Newtonian Mechanics Course

Lesson 1 • Physical Quantities and Units

Introduces scalar and vector quantities, SI units, and dimensional analysis. Provides the measurement framework underlying every mechanical calculation in the course.

Lesson 2 • Vector Algebra Essentials

Covers vector addition, subtraction, and scalar multiplication geometrically and algebraically. These operations are applied directly to force and velocity analysis throughout the course.

Lesson 3 • Mathematical Tools for Mechanics

Reviews calculus concepts—derivatives, integrals, and differential equations—as applied to physical quantities. These tools are used to derive kinematic and dynamic equations in later chapters.

Lesson 1 • Circular and Relative Motion

Introduces angular position, angular velocity, and centripetal acceleration for uniform circular motion, then extends kinematics to relative reference frames. Prepares students for circular dynamics in Chapter 4.

Lesson 2 • Graphical Kinematics

Extracts kinematic information from position-time, velocity-time, and acceleration-time graphs. Graph interpretation reinforces the calculus relationships introduced in Chapter 1.

Lesson 3 • One-Dimensional Motion Analysis

Defines displacement, average and instantaneous velocity, and acceleration along a single axis. Establishes the kinematic vocabulary used in all subsequent motion problems.

Lesson 1 • Free-Body Diagram Methodology

Provides a systematic procedure for isolating a body and representing all external forces. Mastery of this skill is prerequisite for every dynamics problem in the course.

Lesson 2 • Newton's Second Law and Equations of Motion

Derives F = ma and applies it to single and multi-force systems. Students translate free-body diagrams into scalar or vector equations of motion.

Lesson 3 • Newton's First Law and Inertia

Defines inertia and the condition of equilibrium for a particle at rest or in uniform motion. Establishes the concept of net force as the driver of acceleration changes.

Lesson 4 • Applications of Newton's Laws

Solves canonical problems including Atwood machines, inclined planes, and connected blocks. Integrates all three laws and free-body diagram skills into structured problem-solving routines.

Lesson 1 • Centripetal Force and Circular Dynamics

Applies Newton's second law to uniform circular motion, identifying the centripetal force as the net inward force. Solves problems involving banked curves, conical pendulums, and vertical circles.

Lesson 2 • Normal Force and Contact Mechanics

Defines the normal force as a surface reaction perpendicular to contact and analyzes its variation with geometry and applied loads. Provides the basis for friction force calculations.

Lesson 3 • Static and Kinetic Friction

Presents the friction coefficient model, distinguishing static and kinetic regimes. Students determine whether objects slide or remain stationary under applied loads.

Lesson 1 • Kinetic Energy and the Work-Energy Theorem

Derives kinetic energy from Newton's second law and proves the work-energy theorem. Students use this theorem as an alternative to kinematic equations when forces vary with position.

Lesson 2 • Power and Energy Transfer Rates

Defines power as the rate of work done and relates it to force and velocity. Students calculate power requirements for machines and engines in applied scenarios.

Lesson 3 • Work Done by a Force

Defines work using the dot product of force and displacement, including variable-force cases via integration. Establishes the sign convention and physical meaning of positive and negative work.

Lesson 4 • Conservation of Mechanical Energy

States the conservation law for systems with only conservative forces and applies it to pendulums, springs, and projectiles. Identifies when the law applies and when friction invalidates it.

Lesson 1 • Conservation of Linear Momentum

States the conservation law for isolated systems and identifies the conditions under which it applies. Provides the primary tool for analyzing all collision and explosion problems.

Lesson 2 • Two-Dimensional Collision Analysis

Extends momentum conservation to two dimensions using component equations. Students solve glancing collision problems common in billiards, particle physics, and vehicle dynamics.

Lesson 3 • Linear Momentum and Impulse

Defines linear momentum as the product of mass and velocity and derives the impulse-momentum theorem from Newton's second law. Connects force-time history to velocity change.

Lesson 4 • Center of Mass and System Dynamics

Defines the center of mass for discrete and continuous systems and shows that external forces govern its acceleration. Provides a system-level perspective on multi-body dynamics.

Lesson 1 • Torque and Rotational Equilibrium

Defines torque as the rotational effect of a force and applies static equilibrium conditions to rigid bodies. Students solve lever, beam, and ladder problems using torque balance.

Lesson 2 • Newton's Second Law for Rotation

Applies the rotational form of Newton's second law to solve for angular acceleration under net torque. Combines translational and rotational equations for rolling and pulley systems.

Lesson 3 • Moment of Inertia

Derives moment of inertia for common shapes by integration and applies the parallel-axis theorem. Moment of inertia is the rotational analog of mass in Newton's second law for rotation.

Lesson 4 • Angular Kinematics

Defines angular displacement, velocity, and acceleration and derives constant angular acceleration equations by analogy with linear kinematics. Connects angular and linear quantities via radius.

Lesson 1 • Angular Momentum of a Particle

Defines angular momentum as the cross product of position and linear momentum and derives its time derivative as net torque. Establishes the rotational analog of the impulse-momentum theorem.

Lesson 2 • Angular Momentum of Rigid Bodies

Extends angular momentum to rigid bodies rotating about fixed and moving axes. Connects moment of inertia and angular velocity to the angular momentum vector.

Lesson 3 • Conservation of Angular Momentum

States the conservation law for systems with zero net external torque and applies it to spinning skaters, collapsing stars, and rotating platforms. Identifies conditions for conservation.

Lesson 4 • Integrative Dynamics Problem Solving

Combines energy, momentum, and angular momentum methods to solve complex multi-body problems. Develops strategic problem-selection skills for choosing the most efficient solution method.