            - Describe the operation of an incandescent lamp.{986}
        Current Density:
            - Define the vector current density.{985}
            - Paste un-numbered outcome here
    Resistance:
        Subtopic Outcome:
            - Differentiate between resistance and resistivity.{990}
            - State the relationship between resistance of a resistor and its length, cross-sectional area, and resistivity.{993}
            - Define the term equivalent resistance.{1021}
        Conductivity:
            - Define the term conductivity.{991}
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        Resistivity:
            - State the relationship between resistivity and temperature.{994} 
            - Paste un-numbered outcome here
        Superconductors:
            - Describe the phenomenon of superconductivity.{1009}
            - List applications of superconductivity.{1010} 
    Ohm's Law:
        - Describe Ohm’s law.{998}
        - Recognize when Ohm’s law applies and when it does not.{999} 
    Electrical Energy:
        - Calculate the energy efficiency and cost effectiveness of appliances and equipment.{1005}
        - Paste un-numbered outcome here
    Electrical Power:
        - Express electrical power in terms of the voltage and the current.{1003}
        - Describe the power dissipated by a resistor in an electric circuit.{1004}
        - Determine the relationship between the phase angle of the current and voltage and the average power, known as the power factor.{1226} 
        - Explain the width of the average power versus angular frequency curve and its significance using terms like bandwidth and quality factor.{1231} 
    Capacitors:
        Subtopic Outcome:
            - Explain the concepts of a capacitor and its capacitance.{944}
            - Compute the potential difference across the plates and the charge on the plates for a capacitor in a network and determine the net capacitance of a network of capacitors.{950} 
        Capacitance:
            - Describe how to evaluate the capacitance of a system of conductors.{945}
            - Paste un-numbered outcome here
        Capacitors in Series:
            - Explain how to determine the equivalent capacitance of capacitors in series and in parallel combinations.{949}
            - Paste un-numbered outcome here
        Capacitors in Parallel:
            - Explain how to determine the equivalent capacitance of capacitors in series and in parallel combinations.{949}
            - Paste un-numbered outcome here
        Energy Stored in Capacitor:
            - Explain how energy is stored in a capacitor.{954}
            - Use energy relations to determine the energy stored in a capacitor network.{955}
        Capacitor with a Dielectric:
            - Describe the effects a dielectric in a capacitor has on capacitance and other properties.{959}
            - Calculate the capacitance of a capacitor containing a dielectric.{960}
            - Explain the polarization of a dielectric in a uniform electrical field.{970}
            - Describe the effect of a polarized dielectric on the electrical field between capacitor plates.{971}
            - Explain dielectric breakdown.{972} 
    Resistors:
        Subtopic Outcome:
            - Describe the electrical component known as a resistor.{992}
            - Describe the power dissipated by a resistor in an electric circuit.{1004}
        Resistors in Series:
            - Calculate the equivalent resistance of resistors connected in series.{1022}
            - Paste un-numbered outcome here
        Resistors in Parallel:
            - Calculate the equivalent resistance of resistors connected in parallel.{1023}
            - Paste un-numbered outcome here
    Batteries:
        Subtopic Outcome:
            - Explain the basic operation of a battery.{1017}
            - Paste un-numbered outcome here
        Real Batteries:
            - Paste un-numbered outcome here
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        Ideal Batteries:
            - Paste un-numbered outcome here
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    Electromotive Force:
        - Describe the electromotive force (emf) and the internal resistance of a battery.{1016}
        - Paste un-numbered outcome here
    Electrical Measuring Devices:
        Subtopic Outcome:
            - Paste un-numbered outcome here
            - Paste un-numbered outcome here
        Voltmeters:
            - Describe how to connect a voltmeter in a circuit to measure voltage.{1033}
            - Paste un-numbered outcome here
        Ammeters:
            - Describe how to connect an ammeter in a circuit to measure current.{1034}
            - Paste un-numbered outcome here
        Ohmmeters:
            - Describe the use of an ohmmeter.{1035}
            - Paste un-numbered outcome here
    Kichhoff's Rules:
        Subtopic Outcome:
            - Analyze complex circuits using Kirchhoff’s rules.{1029}
            - Paste un-numbered outcome here
        Loop Rule:
            - State Kirchhoff’s loop rule.{1028}
            - Paste un-numbered outcome here
        Junction Rule:
            - State Kirchhoff’s junction rule.{1027}
            - Paste un-numbered outcome here
    RC Circuits:
        Subtopic Outcome:
            - List some applications of RC circuits.{1041}
            - Paste un-numbered outcome here
        Charging a Capacitor:
            - Describe the charging process of a capacitor.{1039}
            - Paste un-numbered outcome here
        Discharging a Capacitor:
            - Describe the discharging process of a capacitor.{1040}
            - Paste un-numbered outcome here
    Inductors:
        Subtopic Outcome:
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        Inductance:
            - Correlate two nearby circuits that carry time-varying currents with the emf induced in each circuit.{1176}
            - Describe examples in which mutual inductance may or may not be desirable.{1177}
            - Correlate the rate of change of current to the induced emf created by that current in the same circuit.{1181}
            - Derive the self-inductance for a cylindrical solenoid.{1182}
            - Derive the self-inductance for a rectangular toroid.{1183} 
        RL Circuits:
            - Analyze circuits that have an inductor and resistor in series.{1192}
            - Describe how current and voltage exponentially grow or decay based on the initial conditions.{1193} 
        RLC Series Circuits:
            - Determine the angular frequency of oscillation for a resistor, inductor, capacitor (𝑅𝐿𝐶) series circuit.{1202}
            - Relate the 𝑅𝐿𝐶 circuit to a damped spring oscillation.{1203} 
        LC Circuits:
            - Paste un-numbered outcome here
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    Alternating-Current Circuits:
        Subtopic Outcome:
            - Define characteristic features of alternating current and voltage, such as the amplitude or peak and the frequency.{1210}
            - Interpret phasor diagrams and apply them to ac circuits with resistors, capacitors, and inductors.{1214}
            - Define the reactance for a resistor, capacitor, and inductor to help understand how current in the circuit behaves compared to each of these devices.{1215}
            - Describe how the current varies in a resistor, a capacitor, and an inductor while in series with an ac power source.{1219}
            - Use phasors to understand the phase angle of a resistor, capacitor, and inductor ac circuit and to understand what that phase angle means.{1220}
            - Calculate the impedance of a circuit.{1221} 
            - Describe how average power from an ac circuit can be written in terms of peak current and voltage and of rms current and voltage.{1225}
            - Determine the peak ac resonant angular frequency for a RLC circuit.{1230}
        Alternating-Current Sources:
            - Paste un-numbered outcome here
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        Transformers:
            - Paste un-numbered outcome here
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# Topic Break

Optics:
    Topic Outcomes: 
        - List the ways in which light travels from a source to another location.
        - Describe Huygens’s principle.
        - Explain the phenomenon of interference.
        - Explain the phenomenon of diffraction and the conditions under which it is observed. 
        - Determine the location of an image and calculate its properties by using a ray diagram.
    Nature of light: 
        - Subtopic outcome:
            - Paste un-numbered outcome here
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        - Reflection:
            - Explain the reflection of light from polished and rough surfaces.
            - Describe the principle and applications of corner reflectors.
            - Use Huygens’s principle to explain the law of reflection.
        - Total internal reflection: 
            - Explain the phenomenon of total internal reflection.
            - Describe the workings and uses of optical fibers.
            - Analyze the reason for the sparkle of diamond.
        - Refraction: 
            - Describe how rays change direction upon entering a medium.
            - Determine the index of refraction, given the speed of light in a medium.
            - Apply the law of refraction in problem solving.
            - Use Huygens’s principle to explain the law of refraction.
        - Dispersion: 
            - Explain the cause of dispersion in a prism.
            - Describe the effects of dispersion in producing rainbows.
            - Summarize the advantages and disadvantages of dispersion.
        - Polarization:
            - Explain the change in intensity as polarized light passes through a polarizing filter.
            - Calculate the effect of polarization by reflection and Brewster’s angle.
            - Describe the effect of polarization by scattering.
            - Explain the use of polarizing materials in devices such as LCDs.
    Interference:
        Subtopic outcome:
            - Use Huygens’s principle to explain interference.
            - Paste un-numbered outcome here
            - Paste un-numbered outcome here          
        Double-slit interference:
            - Define constructive and destructive interference for a double slit.
            - Determine the angles for bright and dark fringes for double slit interference.
            - Calculate the positions of bright fringes on a screen.
        Multiple-slit interference:
            - Describe the locations and intensities of secondary maxima for multiple-slit interference.
            - Paste un-numbered outcome here
        Thin-film interference:
            - Describe the phase changes that occur upon reflection.
            - Describe fringes established by reflected rays of a common source.
            - Explain the appearance of colors in thin films.
        Interferometer:
            - Explain changes in fringes observed with a Michelson interferometer caused by mirror movements.
            - Explain changes in fringes observed with a Michelson interferometer caused by changes in medium.
    Diffraction:
        Subtopic outcome:
            - Use Huygens’s principle to explain diffraction.
            - Describe interference and diffraction effects exhibited by X-rays in interaction with atomic-scale structures.
        Single-slit diffraction:
            - Describe diffraction through a single slit.
            - Calculate the intensity relative to the central maximum of the single-slit diffraction peaks.
            - Calculate the intensity relative to the central maximum of an arbitrary point on the screen.
        Double-slit diffraction:
            - Describe the combined effect of interference and diffraction with two slits, each with finite width.
            - Determine the relative intensities of interference fringes within a diffraction pattern.
            - Identify missing orders, if any.
        Diffraction gratings:
            - Discuss the pattern obtained from diffraction gratings.
            - Explain diffraction grating effects.
            - Applying the formula for diffraction grating.
        Diffraction limit:
            - Describe the diffraction limit on resolution.
            - Describe the diffraction limit on beam propagation.
        Holography:
            - Describe how a three-dimensional image is recorded as a hologram.
            - Describe how a three-dimensional image is formed from a hologram.
            
    Geometric optics:
        Subtopic outcome:
            - Distinguish between real and virtual images.
            - Understand the basic physics of how images are formed by the human eye.
            - Recognize several conditions of impaired vision as well as the optics principles for treating these conditions.
            - Describe the optics of a camera.
            - Characterize the image created by a camera.
            - Understand the optics of a simple magnifier
            - Characterize the image created by a simple magnifier
            - Explain the physics behind the operation of microscopes and telescopes
            - Describe the image created by different instruments and calculate their magnifications
        Plane mirrors:
            - Describe how an image is formed by a plane mirror.
            - Find the location and characterize the orientation of an image created by a plane mirror.
        Spherical mirrors:
            - Describe image formation by spherical mirrors.
            - Use ray diagrams and the mirror equation to calculate the properties of an image in a spherical mirror.
        Refracting surfaces:
            - Describe image formation by a single refracting surface.
            - Determine the location of an image and calculate its properties by using the equation for a single refracting surface.
        Thin lenses:
            - Use ray diagrams to locate and describe the image formed by a lens
            - Employ the thin-lens equation to describe and locate the image formed by a lens
# Topic Break

Relativity:
    Topic Outcomes: 
        - Describe the theoretical and experimental issues that Einstein’s theory of special relativity addressed.
        - State the two postulates of the special theory of relativity.
    Simultaneity: 
        - Show from Einstein's postulates that two events measured as simultaneous in one inertial frame are not necessarily simultaneous in all inertial frames.
        - Describe how simultaneity is a relative concept for observers in different inertial frames in relative motion.
    Time dilation:
        - Explain how time intervals can be measured differently in different reference frames.
        - Describe how to distinguish a proper time interval from a dilated time interval.
        - Describe the significance of the muon experiment.
        - Explain why the twin paradox is not a contradiction.
        - Calculate time dilation given the speed of an object in a given frame.
    Length contraction:
        - Explain how simultaneity and length contraction are related.
        - Describe the relation between length contraction and time dilation and use it to derive the length-contraction equation.
    Lorentz transformation:
        - Describe the Galilean transformation of classical mechanics, relating the position, time, velocities, and accelerations measured in different inertial frames.
        - Derive the corresponding Lorentz transformation equations, which, in contrast to the Galilean transformation, are consistent with special relativity.
        - Explain the Lorentz transformation and many of the features of relativity in terms of four-dimensional space-time.
    Velocity transformation:
        - Derive the equations consistent with special relativity for transforming velocities in one inertial frame of reference into another.
        - Apply the velocity transformation equations to objects moving at relativistic speeds.
        - Examine how the combined velocities predicted by the relativistic transformation equations compare with those expected classically.
    Relativistic doppler shift:
        - Explain the origin of the shift in frequency and wavelength of the observed wavelength when observer and source moved toward or away from each other.
        - Derive an expression for the relativistic Doppler shift.
        - Apply the Doppler shift equations to real-world examples.
    Relativistic momentum:
        - Define relativistic momentum in terms of mass and velocity.
        - Show how relativistic momentum relates to classical momentum.
        - Show how conservation of relativistic momentum limits objects with mass to speeds less than c.
    Relativistic energy:
        - Explain how the work-energy theorem leads to an expression for the relativistic kinetic energy of an object.
        - Show how the relativistic energy relates to the classical kinetic energy, and sets a limit on the speed of any object with mass.
        - Describe how the total energy of a particle is related to its mass and velocity.
        - Explain how relativity relates to energy-mass equivalence, and some of the practical implications of energy-mass equivalence.

# Topic Break
Quantum mechanics:
    Topic outcome:
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    Wave function:
        - Describe the statistical interpretation of the wave function.
        - Use the wave function to determine probabilities.
        - Calculate expectation values of position, momentum, and kinetic energy.
    Heisenberg uncertainty principle:
        - Describe the physical meaning of the position-momentum uncertainty relation.
        - Explain the origins of the uncertainty principle in quantum theory.
        - Describe the physical meaning of the energy-time uncertainty relation.
    Schrodinger equation:
        - Describe the role Schrӧdinger’s equation plays in quantum mechanics.
        - Explain the difference between time-dependent and -independent Schrӧdinger’s equations.
        - Interpret the solutions of Schrӧdinger’s equation.
    Stationary states:
        Subtopic outcome:
            - Describe how to set up a boundary-value problem for the stationary Schrӧdinger equation.
            - Describe the physical meaning of stationary solutions to Schrӧdinger’s equation and the connection of these solutions with time-dependent quantum states.
        Infinite square well:
            - Explain why the energy of a quantum particle in a box is quantized.
            - Explain the physical meaning of Bohr’s correspondence principle.
        Harmonic oscillator:
            - Describe the model of the quantum harmonic oscillator.
            - Identify differences between the classical and quantum models of the harmonic oscillator.
            - Explain physical situations where the classical and the quantum models coincide.
    Quantum tunneling:
        - Describe how a quantum particle may tunnel across a potential barrier
        - Identify important physical parameters that affect the tunneling probability
        - Identify the physical phenomena where quantum tunneling is observed
        - Explain how quantum tunneling is utilized in modern technologies
        
# Topic Break
        
Atomic structure:
    Topic outcome:
        - Paste un-numbered outcome here
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    Hydrogen atom:
        - Describe the hydrogen atom in terms of wave function, probability density, total energy, and orbital angular momentum.
        - Identify the physical significance of each of the quantum numbers (n,l,m) of the hydrogen atom.
        - Distinguish between the Bohr and Schrödinger models of the atom.
        - Use quantum numbers to calculate important information about the hydrogen atom.
    Magnetic dipole moment:
        - Explain why the hydrogen atom has magnetic properties.
        - Explain why the energy levels of a hydrogen atom associated with orbital angular momentum are split by an external magnetic field.
        - Use quantum numbers to calculate the magnitude and direction of the orbital magnetic dipole moment of a hydrogen atom.
    Electron spin:
        - Express the state of an electron in a hydrogen atom in terms of five quantum numbers.
        - Use quantum numbers to calculate the magnitude and direction of the spin and magnetic moment of an electron.
        - Explain the fine and hyperfine structure of the hydrogen spectrum in terms of magnetic interactions inside the hydrogen atom.
    Exclusion principle:
        - Explain the importance of Pauli’s exclusion principle to an understanding of atomic structure and molecular bonding.
    Periodic table:
        - Explain the structure of the periodic table in terms of the total energy, orbital angular momentum, and spin of individual electrons in an atom.
        - Describe the electron configuration of atoms in the periodic table.
    Lasers:
        - Describe the physical processes necessary to produce laser light.
        - Explain the difference between coherent and incoherent light.
        - Describe the application of lasers to a CD and Blu-Ray player.
    Atomic spectra:
        - Describe the absorption and emission of radiation in terms of atomic energy levels and energy differences.
        - Use quantum numbers to estimate the energy, frequency, and wavelength of photons produced by atomic transitions in multi-electron atoms.
        - Explain radiation concepts in the context of atomic fluorescence and X-rays.
    

# Topic Break
Condensed matter physics:
    Topic outcome:
        - Paste un-numbered outcome here
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    Molecular bonds:
        - Distinguish between the different types of molecular bonds.
        - Determine the dissociation energy of a molecule using the concepts ionization energy, electron affinity, and Coulomb force.
        - Describe covalent bonding in terms of exchange symmetry.
        - Explain the physical structure of a molecule in terms of the concept of hybridization.
    Molecular spectra:
        - Use the concepts of vibrational and rotational energy to describe energy transitions in a diatomic molecule.
        - Explain key features of a vibrational-rotational energy spectrum of a diatomic molecule.
        - Estimate allowed energies of a rotating molecule.
        - Determine the equilibrium separation distance between atoms in a diatomic molecule from the vibrational-rotational absorption spectrum.
    Bonding in crystalline solids:
        - Describe the packing structures of common solids. 
        - Explain the difference between bonding in a solid and in a molecule.
        - Determine the equilibrium separation distance given crystal properties.
        - Determine the dissociation energy of a salt given crystal properties.
    Free electron model of metals:
        - Describe the classical free electron model of metals in terms of the concept electron number density.
        - Explain the quantum free-electron model of metals in terms of Pauli’s exclusion principle.
        - Calculate the energy levels and energy-level spacing of a free electron in a metal.
    Band theory of solids:
        - Describe two main approaches to determining the energy levels of an electron in a crystal.
        - Explain the presence of energy bands and gaps in the energy structure of a crystal.
        - Explain why some materials are good conductors and others are good insulators.
        - Differentiate between an insulator and a semiconductor.
    Semiconductors:
        Subtopic outcome:
            - Distinguish between an n-type and p-type semiconductor.
            - Describe the Hall effect and explain its significance.
            - Calculate the charge, drift velocity, and charge carrier number density of a semiconductor using information from a Hall effect experiment.
        Doping:
            - Describe changes to the energy structure of a semiconductor due to doping.
        Semiconductor devices:
            - Describe what occurs when n- and p-type materials are joined together using the concept of diffusion and drift current (zero applied voltage).
            - Explain the response of a p-n junction to a forward and reverse bias voltage.
            - Describe the function of a transistor in an electric circuit.
            - Use the concept of a p-n junction to explain its applications in audio amplifiers and computers.
    Superconductivity:
        - Describe the main features of a superconductor.
        - Describe the BCS theory of superconductivity.
        - Determine the critical magnetic field for T = 0 K from magnetic field data.
        - Calculate the maximum emf or current for a wire to remain superconducting.