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AP Physics C: Mechanics

Study notes
1.1.1 Scalars and Vector Quantities
1.1.2 Representing Vectors Visually
1.1.3 Scalar and Vector Examples in Mechanics
1.1.4 Unit Vector Notation and Position Vectors
1.1.5 Resultant Vectors and Signs in One Dimension
1.2.1 The Object Model and Displacement
1.2.2 Average Velocity
1.2.3 Average Acceleration
1.2.4 What It Means for an Object to Accelerate
1.2.5 Instantaneous Position, Velocity, and Acceleration
1.3.1 Ways to Represent Motion
1.3.2 Constant-Acceleration Kinematic Equations
1.3.3 Vertical Motion Near Earth's Surface
1.3.4 Slopes on Position-Time and Velocity-Time Graphs
1.3.5 Areas on Velocity-Time and Acceleration-Time Graphs
1.4.1 Choosing a Reference Frame
1.4.2 Converting Measurements Between Frames
1.4.3 Relative Velocity and Inertial Frames
1.5.1 Breaking Multidimensional Motion into Components
1.5.2 Velocity and Acceleration in Different Dimensions
1.5.3 Independence of Perpendicular Components
1.5.4 Projectile Motion as a Special Case
2.1.1 Defining a System in Mechanics
2.1.2 Open, Closed, and Changing Systems
2.1.3 Internal Structure and System Behavior
2.1.4 Symmetry and the Center of Mass
2.1.5 Calculating Center of Mass for Discrete Objects
2.1.6 Center of Mass for Continuous Mass Distributions
2.2.1 Forces as Interactions Between Objects
2.2.2 Why an Object Cannot Push Itself
2.2.3 Contact Forces and Their Origin
2.2.4 Drawing Accurate Free-Body Diagrams
2.2.5 Choosing Axes from a Free-Body Diagram
2.3.1 Action-Reaction Force Pairs
2.3.2 Internal Forces and Center-of-Mass Motion
2.3.3 Tension in Strings, Cables, and Chains
2.3.4 Ideal Strings, Massive Strings, and Ideal Pulleys
2.4.1 Net Force and Translational Equilibrium
2.4.2 Constant Velocity and Newton’s First Law
2.4.3 Balanced in One Direction, Unbalanced in Another
2.4.4 Inertial Reference Frames
2.5.1 Unbalanced Forces and Changing Motion
2.5.2 Newton’s Second Law and Center-of-Mass Acceleration
2.5.3 Applying F = ma to Physical Systems
2.6.1 Universal Gravitation Between Masses
2.6.2 Direction of Gravitational Force and Field
2.6.3 Gravitational Field Strength and Weight
2.6.4 When Gravity Can Be Treated as Constant
2.6.5 Apparent Weight, Weightlessness, and the Equivalence Principle
2.6.6 Inertial Mass, Gravitational Mass, and Spherical Mass Distributions
2.7.1 What Kinetic Friction Does
2.7.2 Magnitude of Kinetic Friction
2.7.3 Normal Force in Friction Problems
2.7.4 How Static Friction Prevents Motion
2.7.5 Maximum Static Friction and Comparing Coefficients
2.8.1 Ideal and Nonideal Springs
2.8.2 Hooke’s Law and Spring Force Direction
2.8.3 Equivalent Spring Constant: Core Idea
2.8.4 Springs in Series
2.8.5 Springs in Parallel
2.9.1 Modeling Resistive Forces
2.9.2 Using Newton’s Second Law with Drag
2.9.3 From Velocity Functions to Position and Acceleration
2.9.4 Exponential Motion with Linear Drag
2.9.5 Terminal Velocity
2.10.1 Centripetal Acceleration in Circular Motion
2.10.2 Forces That Produce Circular Motion
2.10.3 Banked Curves and Conical Pendulums
2.10.4 Tangential and Net Acceleration
2.10.5 Period, Frequency, and Uniform Circular Motion
2.10.6 Circular Orbits and Kepler’s Third Law
3.1.1 Defining Translational Kinetic Energy
3.1.2 Kinetic Energy as a Scalar
3.1.3 Kinetic Energy and Reference Frames
3.2.1 What Work Means in Mechanics
3.2.2 Conservative Forces, Path Independence, and Potential Energy
3.2.3 Nonconservative Forces and Dissipated Mechanical Energy
3.2.4 Calculating Work with Dot Products and Integrals
3.2.5 The Work-Energy Theorem and Force-Displacement Graphs
3.3.1 Potential Energy in Systems of Interacting Objects
3.3.2 Choosing the Zero of Potential Energy
3.3.3 Relating Potential Energy to Conservative Force
3.3.4 Reading Forces and Equilibrium from U-x Graphs
3.3.5 Elastic and Gravitational Potential Energy Models
3.3.6 Near-Earth Gravitational Energy and Multi-Object Systems
3.4.1 Energy in Single-Object and Multi-Object Systems
3.4.2 Mechanical Energy and Energy Accounting
3.4.3 When Total Energy Stays Constant
3.4.4 When Mechanical Energy Is Conserved
3.4.5 System Choice, External Work, and Dissipation
3.5.1 Defining Power as the Rate of Energy Change
3.5.2 Average Power from Energy and Work
3.5.3 Instantaneous Power and the Force-Velocity Relationship
4.1.1 Defining Linear Momentum
4.1.2 Momentum as a Vector Quantity
4.1.3 Using Momentum in Collisions and Explosions
4.1.4 Collision Models and Object Systems
4.1.5 Explosion Models in Isolated Systems
4.2.1 Force as the Rate of Change of Momentum
4.2.2 Impulse from Force Over Time
4.2.3 The Direction of Impulse
4.2.4 Reading Force-Time and Momentum-Time Graphs
4.2.5 Change in Momentum and the Impulse-Momentum Theorem
4.2.6 Connecting Impulse to Newton's Second Law
4.3.1 Systems, Total Momentum, and Center of Mass
4.3.2 Calculating and Interpreting Center-of-Mass Velocity
4.3.3 When Momentum Stays Constant
4.3.4 Internal Momentum Changes and Newton's Third Law
4.3.5 Impulse, System Choice, and Solving Interactions
4.3.6 Applying Conservation in Collisions and Explosions
4.4.1 What Makes a Collision Elastic
4.4.2 Kinetic Energy Changes for Individual Objects
4.4.3 What Makes a Collision Inelastic
4.4.4 Where the Missing Kinetic Energy Goes
4.4.5 Perfectly Inelastic Collisions
5.1.1 Angular Displacement and Radians
5.1.2 Rigid Systems and Rotation Sign Conventions
5.1.3 Angular Velocity and Angular Acceleration
5.1.4 Rotational-Linear Kinematics Analogies and Graphs
5.1.5 Constant Angular Acceleration Equations
5.2.1 Arc Length and Angular Displacement
5.2.2 Tangential Speed and Tangential Acceleration
5.2.3 Shared Angular Motion in a Rigid System
5.3.1 What Produces Torque
5.3.2 Lever Arm and Line of Action
5.3.3 Force Diagrams for Rigid Systems
5.3.4 Torque as a Cross Product and Direction
5.4.1 Rotational Inertia as Resistance to Change
5.4.2 Rotational Inertia of a Point Mass and Collections
5.4.3 Calculating Rotational Inertia with Calculus
5.4.4 Center of Mass and Minimum Rotational Inertia
5.4.5 Parallel Axis Theorem and Mass Distribution
5.5.1 Conditions for Rotational Equilibrium
5.5.2 Rotational and Translational Equilibrium Compared
5.5.3 Using Diagrams and the Rotational First Law
5.6.1 When Angular Velocity Changes
5.6.2 Net Torque, Angular Acceleration, and Rotational Inertia
5.6.3 Combining Linear and Rotational Analysis
6.1.1 Defining Rotational Kinetic Energy
6.1.2 Why Moment of Inertia Matters
6.1.3 Translational and Rotational Kinetic Energy
6.1.4 Rotation with a Stationary Center of Mass
6.1.5 Rotational Kinetic Energy as a Scalar
6.2.1 How Torque Transfers Energy
6.2.2 Work Done by a Constant Torque
6.2.3 Work Done by a Variable Torque
6.2.4 Reading Torque-Position Graphs
6.3.1 Angular Momentum of a Rigid System
6.3.2 Angular Momentum of a Moving Object
6.3.3 Why the Choice of Axis Matters
6.3.4 Defining Angular Impulse
6.3.5 Direction and Graphs for Angular Impulse
6.3.6 Angular Impulse-Momentum Theorem
6.4.1 Total Angular Momentum of a System
6.4.2 How Interactions Change Angular Momentum
6.4.3 Internal Impulses and Newton’s Third Law
6.4.4 Changing Shape Without Changing Angular Momentum
6.4.5 Angular Impulse and System Change
6.4.6 When Angular Momentum Is Conserved
6.5.1 Total Kinetic Energy in Rolling Motion
6.5.2 The Rolling-Without-Slipping Condition
6.5.3 Acceleration in Rolling Motion
6.5.4 Why Static Friction Does Not Remove Energy
6.5.5 What Changes When an Object Slips
6.5.6 Kinetic Friction and Energy Loss
6.6.1 A Satellite-Central Body System
6.6.2 Conservation Laws in Orbits
6.6.3 What Stays Constant in Circular Orbits
6.6.4 What Changes in Elliptical Orbits
6.6.5 Gravitational Potential Energy and Circular-Orbit Energy
6.6.6 Escape Velocity
7.1.1 Periodic Motion and the Special Case of SHM
7.1.2 Restoring Force and Displacement
7.1.3 Why the Force Is Called Restoring
7.1.4 Equilibrium Position in Oscillating Systems
7.2.1 Period, Frequency, and Angular Frequency
7.2.2 Period of a Mass-Spring Oscillator
7.2.3 Period of a Simple Pendulum
7.3.1 Sinusoidal Models for Displacement
7.3.2 Minima, Maxima, and Zeros in SHM
7.3.3 The Differential Equation for SHM
7.3.4 Using Phase Constants to Describe Motion
7.3.5 Maximum Speed and Maximum Acceleration
7.3.6 Resonance, Amplitude, and Graphical Analysis
7.4.1 Total Mechanical Energy in SHM
7.4.2 Conservation of Energy in Oscillators
7.4.3 When Kinetic Energy Is Greatest
7.4.4 When Potential Energy Is Greatest
7.4.5 Amplitude and Total Energy
7.5.1 What Makes a Physical Pendulum
7.5.2 Period of a Physical Pendulum
7.5.3 Restoring Torque and the Small-Angle Approximation
7.5.4 Rotational SHM Equation for Pendulums
7.5.5 The Simple Pendulum as a Special Case
7.5.6 Torsion Pendulums and Angular SHM

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