### Standards

#### Next Generation Science Standards (NGSS):

**HS-PS2-2. **Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.

**HS-PS3-1**. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

**HS-PS3-2**. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles or energy stored in fields.

**HS-PS3-3**. Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

#### Massachusetts Curriculum Frameworks (2006):

**2.1** Interpret and provide examples that illustrate the law of conservation of energy.

**2.2** Interpret and provide examples of how energy can be converted from gravitational potential energy to kinetic energy and vice versa.

**2.3** Describe both qualitatively and quantitatively how work can be expressed as a change in mechanical energy.

**2.4** Describe both qualitatively and quantitatively the concept of power as work done per unit time.

**2.5** Provide and interpret examples showing that linear momentum is the product of mass and velocity, and is always conserved (law of conservation of momentum). Calculate the momentum of an object.

#### AP Physics 1 Learning Objectives:

**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**]

**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**]

**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**]

**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**]

**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**]

**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**]

**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.2.2**: 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**]

**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**]

#### Topics from this chapter assessed on the SAT Physics Subject Test:

**Energy and Momentum**, such as potential and kinetic energy, work, power, impulse, and conservation laws.

- What is Linear Momentum?
- Impulse
- Conservation of Momentum
- Collisions
- Center of Mass
- Work
- Energy
- Forms of Energy
- Power