AP Physics C: Mechanics Course Outline

Welcome to your comprehensive guide to AP Physics C: Mechanics! This calculus-based course explores the principles of classical mechanics, from kinematics to gravitation. Designed for students with a strong mathematical foundation, this course develops the analytical skills needed to solve complex physics problems using calculus and differential equations.

"I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world." — Albert Einstein

Projectile Motion Calculator

Initial Velocity (v₀):

Launch Angle (θ):

Initial Height (h₀):

Gravitational Acceleration (g):

Unit 1: Kinematics

This foundational unit explores the mathematical description of motion. You'll apply calculus to develop the relationships between position, velocity, and acceleration in both one and two dimensions, forming the basis for analyzing more complex mechanical systems.

Unit Overview: Kinematics

A comprehensive introduction to kinematics that establishes the calculus-based framework for describing motion, setting the foundation for the entire course.

Motion in One Dimension

Study position, velocity, and acceleration in one dimension, developing and applying the differential and integral relationships between these quantities.

Motion in Two Dimensions

Extend one-dimensional concepts to two dimensions using vector calculus, analyzing projectile motion, relative velocity, and parametric equations.

Unit 2: Newton's Laws of Motion

This unit examines the fundamental principles governing the dynamics of motion. You'll apply Newton's laws to a variety of systems, using calculus to analyze forces, inertia, and circular motion in complex physical scenarios.

Unit Overview: Newton's Laws of Motion

An introduction to the foundational principles that relate force, mass, and acceleration, forming the core of classical mechanics analysis.

First and Second Laws

Explore inertia and the quantitative relationship between force and acceleration, applying differential equations to analyze complex force systems.

Circular Motion

Analyze the dynamics of objects moving in circular paths, examining centripetal acceleration and the forces required to maintain circular motion.

Third Law

Study action-reaction pairs and their implications for multiple-body systems, laying the foundation for momentum conservation concepts.

Unit 3: Work, Energy, and Power

This unit explores energy transformations in mechanical systems. You'll use calculus to analyze work done by variable forces, develop the work-energy theorem, and examine the relationship between conservative forces and potential energy functions.

Unit Overview: Work, Energy, and Power

An introduction to energy concepts in mechanics, providing powerful alternative approaches to analyzing complex systems beyond force analysis.

Work-Energy Theorem

Study the relationship between work and kinetic energy using calculus, developing techniques for analyzing systems with variable forces.

Forces and Potential Energy

Explore the connection between conservative forces and potential energy, using calculus to derive potential energy functions from force fields.

Conservation of Energy

Apply energy conservation principles to analyze complex mechanical systems, using the mathematical relationships between different energy forms.

Power

Analyze the rate of energy transfer in mechanical systems, applying calculus to determine instantaneous and average power in various scenarios.

Unit 4: Systems of Particles & Linear Momentum

This unit examines the motion of particle systems and conservation of momentum. You'll apply calculus to analyze center of mass motion, impulse-momentum relationships, and collisions in both one and two dimensions.

Unit Overview: Systems of Particles and Linear Momentum

An introduction to the analysis of multi-particle systems and momentum conservation, extending Newton's laws to more complex scenarios.

Center of Mass

Study the mathematical definition of center of mass, using calculus to analyze continuous mass distributions and center of mass motion.

Impulse and Momentum

Examine the impulse-momentum theorem, analyzing variable forces and their effects on momentum using integral calculus.

Conservation of Linear Momentum and Collisions

Apply momentum conservation to analyze collisions and explosions in multiple dimensions, examining elastic and inelastic interactions.

Unit 5: Rotation

This unit extends mechanics principles to rotating objects. You'll use calculus to analyze rotational motion, torque, moment of inertia, and angular momentum, drawing parallels between linear and rotational dynamics.

Unit Overview: Rotation

An introduction to rotational mechanics, establishing the mathematical framework for analyzing rotating objects using calculus-based approaches.

Torque and Rotational Statics

Study torque as the rotational analog to force, analyzing static equilibrium in rotational systems with multiple torques.

Rotational Kinematics

Develop the calculus-based relationships between angular position, velocity, and acceleration, connecting rotational and linear motion.

Rotational Dynamics and Energy

Analyze rotational inertia, torque-angular acceleration relationships, and rotational energy, using calculus for continuous mass distributions.

Angular Momentum and Its Conservation

Study angular momentum for particles and rigid bodies, examining conservation principles and applications to complex rotational systems.

Unit 6: Oscillations

This unit explores harmonic motion in mechanical systems. You'll apply differential equations to analyze oscillatory motion in springs and pendulums, studying the mathematical patterns that govern periodic systems.

Unit Overview: Oscillations

An introduction to periodic motion, establishing the mathematical foundation for analyzing systems that exhibit repetitive behavior.

Simple Harmonic Motion, Springs, and Pendulums

Study oscillatory systems through differential equations, analyzing energy transformations and mathematical patterns in periodic motion.

Unit 7: Gravitation

This culminating unit explores Newton's law of universal gravitation. You'll apply calculus to analyze gravitational interactions, potential energy, and orbital motion, connecting fundamental principles from earlier units to astronomical systems.

Unit Overview: Gravitation

An introduction to gravitational physics, exploring Newton's law of universal gravitation and its applications to planetary and satellite motion.

Gravitational Forces

Study Newton's law of universal gravitation, analyzing gravitational forces and fields for various mass distributions using calculus.

Orbits of Planets and Satellites

Apply conservation principles to analyze orbital motion, examining Kepler's laws and the mathematics of elliptical orbits.

Study Tips for AP Physics C: Mechanics

Calculus Applications

Connect Physics to Calculus: Practice translating physical concepts into derivatives and integrals and vice versa
Master Differential Equations: Focus on setting up and solving first and second-order differential equations for motion
Create Rate of Change Diagrams: Sketch position, velocity, and acceleration versus time for various scenarios
Develop Integration Skills: Practice integrating various force functions to find work, impulse, and potential energy
Work with Vector Calculus: Build comfort with vector operations, especially dot products and cross products

Problem-Solving Approach

Identify Core Principles: For each problem, determine which fundamental law or conservation principle applies
Draw Multiple Representations: Create diagrams, graphs, and mathematical equations for each physical scenario
Develop Framework Solutions: Practice template approaches for common problem types (projectiles, circular motion, collisions)
Connect Units: Look for connections between topics, especially in how calculus unifies seemingly different phenomena
Check Dimensional Consistency: Verify that your equations have consistent units as a quick error check

Calculate Your AP Score