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**AP PHYSICS 1:**

**BIG IDEAS AND LEARNING OBJECTIVES**

**KINEMATICS**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.A.1.1:**The student is able to express the motion of an object using narrative, mathematical, and graphical representations.

**[SP 1.5, 2.1, 2.2]**

**3.A.1.2:**The student is able to design an experimental investigation of the motion of an object.

**[SP 4.2]**

**3.A.1.3:**The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations.

**[SP 5.1]**

**DYNAMICS**

**BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.**

**1.C.1.1:**The student is able to design an experiment for collecting data to determine the relationship between the net force exerted on an object its inertial mass and its acceleration.

**[SP 4.2]**

**1.C.3.1:**The student is able to design a plan for collecting data to measure gravitational mass and to measure inertial mass and to distinguish between the two experiments.

**[SP 4.2]**

**BIG IDEA 2: Fields existing in space can be used to explain interactions.**

**2.B.1.1:**The student is able to apply F mg to calculate the gravitational force on an object with mass

*m*in a gravitational field of strength

*g*in the context of the effects of a net force on objects and systems.

**[SP 2.2, 7.2]**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.A.2.1:**The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation.

**[SP 1.1]**

**3.A.3.1:**The student is able to analyze a scenario and make claims (develop arguments, justify assertions) about the forces exerted on an object by other objects for different types of forces or components of forces.

**[SP 6.4, 7.2]**

**3.A.3.2:**The student is able to challenge a claim that an object can exert a force on itself.

**[SP 6.1]**

**3.A.3.3:**The student is able to describe a force as an interaction between two objects and identify both objects for any force.

**[SP 1.4]**

**3.A.4.1:**The student is able to construct explanations of physical situations involving the interaction of bodies using Newton’s third law and the representation of action-reaction pairs of forces.

**[SP 1.4, 6.2]**

**3.A.4.2:**The student is able to use Newton’s third law to make claims and predictions about the actionreaction pairs of forces when two objects interact.

**[SP 6.4, 7.2]**

**3.A.4.3:**The student is able to analyze situations involving interactions among several objects by using freebody diagrams that include the application of Newton’s third law to identify forces.

**[SP 1.4]**

**3.B.1.1:**The student is able to predict the motion of an object subject to forces exerted by several objects using an application of Newton’s second law in a variety of physical situations with acceleration in one dimension.

**[SP 6.4, 7.2]**

**3.B.1.2:**The student is able to design a plan to collect and analyze data for motion (static, constant, or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces.

**[SP 4.2, 5.1]**

**3.B.1.3:**The student is able to reexpress a free-body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object.

**[SP 1.5, 2.2]**

**3.B.2.1:**The student is able to create and use free-body diagrams to analyze physical situations to solve

problems with motion qualitatively and quantitatively.

**[SP 1.1, 1.4, 2.2]**

**3.C.4.1:**The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces.

**[SP 6.1]**

**3.C.4.2:**The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions.

**[SP 6.2]**

**BIG IDEA 4: Interactions between systems can result in changes in those systems.**

**4.A.1.1**The student is able to use representations of the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semiquantitatively.

**[SP 1.2, 1.4, 2.3, 6.4]**

**4.A.2.1:**The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the change in velocity per unit time, and velocity is equal to the change in position per unit time.

**[SP 6.4]**

**4.A.2.2:**The student is able to evaluate using given data whether all the forces on a system or whether all the parts of a system have been identified.

**[SP 5.3]**

**4.A.2.3:**The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system.

**[SP 1.4, 2.2]**

**4.A.3.1:**The student is able to apply Newton’s second law to systems to calculate the change in the center-ofmass velocity when an external force is exerted on the system.

**[SP 2.2]**

**4.A.3.2:**The student is able to use visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center-of-mass velocity of that system.

**[SP 1.4]**

**CIRCULAR MOTION AND GRAVITATION**

**BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.**

**1.C.3.1:**The student is able to design a plan for collecting data to measure gravitational mass and to measure inertial mass and to distinguish between the two experiments.

**[SP 4.2]**

**BIG IDEA 2: Fields existing in space can be used to explain interactions.**

**2.B.1.1:**The student is able to apply F mg to calculate the gravitational force on an object with mass

*m*in a gravitational field of strength

*g*in the context of the effects of a net force on objects and systems.

**[SP 2.2, 7.2]**

M

**2.B.2.1:**The student is able to apply g to calculate the gravitational field due to an object with mass

*M*, r where the field is a vector directed toward the center of the object of mass

*M*.

**[SP 2.2]**

**2.B.2.2:**The student is able to approximate a numerical value of the gravitational field (

*g*) near the surface of an object from its radius and mass relative to those of the Earth or other reference objects.

**[SP 2.2]**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.A.2.1:**The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation.

**[SP 1.1]**

**3.A.3.1:**The student is able to analyze a scenario and make claims (develop arguments, justify assertions) about the forces exerted on an object by other objects for different types of forces or components of forces.

**[SP 6.4, 7.2]**

**3.A.3.3:**The student is able to describe a force as an interaction between two objects and identify both objects for any force.

**[SP 1.4]**

**3.A.4.1:**The student is able to construct explanations of physical situations involving the interaction of bodies using Newton’s third law and the representation of action-reaction pairs of forces.

**[SP 1.4, 6.2]**

**3.A.4.2:**The student is able to use Newton’s third law to make claims and predictions about the action-

reaction pairs of forces when two objects interact.

**[SP 6.4, 7.2]**

**3.A.4.3:**The student is able to analyze situations involving interactions among several objects by using freebody diagrams that include the application of Newton’s third law to identify forces.

**[SP 1.4]**

**3.B.1.2:**The student is able to design a plan to collect and analyze data for motion (static, constant, or accelerating) from force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces.

**[SP 4.2, 5.1]**

**3.B.1.3:**The student is able to re-express a free-body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object.

**[SP 1.5, 2.2]**

**3.B.2.1:**The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively.

**[SP 1.1, 1.4, 2.2]**

**3.C.1.1:**The student is able to use Newton’s law of gravitation to calculate the gravitational force the two objects exert on each other and use that force in contexts other than orbital motion.

**[SP 2.2]**

**3.C.1.2:**The student is able to use Newton’s law of gravitation to calculate the gravitational force between two objects and use that force in contexts involving orbital motion

**[SP 2.2]**

**3.C.2.2:**The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces.

**[SP 7.2]**

**3.G.1.1:**The student is able to articulate situations when the gravitational force is the dominant force and when the electromagnetic, weak, and strong forces can be ignored.

**[SP 7.1]**

**BIG IDEA 4: Interactions between systems can result in changes in those systems.**

**4.A.2.2:**The student is able to evaluate using given data whether all the forces on a system or whether all the parts of a system have been identified.

**[SP 5.3]**

**ENERGY**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.E.1.1:**The student is able to make predictions about the changes in kinetic energy of an object based on considerations of the direction of the net force on the object as the object moves.

**[SP 6.4, 7.2]**

**3.E.1.2:**The student is able to use net force and velocity vectors to determine qualitatively whether kinetic energy of an object would increase, decrease, or remain unchanged.

**[SP 1.4]**

**3.E.1.3:**The student is able to use force and velocity vectors to determine qualitatively or quantitatively the net force exerted on an object and qualitatively whether kinetic energy of that object would increase, decrease, or remain unchanged.

**[SP 1.4, 2.2]**

**3.E.1.4:**The student is able to apply mathematical routines to determine the change in kinetic energy of an object given the forces on the object and the displacement of the object.

**[SP 2.2]**

**BIG IDEA 4: Interactions between systems can result in changes in those systems.**

**4.C.1.1:**The student is able to calculate the total energy of a system and justify the mathematical routines used in the calculation of component types of energy within the system whose sum is the total energy.

**[SP 1.4, 2.1, 2.2]**

**4.C.1.2:**The student is able to predict changes in the total energy of a system due to changes in position and speed of objects or frictional interactions within the system.

**[SP 6.4]**

**4.C.2.1:**The student is able to make predictions about the changes in the mechanical energy of a system when a component of an external force acts parallel or antiparallel to the direction of the displacement of the center of mass.

**[SP 6.4]**

**4.C.2.2:**The student is able to apply the concepts of Conservation of Energy and the Work-Energy theorem to determine qualitatively and/or quantitatively that work done on a two-object system in linear motion will change the kinetic energy of the center of mass of the system, the potential energy of the systems, and/or the internal energy of the system.

**[SP 1.4, 2.2, 7.2]**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.A.2.1:**The student is able to define open and closed systems for everyday situations and apply conservation concepts for energy, charge, and linear momentum to those situations.

**[SP 6.4, 7.2]**

**5.B.1.1:**The student is able to set up a representation or model showing that a single object can only have kinetic energy and use information about that object to calculate its kinetic energy.

**[SP 1.4, 2.2]**

**5.B.1.2:**The student is able to translate between a representation of a single object, which can only have kinetic energy, and a system that includes the object, which may have both kinetic and potential energies

**. [SP 1.5]**

**5.B.2.1:**The student is able to calculate the expected behavior of a system using the object model (i.e., by ignoring changes in internal structure) to analyze a situation. Then, when the model fails, the student can justify the use of conservation of energy principles to calculate the change in internal energy due to changes in internal structure because the object is actually a system.

**[SP 1.4, 2.1]**

**5.B.3.1:**The student is able to describe and make qualitative and/or quantitative predictions about everyday examples of systems with internal potential energy.

**[SP 2.2, 6.4, 7.2]**

**5.B.3.2:**The student is able to make quantitative calculations of the internal potential energy of a system from a description or diagram of that system.

**[SP 1.4, 2.2]**

**5.B.3.3:**The student is able to apply mathematical reasoning to create a description of the internal potential energy of a system from a description or diagram of the objects and interactions in that system.

**[SP 1.4, 2.2]**

**5.B.4.1:**The student is able to describe and make predictions about the internal energy of systems.

**[SP 6.4,**

**7.2]**

**5.B.4.2:**The student is able to calculate changes in kinetic energy and potential energy of a system, using information from representations of that system.

**[SP 1.4, 2.1, 2.2]**

**5.B.5.1:**The student is able to design an experiment and analyze data to examine how a force exerted on an object or system does work on the object or system as it moves through a distance.

**[SP 4.2, 5.1]**

**5.B.5.2:**The student is able to design an experiment and analyze graphical data in which interpretations of the area under a force-distance curve are needed to determine the work done on or by the object or system.

**[SP 4.2, 5.1]**

**5.B.5.3:**The student is able to predict and calculate from graphical data the energy transfer to or work done on an object or system from information about a force exerted on the object or system through a distance.

**[SP 1.4, 2.2, 6.4]**

**5.B.5.4:**The student is able to make claims about the interaction between a system and its environment in which the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic energy plus potential energy).

**[SP 6.4, 7.2]**

**5.B.5.5:**The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance.

**[SP 2.2, 6.4]**

**5.D.1.1:**The student is able to make qualitative predictions about natural phenomena based on conservation of linear momentum and restoration of kinetic energy in elastic collisions.

**[SP 6.4, 7.2]**

**5.D.1.2:**The student is able to apply the principles of conservation of momentum and restoration of kinetic energy to reconcile a situation that appears to be isolated and elastic, but in which data indicate that linear momentum and kinetic energy are not the same after the interaction, by refining a scientific question to identify interactions that have not been considered. Students will be expected to solve qualitatively and/or quantitatively for one-dimensional situations and only qualitatively in two-dimensional situations.

**[SP 2.2, 3.2, 5.1, 5.3]**

**5.D.1.3:**The student is able to apply mathematical routines appropriately to problems involving elastic collisions in one dimension and justify the selection of those mathematical routines based on conservation of momentum and restoration of kinetic energy.

**[SP 2.1, 2.2]**

**5.D.1.4:**The student is able to design an experimental test of an application of the principle of the conservation of linear momentum, predict an outcome of the experiment using the principle, analyze data generated by that experiment whose uncertainties are expressed numerically, and evaluate the match between the prediction and the outcome.

**[SP 4.2, 5.1, 5.3, 6.4]**

**5.D.1.5:**The student is able to classify a given collision situation as elastic or inelastic, justify the selection of conservation of linear momentum and restoration of kinetic energy as the appropriate principles for analyzing an elastic collision, solve for missing variables, and calculate their values.

**[SP 2.1, 2.2]**

**5.D.2.1:**The student is able to qualitatively predict, in terms of linear momentum and kinetic energy, how the outcome of a collision between two objects changes depending on whether the collision is elastic or inelastic.

**[SP 6.4, 7.2]**

**5.D.2.3:**The student is able to apply the conservation of linear momentum to a closed system of objects involved in an inelastic collision to predict the change in kinetic energy.

**[SP 6.4, 7.2]**

**MOMENTUM**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.D.1.1:**The student is able to justify the selection of data needed to determine the relationship between the direction of the force acting on an object and the change in momentum caused by that force.

**[SP 4.1]**

**3.D.2.1:**The student is able to justify the selection of routines for the calculation of the relationships between changes in momentum of an object, average force, impulse, and time of interaction.

**[SP 2.1]**

**3.D.2.2:**The student is able to predict the change in momentum of an object from the average force exerted on the object and the interval of time during which the force is exerted.

**[SP 6.4]**

**3.D.2.3:**The student is able to analyze data to characterize the change in momentum of an object from the average force exerted on the object and the interval of time during which the force is exerted.

**[SP 5.1]**

**3.D.2.4:**The student is able to design a plan for collecting data to investigate the relationship between changes in momentum and the average force exerted on an object over time.

**[SP 4.2]**

**BIG IDEA 4: Interactions between systems can result in changes in those systems.**

**4.B.1.1:**The student is able to calculate the change in linear momentum of a two-object system with constant mass in linear motion from a representation of the system (data, graphs, etc.).

**[SP 1.4, 2.2]**

**4.B.1.2:**The student is able to analyze data to find the change in linear momentum for a constant-mass system using the product of the mass and the change in velocity of the center of mass.

**[SP 5.1]**

**4.B.2.1:**The student is able to apply mathematical routines to calculate the change in momentum of a system by analyzing the average force exerted over a certain time on the system.

**[SP 2.2]**

**4.B.2.2:**The student is able to perform analysis on data presented as a force-time graph and predict the change in momentum of a system.

**[SP 5.1]**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.A.2.1:**The student is able to define open and closed systems for everyday situations and apply conservation concepts for energy, charge, and linear momentum to those situations.

**[SP 6.4, 7.2]**

**5.D.1.1**: The student is able to make qualitative predictions about natural phenomena based on conservation of linear momentum and restoration of kinetic energy in elastic collisions.

**[SP 6.4, 7.2]**

**5.D.1.2:**The student is able to apply the principles of conservation of momentum and restoration of kinetic energy to reconcile a situation that appears to be isolated and elastic, but in which data indicate that linear momentum and kinetic energy are not the same after the interaction, by refining a scientific question to identify interactions that have not been considered. Students will be expected to solve qualitatively and/or quantitatively for one-dimensional situations and only qualitatively in two-dimensional situations.

**[SP 2.2, 3.2, 5.1, 5.3]**

**5.D.1.3:**The student is able to apply mathematical routines appropriately to problems involving elastic collisions in one dimension and justify the selection of those mathematical routines based on conservation of momentum and restoration of kinetic energy.

**[SP 2.1, 2.2]**

**5.D.1.4:**The student is able to design an experimental test of an application of the principle of the conservation of linear momentum, predict an outcome of the experiment using the principle, analyze data generated by that experiment whose uncertainties are expressed numerically, and evaluate the match between the prediction and the outcome.

**[SP 4.2, 5.1, 5.3, 6.4]**

**5.D.1.5:**The student is able to classify a given collision situation as elastic or inelastic, justify the selection of conservation of linear momentum and restoration of kinetic energy as the appropriate principles for analyzing an elastic collision, solve for missing variables, and calculate their values.

**[SP 2.1, 2.2]**

**5.D.2.1:**The student is able to qualitatively predict, in terms of linear momentum and kinetic energy, how the outcome of a collision between two objects changes depending on whether the collision is elastic or inelastic.

**[SP 6.4, 7.2]**

**5.D.2.2:**The student is able to plan data collection strategies to test the law of conservation of momentum in a two-object collision that is elastic or inelastic and analyze the resulting data graphically.

**[SP 4.1, 4.2, 5.1]**

**5.D.2.3:**The student is able to apply the conservation of linear momentum to a closed system of objects involved in an inelastic collision to predict the change in kinetic energy.

**[SP 6.4, 7.2]**

**5.D.2.4:**The student is able to analyze data that verify conservation of momentum in collisions with and without an external friction force.

**[SP 4.1, 4.2, 4.4, 5.1, 5.3]**

**5.D.2.5:**The student is able to classify a given collision situation as elastic or inelastic, justify the selection of conservation of linear momentum as the appropriate solution method for an inelastic collision, recognize that there is a common final velocity for the colliding objects in the totally inelastic case, solve for missing variables, and calculate their values

**. [SP 2.1, 2.2]**

**5.D.3.1:**The student is able to predict the velocity of the center of mass of a system when there is no interaction outside of the system but there is an interaction within the system (i.e., the student simply recognizes that interactions within a system do not affect the center of mass motion of the system and is able to determine that there is no external force).

**[SP 6.4]**

**SIMPLE HARMONIC MOTION**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.B.3.1:**The student is able to predict which properties determine the motion of a simple harmonic oscillator and what the dependence of the motion is on those properties.

**[SP 6.4, 7.2]**

**3.B.3.2:**The student is able to design a plan and collect data in order to ascertain the characteristics of the motion of a system undergoing oscillatory motion caused by a restoring force.

**[SP 4.2]**

**3.B.3.3:**The student can analyze data to identify qualitative or quantitative relationships between given values and variables (i.e., force, displacement, acceleration, velocity, period of motion, frequency, spring constant, string length, mass) associated with objects in oscillatory motion to use that data to determine the value of an unknown.

**[SP 2.2, 5.1]**

**3.B.3.4:**The student is able to construct a qualitative and/or a quantitative explanation of oscillatory behavior given evidence of a restoring force.

**[SP 2.2, 6.2]**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.B.2.1:**The student is able to calculate the expected behavior of a system using the object model (i.e., by ignoring changes in internal structure) to analyze a situation. Then, when the model fails, the student can justify the use of conservation of energy principles to calculate the change in internal energy due to changes in internal structure because the object is actually a system.

**[SP 1.4, 2.1]**

**5.B.3.1:**The student is able to describe and make qualitative and/or quantitative predictions about everyday examples of systems with internal potential energy.

**[SP 2.2, 6.4, 7.2]**

**5.B.3.2:**The student is able to make quantitative calculations of the internal potential energy of a system from a description or diagram of that system.

**[SP 1.4, 2.2]**

**5.B.3.3:**The student is able to apply mathematical reasoning to create a description of the internal potential energy of a system from a description or diagram of the objects and interactions in that system.

**[SP 1.4, 2.2]**

**5.B.4.1:**The student is able to describe and make predictions about the internal energy of systems.

**[SP 6.4,**

**7.2]**

**5.B.4.2:**The student is able to calculate changes in kinetic energy and potential energy of a system, using information from representations of that system.

**[SP 1.4, 2.1, 2.2]**

**TORQUE AND ROTATIONAL MOTION**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.F.1.1:**The student is able to use representations of the relationship between force and torque.

**[SP 1.4]**

**3.F.1.2:**The student is able to compare the torques on an object caused by various forces.

**[SP 1.4]**

**3.F.1.3:**The student is able to estimate the torque on an object caused by various forces in comparison to other situations.

**[SP 2.3]**

**3.F.1.4:**The student is able to design an experiment and analyze data testing a question about torques in a balanced rigid system.

**[SP 4.1, 4.2, 5.1]**

**3.F.1.5:**The student is able to calculate torques on a two-dimensional system in static equilibrium, by examining a representation or model (such as a diagram or physical construction).

**[SP 1.4, 2.2]**

**3.F.2.1:**The student is able to make predictions about the change in the angular velocity about an axis for an object when forces exerted on the object cause a torque about that axis.

**[SP 6.4]**:

**3.F.2.2:**The student is able to plan data collection and analysis strategies designed to test the relationship between a torque exerted on an object and the change in angular velocity of that object about an axis.

**[SP 4.1, 4.2, 5.1]**

**3.F.3.1:**The student is able to predict the behavior of rotational collision situations by the same processes that are used to analyze linear collision situations using an analogy between impulse and change of linear momentum and angular impulse and change of angular momentum.

**[SP 6.4, 7.2]**

**3.F.3.2:**In an unfamiliar context or using representations beyond equations, the student is able to justify the selection of a mathematical routine to solve for the change in angular momentum of an object caused by torques exerted on the object.

**[SP 2.1]**

**3.F.3.3:**The student is able to plan data collection and analysis strategies designed to test the relationship between torques exerted on an object and the change in angular momentum of that object.

**[SP 4.1, 4.2, 5.1, 5.3]**

**BIG IDEA 4: Interactions between systems can result in changes in those systems.**

**4.A.1.1**The student is able to use representations of the center of mass of an isolated two-object system to analyze the motion of the system qualitatively and semiquantitatively.

**[SP 1.2, 1.4, 2.3, 6.4]**

**4.D.1.1:**The student is able to describe a representation and use it to analyze a situation in which several forces exerted on a rotating system of rigidly connected objects change the angular velocity and angular momentum of the system.

**[SP 1.2, 1.4]**

**4.D.1.2:**The student is able to plan data collection strategies designed to establish that torque, angular velocity, angular acceleration, and angular momentum can be predicted accurately when the variables are treated as being clockwise or counterclockwise with respect to a well-defined axis of rotation, and refine the research question based on the examination of data. [

**SP 3.2, 4.1, 4.2, 5.1, 5.3]**

**4.D.2.1:**The student is able to describe a model of a rotational system and use that model to analyze a situation in which angular momentum changes due to interaction with other objects or systems.

**[SP 1.2, 1.4]**

**4.D.2.2:**The student is able to plan a data collection and analysis strategy to determine the change in angular momentum of a system and relate it to interactions with other objects and systems.

**[SP 4.2]**

**4.D.3.1:**The student is able to use appropriate mathematical routines to calculate values for initial or final angular momentum, or change in angular momentum of a system, or average torque or time during which the

torque is exerted in analyzing a situation involving torque and angular momentum.

**[SP 2.2]**

**4.D.3.2:**The student is able to plan a data collection strategy designed to test the relationship between the change in angular momentum of a system and the product of the average torque applied to the system and the time interval during which the torque is exerted.

**[SP 4.1, 4.2]**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.E.1.1:**The student is able to make qualitative predictions about the angular momentum of a system for a situation in which there is no net external torque.

**[SP 6.4, 7.2]**

**5.E.1.2:**The student is able to make calculations of quantities related to the angular momentum of a system when the net external torque on the system is zero.

**[SP 2.1, 2.2]**

**5.E.2.1:**The student is able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses.

**[SP 2.2]**

**BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.**

**1.B.1.1:**The student is able to make claims about natural phenomena based on conservation of electric charge.

**[SP 6.4]**

**1.B.1.2:**The student is able to make predictions, using the conservation of electric charge, about the sign and relative quantity of net charge of objects or systems after various charging processes, including conservation of charge in simple circuits.

**[SP 6.4, 7.2]**

**1.E.2.1**The student is able to choose and justify the selection of data needed to determine resistivity for a given material.

**[SP 4.1]**

**ELECTRIC CHARGE AND ELECTRIC FORCE**

**1.B.1.1:**The student is able to make claims about natural phenomena based on conservation of electric charge.

**[SP 6.4]**

**1.B.1.2**: The student is able to make predictions, using the conservation of electric charge, about the sign and relative quantity of net charge of objects or systems after various charging processes, including conservation of charge in simple circuits.

**[SP 6.4, 7.2]**

**1.B.2.1**The student is able to construct an explanation of the two-charge model of electric charge based on evidence produced through scientific practices.

**[SP 6.2]**:

**1.B.3.1:**The student is able to challenge the claim that an electric charge smaller than the elementary charge has been isolated.

**[SP 1.5, 6.1, 7.2]**

**BIG IDEA 3: The interactions of an object with other objects can be described by forces.**

**3.C.2.1:**The student is able to use Coulomb’s law qualitatively and quantitatively to make predictions about the interaction between two electric point charges.

**[SP 2.2, 6.4]**

**3.C.2.2**: The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces.

**[See SP 7.2]**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.A.2.1:**The student is able to define open and closed systems for everyday situations and apply conservation concepts for energy, charge and linear momentum to those situations.

**[SP 6.4**,

**7.2]**

**DC CIRCUITS**

**BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.**

**5.B.9.1:**The student is able to construct or interpret a graph of the energy changes within an electrical circuit with only a single battery and resistors in series and/or in, at most, one parallel branch as an application of the conservation of energy (Kirchhoff’s loop rule).

**[SP 1.1, 1.4]**

**5.B.9.2:**The student is able to apply conservation of energy concepts to the design of an experiment that will demonstrate the validity of Kirchhoff’s loop rule (∑ΔV=0) in a circuit with only a battery and resistors either in series or in, at most, one pair of parallel branches.

**[SP 4.2, 6.4, 7.2]**

**5.B.9.3:**The student is able to apply conservation of energy (Kirchhoff’s loop rule) in calculations involving the total electric potential difference for complete circuit loops with only a single battery and resistors in series and/or in, at most, one parallel branch.

**[SP 2.2, 6.4, 7.2]**

**5.C.3.1:**The student is able to apply conservation of electric charge (Kirchhoff’s junction rule) to the comparison of electric current in various segments of an electrical circuit with a single battery and resistors in series and in, at most, one parallel branch and predict how those values would change if configurations of the circuit are changed.

**[SP 6.4, 7.2]**:

**5.C.3.2:**The student is able to design an investigation of an electrical circuit with one or more resistors in which evidence of conservation of electric charge can be collected and analyzed.

**[SP 4.1, 4.2, 5.1]**

**5.C.3.3:**The student is able to use a description or schematic diagram of an electrical circuit to calculate unknown values of current in various segments or branches of the circuit.

**[SP 1.4, 2.2]**

**MECHANICAL WAVES AND SOUND**

**BIG IDEA 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.**

**6.A.1.1:**The student is able to use a visual representation to construct an explanation of the distinction between transverse and longitudinal waves by focusing on the vibration that generates the wave.

**[SP 6.2]**

**6.A.1.2:**The student is able to describe representations of transverse and longitudinal waves.

**[SP 1.2]**

**6.A.2.1:**The student is able to describe sound in terms of transfer of energy and momentum in a medium and relate the concepts to everyday examples.

**[SP 6.4, 7.2]**:

**6.A.3.1:**The student is able to use graphical representation of a periodic mechanical wave to determine the amplitude of the wave.

**[SP 1.4]**

**6.A.4.1:**The student is able to explain and/or predict qualitatively how the energy carried by a sound wave relates to the amplitude of the wave, and/or apply this concept to a real-world example.

**[SP 6.4]**

**6.B.1.1:**The student is able to use a graphical representation of a periodic mechanical wave (position versus time) to determine the period and frequency of the wave and describe how a change in the frequency would modify features of the representation.

**[SP 1.4, 2.2]**

**6.B.2.1:**The student is able to use a visual representation of a periodic mechanical wave to determine wavelength of the wave.

**[SP 1.4]**

**6.B.4.1:**The student is able to design an experiment to determine the relationship between periodic wave speed, wavelength, and frequency and relate these concepts to everyday examples.

**[SP 4.2, 5.1, 7.2]**

**6.B.5.1:**The student is able to create or use a wave front diagram to demonstrate or interpret qualitatively the observed frequency of a wave, dependent upon relative motions of source and observer.

**[SP 1.4]**

**6.D.1.1:**The student is able to use representations of individual pulses and construct representations to model the interaction of two wave pulses to analyze the superposition of two pulses.

**[SP 1.1, 1.4]**

**6.D.1.2:**The student is able to design a suitable experiment and analyze data illustrating the superposition of mechanical waves (only for wave pulses or standing waves).

**[SP 4.2, 5.1]**

**6.D.1.3:**The student is able to design a plan for collecting data to quantify the amplitude variations when two or more traveling waves or wave pulses interact in a given medium.

**[SP 4.2]**

**6.D.2.1:**The student is able to analyze data or observations or evaluate evidence of the interaction of two or

more traveling waves in one or two dimensions (i.e., circular wave fronts) to evaluate the variations in resultant amplitudes.

**[SP 5.1]**

**6.D.3.1:**The student is able to refine a scientific question related to standing waves and design a detailed plan for the experiment that can be conducted to examine the phenomenon qualitatively or quantitatively.

**[SP 2.1, 3.2, 4.2]**

**6.D.3.2:**The student is able to predict properties of standing waves that result from the addition of incident and reflected waves that are confined to a region and have nodes and antinodes.

**[SP 6.4]**

**6.D.3.3:**The student is able to plan data collection strategies, predict the outcome based on the relationship under test, perform data analysis, evaluate evidence compared to the prediction, explain any discrepancy and, if necessary, revise the relationship among variables responsible for establishing standing waves on a string or in a column of air.

**[SP 3.2, 4.1, 5.1, 5.2, 5.3]**

**6.D.3.4:**The student is able to describe representations and models of situations in which standing waves result from the addition of incident and reflected waves confined to a region.

**[SP 1.2]**

**6.D.4.1:**The student is able to challenge with evidence the claim that the wavelengths of standing waves are determined by the frequency of the source regardless of the size of the region.

**[SP 1.5, 6.1]**

**6.D.4.2:**The student is able to calculate wavelengths and frequencies (if given wave speed) of standing waves based on boundary conditions and length of region within which the wave is confined, and calculate numerical

values of wavelengths and frequencies. Examples should include musical instruments.

**[SP 2.2]**

**6.D.5.1:**The student is able to use a visual representation to explain how waves of slightly different frequency give rise to the phenomenon of beats.

**[SP 1.2]**