AP Physics C Mechanics Review

Kinematics – 18% Chapters 2,3,4 Position vs. displacement Speed vs. Velocity Acceleration Kinematic Equations for constant acceleration Vectors and Vector Addition Projectile Motion – x,y motion are independent Uniform Circular Motion

Kinematics – Motion in One and Two Dimensions Key Ideas and Vocabulary Motion in the x is independent from motion in the y Displacement, velocity, acceleration Graphical Analysis of Motion – x vs. t - Slope is velocity v vs. t - Slope is acceleration - Area is displacement a vs. t – Can be used to find the change in velocity Centripetal Acceleration is always towards the center of the circle

Kinematics – Motion in One and Two Dimensions Constant Acceleration Motion Equations Centripetal Acceleration 

Newton’s Laws of Motion – 20% Chapters 5 & 6 Newton’s Three Laws of Motion Inertia Fnet = ma Equal and opposite forces Force Weight vs. Mass Free Body Diagrams Tension, Weight, Normal Force Friction – Static and Kinetic, Air Resistance Centripetal Forces and Circular Motion Drag forces and terminal speed

Newton’s Laws of Motion Second Law Problems Newton’s Second Law – Draw free body diagram identifying forces on a single object Break forces into components Apply 2nd Law and solve x & y components simultaneously Inclined Plane – Rotate axes so that acceleration is in the same direction as the x-axis

Newton’s Laws of Motion Circular Motion Problems Draw free body diagram identifying forces on a single object Break forces into components Apply 2nd Law and solve x & y components simultaneously Remember that the acceleration is centripetal and that it is caused by some force

Newton’s Laws of Motion Air Resistance – Drag Force Identify forces and draw free body diagrams May involve a differential equation Example: Separate variables and solve. Should end up with something that decreases exponentially Terminal Velocity – Drag force and gravity are equal in magnitude – Acceleration is equal to zero

Work, Energy, Power – 14% Chapters 7 & 8 Kinetic Energy Work – by constant force and variable force Spring Force Power Potential Energy – gravitational, elastic Mechanical Energy Conservation of Energy Work Energy Theorem

Work, Energy and Power Key Equations Work by a Constant Force Power Kinetic Energy Work-Energy Theorem

Work, Energy and Power Key Equations

Potential Energy Curves Slope of U curve is –F Total energy will be given, the difference between total energy and potential energy will be kinetic energy

Systems & Linear Momentum – 12% Chapters 9 & 10 Center of Mass Linear Momentum Conservation of Momentum Internal vs. External forces Collisions – Inelastic, Elastic Impulse

Systems & Linear Momentum Key Equations Center of Mass Momentum Conservation of Momentum Impulse

Systems & Linear Momentum Center of Mass, Internal and External forces Center of Mass can be calculated by summing the individual pieces of a system or by integrating over the solid shape. If a force is internal to a system the total momentum of the system does not change Only external forces will cause acceleration or a change in momentum. Usually we can expand the system so that all forces are internal.

Systems & Linear Momentum Collisions Inelastic collisions – (objects stick together) Kinetic energy is lost Momentum is conserved Elastic Collisions – (objects bounce off) Kinetic energy is conserved

Systems & Linear Momentum Impulse Impulse is the change in momentum Momentum will change when a force is applied to an object for a certain amount of time Area of Force vs Time curve will be the change in momentum

Systems & Linear Momentum Conservation of Momentum Momentum will always be conserved unless an outside force acts on an object. Newton’s Second Law could read: Newton’s Third Law is really a statement of conservation of momentum Set initial momentum equal to final momentum and solve – make sure to solve the x and y components independently

Circular Motion and Rotation – 18% Chapters 11 & 12 Uniform Circular Motion (chap 4 & 6) Angular position, Ang. velocity, Ang. Acceleration Kinematics for constant ang. Acceleration Relationship between linear and angular variables Rotational Kinetic Energy Rotational Inertia – Parallel Axis Theorem Torque Newton’s Second Law in Angular form

Circular Motion and Rotation – 18% Chapters 11 & 12 Rolling bodies Angular momentum Conservation of Angular momentum

Circular Motion and Rotation Basic Rotational Equations Circular Love and Angular Kinematics Angular Velocity & Acceleration

Circular Motion and Rotation Linear to Rotation As a general rule of thumb, to convert between a linear and rotational quantity, multiply by the radius r

Circular Motion and Rotation Rolling and Kinetic Energy A rolling object has both translational and rotational kinetic energy.

Circular Motion and Rotation Moment of Inertia How something rotates will depend on the mass and the distribution of mass Parallel Axis Theorem – allows us to calculate I for an object away from its center of mass I for the Center of Mass m – total mass H – distance from com to axis of rotation

Circular Motion and Rotation Moment of Inertia For objects made of multiple pieces, find the moment of inertia for each piece individually and then sum the moments to find the total moment of inertia Axis of rotation m2 m1 L

Circular Motion and Rotation Torque Rotational analog for force – depends on the force applied and the distance from the axis of rotation If more than one torque is acting on an object then you simply sum the torques to find the net torqu

Circular Motion and Rotation Angular Momentum Angular momentum will always be conserved in the same way that linear momentum is conserved As you spin, if you decrease the radius (or I) then you should increase speed to keep angular momentum constant

Circular Motion and Rotation Newton’s 2nd Law for Rotation

Oscillations and Gravity – 18% Chapters 14 & 16 Frequency, Period, Angular Frequency Simple Harmonic Motion Period of a Spring Pendulums Period Simple Physical

Oscillations All harmonic motion will can modeled by a sine function The hallmark of simple harmonic motion is Knowing the acceleration you can find ω.

Oscillations Springs and Simple Pendulums Ideal Spring Simple Pendulum

Oscillations Physical Pendulum A physical pendulum is any pendulum that is not a string with a mass at the end. It could be a meter stick or a possum swinging by its tail.

Oscillations and Gravity – 18% Chapters 14 & 16 Law of Gravitation Superposition – find force by adding the force from each individual object Shell Theorem – mass outside of shell doesn’t matter Gravitational Potential Energy Orbital Energy – Kinetic plus Potential Escape Speed Kepler’s Laws’ Elliptical Orbits Equal area in equal time (Cons. of Ang. Momentum) T2 α R3 - can be found from orbital period and speed

Gravity A very serious matter Universal Law of Gravity Gravitational Potential Energy Circular Orbit Speed