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  • PHYS101: Introduction to Mechanics
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  • Unit Vector Notation
    Course Introduction
    Course Syllabus
    Unit 1: Introduction to Physics
    1.1: Scientific Theory, Law, and Models
    An Introduction to Physics
    1.2: Physical Quantities and Units
    Physical Quantities and Units
    1.3: Converting S.I. and Customary U.S. Units
    Unit Conversion and Dimensional Analysis
    Metric Units, Converting Units, Significant Figures
    1.4: Uncertainty, Accuracy, Precision, and Significant Figures
    Accuracy, Precision, and Significant Figures
    1.5: Scientific Notation
    Review of Scientific Notation
    Applying Scientific Notation
    Converting Scientific Notation to Standard Notation
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Kinematics in a Straight Line
    2.1: Vectors, Scalars, and Coordinate Systems
    Vectors, Scalars, and Coordinate Systems
    2.2: Instantaneous and Average Values for Physical Quantities
    Time, Velocity, and Speed
    2.3: Distance and Displacement
    Displacement
    Distance and Displacement as Scalar Vectors
    Displacement vs. Distance
    Displacement Time Graphs
    Vectors and Scalars
    2.4: Speed and Velocity
    Time, Velocity, and Speed
    More on Speed and Velocity
    Speed and Velocity vs. Distance and Displacement
    2.5: Motion with Constant Acceleration
    Acceleration
    More on Acceleration
    Motion Equations for Constant Acceleration in One Dimension
    Average Acceleration
    Acceleration Equations
    2.6: Falling Objects
    Falling Objects
    Vertical Motion in Free Fall
    Zero Gravity Demonstration
    2.7: Calculating the Kinematic Quantities of Objects in Constant Acceleration
    Kinematic Equations for Objects in Free Fall
    Constant Acceleration Equations
    More on Free Fall
    Problem-Solving Basics for One-Dimensional Kinematics
    Kinematic Equations in Constant Acceleration
    Displacement with Constant Acceleration
    2.8: Graphical Analysis
    Graphical Analysis of One-Dimensional Motion
    Interpreting Velocity Graphs
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Kinematics in Two Dimensions
    3.1: Introduction to Kinematics in Two Dimensions using Vectors
    Kinematics in Two Dimensions
    Unit Vectors and Engineering Notation
    3.2: Adding and Subtracting Vectors
    Vector Addition and Subtraction
    Vector Addition Using the Graphical Method
    3.3. Adding Vectors Analytically: Determining the Components, Magnitude, and Direction of a Vector
    Analytical Methods for Vector Addition and Subtraction
    More on Vector Addition
    Vector Components on a Grid
    Projectiles at an Angle
    Visualizing Vectors in Two Dimensions
    Unit Vector Notation
    3.4: Projectile Motion and Trajectory
    Projectile Motion
    More on Projectile Motion
    Another Way to Determine Time In Air
    Horizontally-Launched Projectiles
    Launching and Landing at Different Elevations
    Total Displacement for a Projectile
    Total Final Velocity for a Projectile
    Projectiles on an Incline
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Dynamics
    4.1: Newton's First Law of Motion
    Newton's First Law of Motion and Inertia
    Force and Newton's Laws
    The Historical Context
    More on Newton's First Law of Motion
    4.2: Newton's Second Law of Motion
    Newton's Second Law of Motion
    Using Newton's Second Law
    F=ma
    Examples of Newton's Second Law
    More on Newton's Second Law
    4.3: Free-Body Diagrams
    The Concept of Force
    4.4: Newton's Third Law of Motion
    Symmetry in Forces
    Newton's Third Law and F=ma
    More on Newton's Third Law
    Examples of Newton's Third Law
    4.5: Solving Problems Using Newton's Second Law: Weight
    Problem-Solving Strategies
    Further Applications of Newton's Laws of Motion
    Identifying and Labeling Types of Forces
    Mass and Weight
    Characteristics of Forces
    Gravity and Weight
    Resultant Forces
    4.6: Newton's Law of Gravity
    Newton's Universal Law of Gravitation
    Introduction to Gravity
    Introduction to Newton's Law of Gravitation
    Gravity for Astronauts in Orbit
    Would a Brick or Feather Fall Faster?
    4.7: Solving Problems Using Newton's Second Law: Normal Force
    Normal Force
    Identifying and Labeling Types of Forces
    More on Normal Force
    Normal Force and Contact Force
    Normal Force in an Elevator
    Multiple Forces Alongside Normal Force
    Ice Accelerating Down An Incline
    4.8: Solving Problems Using Newton's Second Law: Tension
    Tension
    Identifying and Labeling Types of Forces
    Tension Forces
    4.9: Solving Problems Using Newton's Second Law: Friction
    Identifying and Labeling Types of Forces
    Friction
    Kinetic and Static Friction Forces
    Friction and Force from Springs
    Comparing Static and Kinetic Friction
    Examples of Static and Kinetic Friction
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Rotational Kinematics
    5.1: Centripetal Force
    Centripetal Acceleration
    Circular Motion and Centripetal Acceleration
    Centripetal Force
    Tennis Ball on a String
    More on Centripetal Force
    Visualizing Centripetal Acceleration
    More on Centripetal Force And Acceleration
    Example: Loop de Loop
    5.2: Centripetal Force and the Universal Law of Gravitation
    Satellites and Kepler's Laws
    Kepler's Three Laws of Planetary Motion
    5.3: Angular Position, Velocity, and Acceleration
    Rotation Angle and Angular Velocity
    Angular Acceleration
    5.4: Kinematics of Rotational Motion
    Kinematics of Rotational Motion
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Rotational Statics and Dynamics
    6.1: Conditions for Equilibrium
    The First Condition for Equilibrium
    Static Equilibrium, Torque, and Stability
    6.2: Torque
    Rotational Inertia
    Rotational Kinematics and Dynamics
    The Second Condition for Equilibrium
    Moment of Inertia
    The Race Between a Ring and a Disc
    6.3: Applications of Statics
    Torques on a Seesaw
    Applications of Statics
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 6 Assessment
    Unit 7: Work and Energy
    7.1: Calculating Work and Force
    Introduction to Work
    Work Example Problems
    7.2: Work, Potential Energy, and Linear Kinetic Energy
    Kinetic Energy and the Work-Energy Theorem
    Work, Kinetic Energy, and Potential Energy
    More on the Work-Energy Theorem
    More on Work and Energy
    Work as the Transfer of Energy
    Example of Work and Energy
    7.3: Conservative Forces and Potential Energy
    Non-Conservative Forces
    Conservative Forces and Potential Energy
    Conservative Forces
    More on Non-Conservative Forces
    7.4: Conservation of Energy
    Conservation of Energy
    The Equation for Conservation of Mechanical Energy
    More on Conservation of Energy
    The Equation for Non-Conservative Work
    Thermal Energy from Friction
    7.5: Rotational Kinetic Energy
    Rotational Kinetic Energy
    Deriving Rotational Kinetic Energy
    More on Rotational Kinetic Energy
    7.6: Power
    Power
    More on Power
    Work, Energy, and Power in Humans
    Unit 7 Assessment
    Unit 7 Assessment
    Unit 8: Momentum and Collisions
    8.1: Linear Momentum
    Linear Momentum and Force
    Momentum, Impulse, and the Conservation of mV
    More on Momentum
    8.2: Momentum and Newton's Second Law
    Momentum and Newton's Second Law
    Impulse
    More on Impulse
    Example of Impulse and Momentum in Dodgeball
    Force vs. Time Graphs
    8.3: Elastic, Inelastic, and Totally Inelastic Collisions
    Elastic Collisions in One Dimension
    Conserving Momentum in Elastic Collisions
    What are Inelastic and Elastic Collisions?
    Inelastic Collisions in One Dimension
    Conserving Momentum in Inelastic Collisions in Two Dimensions
    Elastic and Inelastic Collisions
    Perfectly Inelastic Collisions
    Elastic and Inelastic Collisions in One Dimension
    8.4: Solving Problems Involving Conservation of Linear Momentum in Collisions
    Elastic Collisions in One Dimension
    Calculating Velocity
    Linear Momentum and the Conservation of Momentum
    Example: Bouncing Fruit Colliding
    Example: An Ice Skater Throws a Ball
    Two-Dimensional Momentum
    8.5: Conservation of Angular Momentum
    Angular Momentum and Its Conservation – IP
    Controlling Angular Velocity on a Rotating Stool
    Conserving Angular Momentum
    Unit 8 Assessment
    Unit 8 Assessment
    Study Guide
    PHYS101 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    PHYS101: Certificate Final Exam
    Saylor Direct Credit
    Archived Materials
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  1. PHYS101: Introduction to Mechanics
  2. Unit 3: Kinematics in Two Dimensions
  3. 3.3. Adding Vectors Analytically: Determining the Components, Magnitude, and Direction of a Vector
  4. Unit Vector Notation

Unit Vector Notation

Completion requirements

This video demonstrates how to add vectors using the graphical and analytical methods.

Source: Khan Academy, https://www.youtube.com/watch?v=595Tiga1gIg
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Last modified: Wednesday, 3 July 2024, 3:08 PM
Back to '3.3. Adding Vectors Analytically: Determining the Components, Magnitude, and Direction of a Vector'
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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.