PI.1: Constant Velocity

PI.1.1: Develop graphical, mathematical, and pictorial representations (e.g. a motion map) that describe the relationship between the clock reading (time) and position of an object moving at a uniform rate and apply those representations to qualitatively and quantitatively describe the motion of an object.

Distance-Time and Velocity-Time Graphs - Metric

PI.1.2: Describe the slope of the graphical representation of position vs. clock reading (time) in terms of the velocity of the object.

Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs - Metric

PI.1.3: Rank the velocities of objects in a system based on the slope of a position vs. clock reading (time) graphical representation. Recognize that the magnitude of the slope representing a negative velocity can be greater than the magnitude of the slope representing a positive velocity.

Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs - Metric

PI.1.4: Describe the differences between the terms “distance,” “displacement,” “speed,” “velocity,” “average speed,” and “average velocity” and be able to calculate any of those values given an object moving at a single constant velocity or with different constant velocities over a given time interval.

Distance-Time and Velocity-Time Graphs - Metric

PI.2: Constant Acceleration

PI.2.1: Develop graphical, mathematical, and pictorial representations (e.g. a motion map) that describe the relationship between the clock reading (time) and velocity of an object moving at a uniformly changing rate and apply those representations to qualitatively and quantitatively describe the motion of an object.

Atwood Machine
Feed the Monkey (Projectile Motion)
Free-Fall Laboratory
Golf Range

PI.2.2: Describe the slope of the graphical representation of velocity vs. clock reading (time) in terms of the acceleration of the object.

Distance-Time and Velocity-Time Graphs - Metric

PI.2.3: Rank the accelerations of objects in a system based on the slope of a velocity vs. clock reading (time) graphical representation. Recognize that the magnitude of the slope representing a negative acceleration can be greater than the magnitude of the slope representing a positive acceleration.

Distance-Time and Velocity-Time Graphs - Metric

PI.2.4: Given a graphical representation of the position, velocity, or acceleration vs. clock reading (time), be able to identify or sketch the shape of the other two graphs.

Free-Fall Laboratory

PI.2.5: Qualitatively and quantitatively apply the models of constant velocity and constant acceleration to determine the position or velocity of an object moving in free fall near the surface of the Earth.

Feed the Monkey (Projectile Motion)
Free-Fall Laboratory
Golf Range

PI.3: Forces

PI.3.1: Understand Newton’s first law of motion and describe the motion of an object in the absence of a net external force according to Newton’s first law.

Fan Cart Physics

PI.3.2: Develop graphical and mathematical representations that describe the relationship among the inertial mass of an object, the total force applied, and the acceleration of an object in one dimension where one or more forces is applied to the object and apply those representations to qualitatively and quantitatively describe how a net external force changes the motion of an object.

Atwood Machine
Fan Cart Physics
Free-Fall Laboratory

PI.3.4: Understand Newton’s third law of motion and describe the interaction of two objects using Newton’s third law and the representation of action-reaction pairs of forces.

Fan Cart Physics

PI.3.7: Explain that the equivalence of the inertial and gravitational masses leads to the observation that acceleration in free fall is independent of an object’s mass.

Free-Fall Laboratory

PI.4: Energy

PI.4.1: Evaluate the translational kinetic, gravitational potential, and elastic potential energies in simple situations using the mathematical definitions of these quantities and mathematically relate the initial and final values of the translational kinetic, gravitational potential, and elastic potential energies in the absence of a net external force.

Energy of a Pendulum
Inclined Plane - Sliding Objects
Potential Energy on Shelves
Roller Coaster Physics

PI.4.2: Identify the forms of energy present in a scenario and recognize that the potential energy associated with a system of objects and is not stored in the object itself.

Energy of a Pendulum
Inclined Plane - Sliding Objects
Roller Coaster Physics

PI.4.3: Conceptually define “work” as the process of transferring of energy into or out of a system when an object is moved under the application of an external force and operationally define “work” as the area under a force vs. change in position curve.

Pulley Lab

PI.4.4: For a force exerted in one or two dimensions, mathematically determine the amount of work done on a system by an unbalanced force over a change in position in one dimension.

Inclined Plane - Simple Machine

PI.4.5: Understand and apply the principle of conservation of energy to determine the total mechanical energy stored in a closed system and mathematically show that the total mechanical energy of the system remains constant as long as no dissipative (i.e. nonconservative) forces are present.

Air Track
Energy Conversion in a System
Inclined Plane - Sliding Objects

PI.4.6: Develop and apply pictorial, mathematical or graphical representations to qualitatively and quantitatively predict changes in the mechanical energy (e.g. translational kinetic, gravitational, or elastic potential) of a system due to changes in position or speed of objects or non-conservative interactions within the system.

Inclined Plane - Sliding Objects

PI.5: Linear Momentum In One Dimension

PI.5.1: For an object moving at constant rate, define linear momentum as the product of an object’s mass and its velocity and be able to quantitatively determine the linear momentum of a single object.

2D Collisions
Air Track

PI.5.3: Demonstrate that when two objects interact through a collision or separation that both the force experienced by each object and change in linear momentum of each object are equal and opposite, and as the mass of an object increases, the change in velocity of that object decreases.

2D Collisions
Air Track

PI.5.4: Determine the individual and total linear momentum for a two-body system before and after an interaction (e.g. collision or separation) between the two objects and show that the total linear momentum of the system remains constant when no external force is applied consistent with Newton’s third law.

2D Collisions
Air Track

PI.5.5: Classify an interaction (e.g. collision or separation) between two objects as elastic or inelastic based on the change in linear kinetic energy of the system.

2D Collisions
Air Track

PI.5.6: Mathematically determine the center of mass of a system consisting of two or more masses. Given a system with no external forces applied, show that the linear momentum of the center of mass remains constant during any interaction between the masses.

2D Collisions

PI.6: Simple Harmonic Oscillating Systems

PI.6.1: Develop graphical and mathematical representations that describe the relationship between the amount of stretch of a spring and the restoring force and apply those representations to qualitatively and quantitatively describe how changing the stretch or compression will affect the restoring force and vice versa, specifically for an ideal spring.

Determining a Spring Constant

PI.6.2: Describe the slope of the graphical representation of restoring force vs. change in length of an elastic material in terms of the elastic constant of the material, specifically for an ideal spring.

Determining a Spring Constant

PI.6.4: Develop graphical and mathematical representations which describe the relationship between the strength of gravity, length of string, and period of a simple mass-string (i.e. pendulum) system apply the those representations to qualitatively and quantitatively describe how changing the length of string or strength of gravity will affect the period of the system in the limit of small amplitudes.

Period of a Pendulum

PI.7: Mechanical Waves and Sound

PI.7.1: Differentiate between transverse and longitudinal modes of oscillation for a mechanical wave traveling in one dimension.

Longitudinal Waves

PI.7.2: Understand that a mechanical wave requires a medium to transfer energy, unlike an electromagnetic wave, and that only the energy is transferred by the mechanical wave, not the mass of the medium.

Longitudinal Waves

PI.7.5: Apply the mechanical wave model to sound waves and qualitatively and quantitatively determine how the relative motion of a source and observer affects the frequency of a wave as described by the Doppler Effect.

Doppler Shift
Doppler Shift Advanced

PI.7.6: Qualitatively and quantitatively apply the principle of superposition to describe the interaction of two mechanical waves or pulses.

Ripple Tank
Sound Beats and Sine Waves

PI.7.7: Qualitatively describe the phenomena of both resonance frequencies and beat frequencies that arise from the interference of sound waves of slightly different frequency and define the beat frequency as the difference between the frequencies of two individual sound wave sources.

Longitudinal Waves

PI.8: Simple Circuit Analysis

PI.8.1: Develop graphical, mathematical, and pictorial representations that describe the relationship between length, cross-sectional area, and resistivity of an ohmic device and apply those representations to qualitatively and quantitatively describe how changing the composition, size, or shape of the device affect the resistance.

Circuit Builder

PI.8.5: Qualitatively and quantitatively describe how changing the voltage or resistance of a simple series (i.e. loop) circuit affects the voltage, current, and power measurements of individual resistive devices and for the entire circuit.

Advanced Circuits
Circuit Builder
Circuits

PI.8.6: Qualitatively and quantitatively describe how changing the voltage or resistance of a simple parallel (i.e. ladder) circuit affects the voltage, current, and power measurements of individual resistive devices and for the entire circuit.

Advanced Circuits
Circuit Builder
Circuits

PI.8.9: Use a description or schematic diagram of an electrical circuit to calculate unknown values of current, voltage, or resistance in various components or branches of the circuit according to Ohm’s Law, Kirchhoff’s junction rule, and Kirchhoff’s loop rule.

Advanced Circuits
Circuit Builder
Circuits